ABSTRACT
Title of Dissertation: PRECEDENCE AND THE LACK THEREOF:
PRECEDENCE-RELATION-ORIENTED PHONOLOGY
Maxime Papillon, Doctor of Philosophy, 2020
Dissertation Directed by: Professor William Idsardi
Department of Linguistics
The study of representations, their limits and capacities, is an indispensable part of the
formal study of language. The representations are the limits of what can be stored and
computed upon, and the details of a representation have a major influence on the form of
any analysis. Broadly, the goal of this thesis is to explore a lower bound of complexity
for the phonological module. By exploring the capacities of a representation that I will
argue requires fewer stipulations than anything offered before it, I will defend the claim
that the freedom of this more powerful representation matches the power of morphology.
More specifically I will argue that the representation of phonology is not strings, but directed
graphs, and that this representation is simpler and more powerful and that its power exactly
matches the set of attested phenomena of word-formation and phonology. The goal of this
dissertation is to expand on the theory of Multiprecedence (Raimy, 2000), which is both
promising and under-explored.
PRECEDENCE AND THE LACK THEREOF:
PRECEDENCE-RELATION-ORIENTED PHONOLOGY
by
Maxime Papillon
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2020
Advisory Committee:
Professor William Idsardi, Chair/Advisor
Professor Naomi Feldman
Professor Omer Preminger
Professor Norbert Hornstein
Professor Bob Slevc
?c Copyright by
Maxime Papillon
2020
Acknowledgment
I have many people to thank for making this thesis possible. I would like to thank
my thesis committee. My supervisor Bill Idsardi guided me for the past five years into
exploring the questions that had been interesting me for so long. I would also like to thank
Naomi Feldman, Omer Preminger, Norbert Hornstein, and Bob Slevc for their feedback and
pointed questions and commentary.
There is my cohort who provided me the best social support you can ask for. I thank Suy-
oung Bae, Annemarie van Dooren, Phoebe Gaston, Chia-Hsuan Liao, and Paulina Lyskawa.
I want to thank the members of all the groups, classes, and meetings with which I
shared the ideas of this research at various stages. I particularly thank the members of the
Phonology Circle who attended multiple stages of this research: Christian Brodbeck, Zara
Harmon, Cassidy Henry, Nika Jurov, Justin Malc?ic? Thomas Schatz, and Craig Thornburn.
I thank Armel Jolin and Marjorie Leduc for bearing with me as i taught them the intricacies
of the system. I thank the students who attented the EGG 2016, and the UMD students
who attended my class on Long-Distance Phenomena in Phonology.
I thank all my fellow students and post-doctorate colleagues with whom I discussed
every topic of linguistic in or out of this dissertation. I cannot possibly list everyone I ever
conversed with, but i want to single out Aaron Doliana, Mina Hirzel, Nick Huang, Gesoel
Mendes, and Sigwan Thivierge for the stimulating linguistic conversations.
I would also never have made it here without my previous supervisors: Charles Reiss
who first introduced me to the ideas expanded in this thesis, and Marc Brunelle who helped
me sharpen my interest in the phonetic complexity of Language and languages. I also want
to thank all the undergraduate professors who guided me here: Alan Bale, Mark Hale, Dana
Isac, and Madelyn Kissock.
I am also thankful for the financial support of the Canadian Social Sciences and Hu-
manities Research Council who supported the research presented here.
I also want to thank my family who supported me in my health issues. And particularly
thank you Amy for your constant support.
ii
Table of Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Preliminaries: Raimy (2000), strings and precedence . . . . . . . . . . . . . . . . 5
2.1 Raimy 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Detailed Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Going Full PROP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Tone and Harmony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 Basic geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Basic examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.1 Mende tone melodies . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 Vowel Harmony in Akan . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Siane Tone patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.4 Finnish Transparent vowels and Turkish opaque vowels . . . . . . . 25
3.2.5 Disharmony and Antiharmony . . . . . . . . . . . . . . . . . . . . . 30
3.2.6 Underlying vs. harmonic rounding in Moloko . . . . . . . . . . . . . 32
3.3 Plugging-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Parafixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Tone Donation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.3 Digo Verbal Tonology . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.4 Digo in Kisseberth (1984) . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Summing up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 PROP compared to its alternatives . . . . . . . . . . . . . . . . . . . . . . . 58
4 Affix position and Reduplicative size . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 Affix position in Tamazight Berber . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Circumfixation in Georgian and Amatlan Zapotec . . . . . . . . . . . . . . 66
4.3 Variable-position affixes in Afar . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Unpredictable Infixation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5 Free variation of reduplicant location in Tagalog . . . . . . . . . . . . . . . 74
4.6 Reduplicant size in Malagasy . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.7 Unpredictable Reduplicant size in Woleaian . . . . . . . . . . . . . . . . . . 79
4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Phonologically-Conditioned Allomorphy . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Background: representing alternatives . . . . . . . . . . . . . . . . . . . . . 83
5.2 Basic geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Consonant/Vowel Sensitivity in Korean . . . . . . . . . . . . . . . . 88
5.3.2 Partial suppletion in English a/an . . . . . . . . . . . . . . . . . . . 89
5.3.3 ? Approximant sensitivity in Swedish . . . . . . . . . . . . . . . . . 90
5.3.4 ?Nasal sensitivity in Nishnaabemwin . . . . . . . . . . . . . . . . . 91
5.3.5 Feature-level suppletion in Bari . . . . . . . . . . . . . . . . . . . . . 92
iii
5.3.6 Default allomorphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.7 Non-sticky-end default in Russian and Tahitian . . . . . . . . . . . . 99
5.3.8 Opaque Allomorphy in Japanese . . . . . . . . . . . . . . . . . . . . 101
5.3.9 Non-Attaching Allomorphs . . . . . . . . . . . . . . . . . . . . . . . 102
5.4 Further Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4.1 Terminology: ?Allomorphy?, ?Suppletion?, ?Irregularity? . . . . . . . . 104
5.4.2 PROP vs. Hudson & Hooper . . . . . . . . . . . . . . . . . . . . . . 107
5.4.3 PROP vs. Subcategorization . . . . . . . . . . . . . . . . . . . . . . 108
5.4.4 Outward-sensitive allomorphy, and root allomorphy . . . . . . . . . 110
5.4.5 The gradability of suppletion . . . . . . . . . . . . . . . . . . . . . . 113
5.4.6 PROP and surface optimization . . . . . . . . . . . . . . . . . . . . . 114
5.4.7 Scheer (2016) and melody-sensitivity in PCA . . . . . . . . . . . . . 116
6 Morphologically-Conditioned Allomorphy . . . . . . . . . . . . . . . . . . . . . . 132
6.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.1.1 Romanian stem-allomorphy determining the suffix . . . . . . . . . . 132
6.1.2 English Adjectivizer . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.1.3 Allomorphy and Affix position in Nisga?a . . . . . . . . . . . . . . . 138
6.1.4 Lexically conditioned masculine marker in Catalan . . . . . . . . . . 141
6.1.5 Final Consonants in French Adjectives . . . . . . . . . . . . . . . . . 144
6.1.6 Hungarian bidirectionally-conditioned allomorphy in Plural Possessives150
6.1.7 French preposition+article forms . . . . . . . . . . . . . . . . . . . . 151
7 Interaction of parallel structures with reduplication . . . . . . . . . . . . . . . . . 156
7.1 Tuvan vowel and harmony overwrite in reduplication . . . . . . . . . . . . . 158
7.2 Tone remaining on a single copy in Yao . . . . . . . . . . . . . . . . . . . . 162
7.3 Tone-overwrite and semi-parallelism in Hausa . . . . . . . . . . . . . . . . . 163
7.4 Sye allomorphy in reduplication . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.5 Muskogean reduplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
7.6 Reduplication with a ?weakened? copy as partial reduplication . . . . . . . . 172
8 Using and learning graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.1 Phonetic implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.1.1 Nesting Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.1.2 Resuming gestures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2 Acquiring the parallel features of vowel harmony . . . . . . . . . . . . . . . 184
8.3 Planning parallel articulations . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8.4 Alignment as a coordination problem . . . . . . . . . . . . . . . . . . . . . . 189
9 Further Phenomena, Analyses, Observations, and Suggestions . . . . . . . . . . . 190
9.1 Regular Phonological Processes . . . . . . . . . . . . . . . . . . . . . . . . . 190
9.1.1 Phonological Processes on Graphs in Raimy (2000) . . . . . . . . . . 190
9.1.2 Phonological processes on Graphs in PROP . . . . . . . . . . . . . . 195
9.2 Regular alternations as partial overlap . . . . . . . . . . . . . . . . . . . . . 201
9.3 Metathesis & Coalescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
9.3.1 Faroese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
9.3.2 Rotuman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
9.3.3 Indonesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
9.3.4 Spanish root allomorphy . . . . . . . . . . . . . . . . . . . . . . . . . 213
9.4 Complex segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
9.5 Ineffability and paradigmatic gaps . . . . . . . . . . . . . . . . . . . . . . . 217
9.6 Templatic Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
iv
9.7 Parallel features not pronounced throughout the form . . . . . . . . . . . . 221
9.8 Featural parafix in Mokulu . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.9 Peak Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
9.10 Self-placing affixes & Prosodic Optimization . . . . . . . . . . . . . . . . . . 227
9.11 Above the ?word?: graphs all the way up . . . . . . . . . . . . . . . . . . . . 230
9.12 Intonation as morphemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
9.13 Syllables and Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
9.14 Bracketing Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
9.15 Marginal Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
9.15.1 Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
9.15.2 Ablaut Reduplication . . . . . . . . . . . . . . . . . . . . . . . . . . 248
10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
v
Chapter 1
Introduction
Wherever we go we are impressed by the fact that pattern is one thing, the
utilization of pattern quite another... we cannot but conclude that linguistic
form may and should be studied as types of patterning, apart from the associated
functions. Sapir, 1921, p.61-62
The study of representations, their limits and capacities, is an indispensable part of the
formal study of language. The representations are the limits of what can be stored and
computed upon, and the details of a representation have a major influence on the form of
any analysis.
Broadly, the goal of this thesis is to explore a lower bound of complexity for the phono-
logical module. By exploring the capacities of a representation that I will argue requires
fewer stipulations than anything offered before it, I will defend the claim that the freedom
of this more powerful representation matches the power of morphology.
More specifically I will argue that the representation of phonology is not strings, but
directed graphs, and that this representation is simpler and more powerful and that its
power exactly matches the set of attested phenomena of word-formation and phonology.
The ideas described in this thesis are most obviously a development of the ideas expressed
in Raimy (1999, 2000) in that it explores the full extent of the representational power of
directed graphs in phonology, as the main data structure needed. This thesis also pursues
more generally the program we could call ?nonlinear generative phonology? after the title
of Clements (1980) in drawing from the insights of autosegmental phonology, especially as
it pertains to moving away from strings as a data structure and taking features to have an
amount of independence from each others, forming independent autosegments.
I also see this work as pushing the limits of underspecification theory, broadly the view
that the phonology operates on forms which, underlyingly and in the course of computation,
1
contain less information than a strict description of the surface pronunciation (Clements
1988 and Archangeli 1988, among many others). But beyond underspecification at the level
of the content of segments, I propose underspecification of the very linear order of segments,
such that, underlyingly and in the course of the computation, the linear order of two or more
segments may be undetermined. PROP takes precedence to be phonological information,
and as such this can be seen as pushing Archangeli?s stated goal that ?underspecification
theory applies to all phonological information, not simply to feature values? (p.12) even fur-
ther than she did. Furthermore, paralleling the advances of underspecification theory such
as Keating (1988) who pursued the idea of underspecification all the way into the phonetics,
resolved by general principles of motor planning, I similarly attribute some resolution of
underspecified ordering to downstream planning and articulatory compatibility as we will
see through out the thesis.
Empirically, most of what is discussed in this thesis belongs to what could broadly be
termed ?non-canonical phonology?: tone, vowel harmony, reduplication, allomorphy. These
phenomena have long been at the forefront of debates over the fundamentals of phonology
and morphology. It is crucial to explore the most powerful phenomena of the world?s
languages to truly appreciate the capacities of Phonology as a unified system. I am not the
first of course. Hyman (2018), for instance, claims that tone is important for phonology,
using the slogan-like claim that ?Tone is like segmental phonology in every way?only more
so? and, expanding on a similar claim from Hyman (2011), notes that:
anyone who is interested in the outer limits of what is possible in phonology and
morphology would thus be well-served to understand how tone systems work
Reduplication has also played a central role in phonological theory in the last few decades
as a domain where the most complex phonological data enriched the theory.
This dissertation is intended to be of cross-linguistic coverage. The discussion of the
many phenomena involved will lead us to discuss at least briefly some patterns from many
dozen languages.
Chapter 2 is a brief recapitulation and expansion of the original theory of Raimy (2000)
from which I depart. Raimy?s theory was only intended to account for reduplication and
2
other affix types like prefixes, suffixes and infixes. I will from now on refer to this theory
as it is described in Raimy (2000) and subsequent papers as Multiprecedence and I will
distinguish it from Precedence-Relation Oriented Phonology (PROP) which is the radical
extention from it I will argue for in this dissertation.
Chapter 3 tackles together two immense topics: vowel harmony and word-tone phenom-
ena. With a simple assumption I will show that the basic structure of Multiprecedence can
be readily expanded to account for these phenomena in a fundamental way that naturally
derives from the representation.
In chapter 4 I will discuss the positioning of affixes and how they can also benefit from
PROP analyses. This chapter is importantly a jumping off point to the following chapters.
In chapter 5 I discuss Phonologically-Conditioned Allomorphy. A simple representa-
tional possiblity allows for multiple interesting types of PCA to be handled in a completely
novel way within the phonology. This radically novel way to handle suppletion has multiple
empirical and conceptual advantages when it comes to coverage and to the design of the
linguistic system, which will be discussed in this chapter.
Chapter 6 extends the ideas of chapter 5 to Morphologically-conditioned Allomorphy by
incorporating some ideas from chapter 4.
Chapter 7 incorporates the insights of the previous chapters and explore their inter-
action with reduplication so as to fully incorporate PROP as a continuation of Raimy?s
Multiprecedence.
Chapter 8 is a promisory note on the theory of PROP, taking the assumptions and
claims made in the previous chapters and relates them to what they imply about phonetics,
acquisition, and psycholinguistics.
And finally chapter 9 is a cursory discussion of ideas that remain to be explored in
detail within the world of PROP on top of the main ones of the previous chapters, in-
cluding the inclusion of regular phonological processes into PROP and how some of them
may be replaced or illuminated by PROP principles, a discussion of complex segments, of
the morphology of ineffable forms, other word-formation phenomena that did not fit into
previous chapters, as well as what PROP could do for the phonology of structures above
the word-level.
3
The discussion to come is at times recapitulative of things other theories do well and at
other times wildly speculative. The goal of this dissertation is to expand on a theory that
is both promising and under-explored.
4
Chapter 2
Preliminaries: Raimy (2000), strings and
precedence
This chapter will introduce the theory of Precedence-Relation-Oriented Phonology (PROP).
Because it derives mostly from the Multiprecedence representation used in Raimy (1999,
2000), section 2.1 will summarize the theory of Multiprecedence and section 2.2 will distill
the parts of Multiprecedence that will be used in the rest of this dissertation.
2.1 Raimy 2000
The basic point of departure from standard phonology that Raimy took was to ask was what
could happen if instead of using the string as our basic representation we used a structure
with fewer stipulations: sets of pairs of segments in a precedence relation from the first to the
second, bounded by a START point and and END point. He used this structure to derive
morphophonological phenomena in a novel way that allowed him to account in a derivational
theory for difficult phenomena in the interaction of regular phonology with reduplication
and infixation. This section will cover the mechanics and some of the empirical facts that
this representation could derive elegantly, and it will summarize some of the directions that
have been explored by others working in Multiprecedence Phonology.
2.1.0.1 Precedence relations
Consider a string like (1-a), the familiar way to think of what phonology operates over.
An alternative way to encode that same information is in the form of a set of precedence
statements like (1-b). For legibility the set of pairs in (1-b) can be represented in the form
of a graph diagram; adding the convention that of using # and % for the START and END
symbols respectively we get the picture in (1-c). In general I will refer to this view as the
5
graph representation.
(1) a. k?t
b. {?START, k?, ?k,??, ??, t?, ?t, END?}
c. #? k ? ?? t? %
The main difference between such a representation and a string-based one is that since
the precedence pairs are all there is, there is no restriction as to what the set of them can
be. For instance segments can be in precedence relations with multiple other segments as
in (2), two segments can be in a precedence relation with each other as in (3), and segments
can precede themselves as in (4).
(2) a. {?a, b?, ?a, c?}
b.
b
a
c
(3) a. {?a, b?, ?b, a?}
b.
a b
(4) a. {?a, a?}
b.
a
In Raimy?s system the geometrical possibilities of the representation end up carrying
weight in describing the interaction of morphology and phonology. The goal of this paper
6
is to show that the geometrical possibilities of multiprecendence go beyond loops and can
serve to account for other phenomena of morphology and phonology.
2.1.0.2 Affixation and Reduplication
In this system all affixation involves adding precedence links and segments to a stem1.
Suffixation looks like (5-a), which shows the English plural, and infixation like (5-b), which
shows the Atayal animate action focus to which we will return in ch.4. Crucially, (5-c),
which shows the Indonesian plural, is how to represent reduplication. All three of these
structure have to be handled by a serialization algorithm, in order to be actualized by the
motor system, which selects a path through the graph to be sent to the articulators. The
details of such a serialization algorithm would take us too far astray; I direct the reader to
Fitzpatrick and Nevins (2004), and Idsardi and Raimy (2013) for formal proposals. The
general intuition is that serialization attempts to traverse as many arcs of the graph as it
can with as little redundancy as possible, hence why it follows the path with the affix in
(5-a) and (5-b) rather than bypass it and why it takes the loop in (5-c) but does not loop
more than once.
z
(5) a.
# k ? t % =? # k ? t z %
m
b.
# h N u % =? # h m N u %
c. # b u k u %
=? # b u k u b u k u %
For Raimy, the multiprecedence structures on the left can be built either by vocabulary
items or by readjustment rules specified to add structures like (6) to a root (7) to give the
form in (8). The moniker ?last segment? is an informal way to refer to that part of the affix
that is responsible for attaching it to the stem in the right location. This was named a
1There are at least three uses of ?stem? in the literature. I will use the term ?stem? in the sense of e.g.
Nida (1949, p.83), Pinker (1999, p.115-116, 295) to refer to any form onto which an affix can be added, and
hence any affixation operation is adding an affix onto a stem
7
sticky end by Samuels (2009) and we will discuss this mechanism below.
(6) a. {?lastsegment, z?, ?z,%?}
b. lastsegment? z ? %
(7) a. {?START, k?, ?k,??, ??, t?, ?t, END?}
b. #? k ? ?? t? %
(8) a. {?START, k?, ?k,??, ??, t?, ?t, END?, ?t, z?, ?z, END?}
z
b.
# k ? t %
This representation can generate a vast number of patterns from numerous languages, like
reduplication that adds phonological material between the copies such as the Bambara redu-
plication wulu-o-wulu ?whichever dog? <wulu ?dog? (Culy, 1985) in (9) or fixed segmentism
in English schm-reduplication in (10), as well as account for a number of over- and under-
application phenomena of phonology that McCarthy and Prince (1995) had claimed were
not derivable in serial models. Raimy also shows how multiprecedence is restrictive enough
to predict the impossibility of some unattested patterns that competing theories can easily
generate. I will direct the reader to Raimy for a complete demonstration of the empirical
coverage of Multiprecedence.
(9) wulu-o-wulu
o
# w u l u %
(10) table-schmable
S m
# t e b l %
8
A crucial take-away of this theory is that according to it there is nothing special about
reduplication as a word-formation operation. Affixation is adding material onto a stem,
and reduplication is the case where that otherwise unremarkable affixation creates a loop
in the representation. There is therefore nothing morphologically or phonologically special
about reduplication, except for the fact that the representation it creates has a loop in its
geometry. The link between the final /u/ an the intial /b/ in (5-c) is of the same nature
as as the link between the /b/ and the /u/ that follows it. There is no special ?back arrow?
symbol (pace Downing 2001 and Paschen 2018, p.3.
2.2 Detailed Mechanics
Before going beyond Raimy (2000), it is important that we take the time to examine the
machinery of multiprecedence.
2.2.0.1 Start and End
The Start and and End symbols are probably the most glaring difference between the graphs
used so far and classical phonology based on strings. Those symbols are necessary in the
multiprecedence model, because when loops are involved there is no way to know where to
start without an explicit symbol. For instance in (11) it is impossible to decide where to
start and end the loop; the only way is to mark segments as initial and final. There are
multiple ways this could be done.
(11)
b
a c
d
A simple way would be to directly mark it on the segments by augmenting the graph
with a representation for initials and final states borrowed from Finite State Automata as
in (12).
9
(12)
b
aS c
dF
This makes it an information about the node itself whether or not it begins the word.
One empirical problem with this approach is that the first and last segments of the out put
form can change, e.g. through the addition of prefixes and suffixes.
Another possibility is to add a sort of empty segment as in (13).
(13)
b c
# a d %
This gets around the empirical problem, as material can be added between these empty
segments and the overt phonological material of the stem.
One may be tempted to see this as a deficiency of the graph model, but phonological
models based on strings also need boundary symbols, typically both marked with #, to
which phonological rules may be sensitive. Even outside of the world of phonology hav-
ing special start- and end-of-string characters are a common way to deal with strings in
computer implementations of string, e.g. null-terminated strings in C. in order to dal with
strings in a formal way the implementation always has to handle the start and end of the
string in a special way. This is a case where multiprecedence is more explicit, not more
complex. This is a distinction to which we will return in 2.3.0.1
2.2.0.2 Sticky-Ends
An important mechanics of Raimy?s system is the sticky end, the part of the underlying
form of affixes that allows them to attach onto a stem. The name ?sticky-ends? is from
Samuels (2009) and I will borrow it here. It largely builds on the notion of pivot points
from Yu (2003).
Sticky-ends are needed in this system for all affixes that attach to anything else than #
10
or %. Because sticky-ends can attach to multiple stems, they cannot know in advance what
segment they attach to, and as such they must specify their target intensionally through
the target?s feature and/or relation to other segments within the form.
For instance suffixes must be specified to precede %, but also to follow the last segment
of the stem, as in (6) above. This is done through a sticky-end that picks out the last
segment of a word. This can be defined intensionally by making the sticky-end seek a
segment x satisfying the relation x ? %. Thus (6) could be more properly represented as
(14) with one sticky-end seeking a segment that precedes %, and one end that seeks %.
(14) [ ? %]? z ? %
These sticky ends can also be specified to seek segments with particular features. Consider
infixation in native roots in Tagalog as in (15)2.
(15) Tagalog um-infixation (Kager (1999), citing French (1988))
alis um-alis ?leave?
tawag t-um-awag ?rewarded?
This can be handled with the affix in (16). This affix has three ends. One simply targets
the beginning of the word, then the sticky-end pictured to the right seeks segments that
are vowels. And finally the sticky-end pictured at the bottom seeks segments that both
follow the # and are consonants. Note that not every stem will have such a segment, e.g.
vowel-initial roots, in which case that sticky-end will simply be unable to attach. This is
in fact exactly what we see in the formation of um-alis in (17). The affix attached to #
and to every vowel of the word, that is, it added an ordered pair between # and /u/, as
well as an ordered pair between /m/ and each of the vowels of the stem. But there was no
segment in the stem satisfying the conditions of the other sticky-end which therefore did
not add any precedence pairs to the graph. The affix in (17) thus ends up following # and
preceding /a/, because this order satisfies all the precedence relations stated in the graph,
thus surfacing as a prefix.
2Non-native roots, which may have onset clusters and have been reported to have variable realizations
(e.g. Klein (2005), introduce some complications that would take us beyond the scope of this introduction.
11
(16) Tagalog um-infix
# u m [+V]
[#? [+C]]
(17) um-alis
u m
# a l i s %
(18) t-um-awag
u m
# t a w a g %
In the formation of t-um-alis in (18) on the other hand all ends of the affix manage to
attach, adding a link from # to /u/, one from /t/ to /u/, and one from /m/ to every vowel
of the stem. the affix -um- therefore ends up following /t/ and preceding the first /a/,
because this order satisfies every ordering relation stated in the graph, and thus it surfaces
as an infix between these segments.
I will use the square brackets for sticky-ends. This usage is intuitively closely related to
the use of square brackets in classical phonological rules, in which forms like [+high, -back]
are meant to capture not a segment, but a natural class, namely an intensional description.
In fact the square brackets are ambiguous as they are also used to refer to segments qua
feature bundles. Here I will follow the convention of Bale et al. (2014) and reserve square
brackets for intensional definitions (both in rules and in sticky-ends), and use curly brackets
to refer to segments qua feature bundles. Thus from now on, [+high, -back] refers the set
of all segments that are supersets of the set {+high, -back}, whereas {+high, -back} refers
to sets of features, namely segments.
12
More formally one can read brackets as denoting properties, and sticky-ends as machines
seeking segments with those properties. Consider the following properties:
? [[+F ] is the] property of having feature +F ,
? [+F ]? is the property of following a segment with the property of having feature
[+F , ]
? [+F ] ? [+G] is the property of having feature +G and following a segment with
[the pro[perty of hav]]ing feature +F ,
? ? [+F ] ? is the property of preceding a segment with the property of
[following a[ sement w]i]th the property of having feature +F,
? [+G]? [+F ]? is the property of following a segment having feature +G and
f[o[llowing a s]egme[nt having]f]eature +F,
? ? [+G] ? [+F ]? is the property of i) preceding a segment that has the
propoety of preceding a segment having feature +G and ii) following a segment having
feature +F,
? ...and so on.
This is obviously too powerful. This is simply a way for me to describe the sticky-ends
I need. Attempts have been made at working out a restrictive theory of sticky-ends in
Multiprecedence by Yu (2003) and Samuels (2009) and I trust that they are on the right
track, but I occasionally need more sensitivity to context and features than they do so I
take the liberty of employing powerful sticky-ends and let the issue of working out their
limitations to further research. This thesis is about the geometry of representation. Any
more restricted system of sticky-ends capable of generating at least the ones I need in this
dissertation will be good enough.
2.2.0.3 Raimy (2000) is not PROP
Raimy?s (2000) phonology contains more than the precedence relation introduced in 2.1.
Raimy maintains autosegmental assumptions of layers of elements associated to each others,
13
hence it relies on relation other than precedence. For instance the following appears in his
analysis of Malay nasal harmony.
(19) Autosegmental feature spreading in Raimy(2000,p.18)
[+nas]
# a N e n %
[+nas]
# a N e n %
Raimy also did not conceive of the back arcs as independent morphemes, but as the
effect of readjustment rules (p.4), but already in Harisson and Raimy (2004) there is a de-
fense of reduplication arcs as morphemes and reduplication as a fully item-and-arrangement
phenomenon. PROP however goes much farther in this assumption as wel will see in the
following chapters.
2.3 Going Full PROP
2.3.0.1 Simplicity vs. graphics vs. power
I am claiming that the repsentational system of (20-b) contains fewer stipulations than one
for (20-a). To understand this claim it is important to distinguish a) the fact that directed
graphs are less stuipulative (and thus simpler) than strings in the way mentioned above
from b) the graphical conventions of our writing system that allows us to easily represent
strings as left-to-right lists of symbols, and c) the richer set of structures allowed in graphs
than than in strings. a) is a mathematical fact about the properties of the data structure.
Strings are graphs with a total order relation, namely the relation is total, transitive, and
antisymmetric. A graph without these properties is a simpler mathematical object with
fewer assumptions. It is true that thanks to b) we can represent strings in fewer symbols
than graphs as in (20-a), but that is because our writing system implicitly packages all
these stipulations, representing linear order in time as linear left-to-rightness on a the page.
14
We should not allow this purely pictorial fact of writing to influence impressions about
complexity. Strings do require a logical relation of precedence between pairs of elements as
well as a notion of start and end; the graph notation is simply actually writing those down.
The presence of arrows and special START and END symbols in (20-b) is explicitness, not
complexity.
(20) a. k?t
b. #? k ? ?? t ? %
And as said in c) it is true that we can do more with less stipulative graphs than with
strings (since all strings are graphs but not vice versa). As seen above graphs can contain
branchings, loops, and parallel paths that strings cannot represent. But this is representa-
tional power, not complexity. My claim is that talking about generic graphs rather than
strings is making fewer assumptions about what phonology is and therefore it is a simpler
claim. But it is indeed powerful. Simpler things often offer more possibilities. The point of
this paper is to argue that this power matches very well with all the less string-like phenom-
ena of phonology and morphology that are attested. This simpler-than-string phonology is
powerful, and it seems to contain just the right power to do morphology.
2.3.0.2 Complexity and power in phonological representations
It is already standard for phonology to be made more powerful than strings, thanks to au-
tosegmental phonology, morphological planes, feature geometries, prosodic structures, and
Optimality Theory correspondence relations. But all those approaches add this power by
also adding stipulations to the representation, adding new relations, types, and restrictions,
and therefore complexity in the above sense. For instance a representation like in (21-a)
contains at least two types of relations: the more stipulative linear precedence relations
between melodic segments and between timing slots, and the arcs connecting melodic seg-
ments and timing slots. This representation is at least as complex as (21-b-c), where P is
the set of precedence statements and A is a set of autosegmental associations.
15
k ? t
(21) a.
?1 ?2 ?3
b. ?P,A?
c. ?{?START, k?, ?k,??, ??, t?, ?t, END?, ?START,?1?,
??1,?2, ?, ??2,?3?, ??3, END?, },
{?k,?1?, ??,?2?, ?t,?3?}?
Similarly a typical representation from Optimality Theory contains multiple types of rela-
tions between segments, including precedence and any graph-theoretic relations used above,
but also the relations of correspondence including Input-Ouput (I-O), Base-Reduplicant (B-
R), and sometimes Input-Reduplicant (I-R) . A basic reduplicated structure like (22-a) will
therefore be computed over a representation as complex as (22-b) with a set of all the prece-
dence relations in the input and output, the I-O correspondences, the B-R correspondences,
and the I-R correspondences as a bare minimum, which can be expanded as (22-c), the
actual representation over which correspondence theory needs to be computed (see Raimy
and Idsardi (1997).
(22) a. OT correspondences
b u k u
I-R
I-O
b u k u b u k u
B-R
b. ?P, IO,BR, IR?
c. ?{?START input, binput1 ?, ?b
input
1 , u
input
2 ?, ?u
input, kinput2 3 ?,
?kinput, uinput3 4 ?, ?u
input
4 , END
input, ?, ?START output, bred1 ?,
?bred1 , ured2 ?, ?ured, kred2 3 ?, ?kred, ured3 4 ?,
16
?ured, bbase?, ?bbase, ubase?, ?ubase, kbase4 1 1 2 2 3 ?,
?kbase, ubase?, ?ubase, ENDoutput3 4 4 ?},
{?binput1 , bbase1 ?, ?u
input, ubase?, ?kinput, kbase2 2 3 3 ?, ?u
input
4 , u
base
4 ?},
{?bbase, bred?, ?ubase, ured?, ?kbase1 1 2 2 3 , kred3 ?, ?ubase4 , ured4 ?},
{?binput1 , bred?, ?u
input, ured1 2 2 ?, ?k
input, kred?, ?uinput, ured3 3 4 4 ?}?
As such, PROP representations like (23) are intended to be both more explicit about the
information they contain, and simultaneously containing less information total.
(23) a. k?t
b. {?START, k?, ?k,??, ??, t?, ?t, END?}
c. #? k ? ?? t? %
In a way, the goal of this paper is to embrace the added power of PROP without introducing
the added complexity of its competitors. All the phenomena that have led to doing phonol-
ogy on graphs, tones, vowel harmony, floating features, make a convincing case in favor of
something more powerful than strings in phonology, and we will return to those phenomena
in the upcoming chapters. But instead of gaining this representational power by adding
machinery, creating what are essentially strings with stuff around them, I propose that we
do it by relaxing the stipulations on the string representation. If the limitations of strings
can be circumvented either by adding complexity or by removing it, the latter is definitely
a sensible direction to explore. Let?s add power by simplifying.
2.3.0.3 THESIS: PROP is exactly what we need for language
The main thesis of this dissertation is this: the range of phenomena of morphology and
phonology is exactly that which follows for free from the assumptions (or lackthereof) of
PROP. The power of morphology and phonology reduce to the possible configurations of
a PROP directed graph. The different geometrical configurations that a string cannot
represent but that can be represented in PROP will capture exactly the range of non-
concatenative morphology and non-linear phonology.
17
Chapter 3
Tone and Harmony
In this chapter I will show that the representational power of PROP can derive phenomena
of harmony and word-level tone from simple geometrical configurations made available for
free by directed graphs.
3.1 Basic geometry
Expanding upon the representational possibilities of PROP, a geometrical pattern that can
now exist is one containing separate streams, each of which contains phonological material.
I will propose here that this representation is capable of accounting for tone spreading
phenomena and harmony patterns.
(1)
a b c d
# %
w x y z
For the case of graphs without loops like (1) in which the the relation described by the
graph is a partially ordered set, I will refer to incomparable elements of the partial sets
?those pairs x,y in the graph for which is is neither stated that x transitively precedes y nor
that y transitively precedes x? as being in parallel. The assumption I propose to follow here
is that parallel nodes can surface simultaneously as long as they are phonetically compatible,
18
such that
(2) possible phonological form giving rise to surface {+rd,+hi}.
[+rd]
# %
[+hi]
Intuitively, the claim is that the phonetic output of a graph like (1) is a surface form in
which abcd is more or less coextensive in time with wxyz. The phonology does not transmit
any ordering relation between the two to the motor control systems, and as such they are
coextensive in time.
However coextensivity is too strong of a claim. A bit less restrictively, since the output
of the phonology specifies nothing at all about the order it is up to the motor planning of
the muscles involved in the realization of phonological material to produce an output that
satisfies the input as they ?want?. In many cases the result will not be perfect simultaneity,
as the motor movements of some features may be incompatible, or some motor movements
faster or slower than others. If in (1) the features of a and w cannot be produced simulta-
neously, then one or the other will have to wait. We will come back to this discussion as
we see more concrete examples.
3.2 Basic examples
3.2.1 Mende tone melodies
Since Leben (1973, 1978) nouns in Mende (Bantu) are commonly analysed as having one of
five tone melodies, sequences of L(ow) and H(igh) tones, normally couched in Autosegmental
19
Phonology1.
pattern ? ?? ???
H kO? pE?lE? ha?wa?ma?
L kpa? bE?lE? kpa?ka?l??
(3) (from Odden, 1995)
HL mbu? ke?nya? fe?ma?la?
LH mba? n??ka? nda?vu?la?
LHL mb?a nya?ha? n??k??l??
The PROP analysis consists in seeing the tone melody as a parallel stream from # to
%. This captures the notion of the independence of the tonal pattern from the segmental
material behind the autosegmental analysis while using the simpler PROP representation.
Intuitively we can see that once this type of graph is sent to the articulators, the segmental
and tonal material are pronounced relatively independently.
(4) mb?a
L H L
# m b a %
(5) n??k??l??
L H L
# n i k i l i %
All that the representation encodes is what precedes what. The melodic autosegments
are ordered with regard to each others, and the tone autosegments are ordered with regard
to each others, but the tones and the melodic autosegments are not explicitly ordered with
1Tones on a vowel V are notated as such:
? V? = high tone
? V? = low tone
? V? = rising tone contour
? V? = falling tone contour
? V? = rising-falling tone contour
20
regard to each others. What the representation says is that both of them must occur
between # and %. This captures the relative independence of Mende tone patterns from
their melody. This is enough to capture the set of contrasts in Mende. It is however not
enough to completely derive the phonetics. For instance I have provided no explanation as
to why none of the tones ends up surfacing on the /m/ of (4), which is perfectly plausible
phonetically. The important concern for me here is that the above captures the set of
contrasts of Mende. The details of implementation is less important and could be done in
many ways, including language-specific phonetic conventions in which the speaker knows to
pronounce these graphs in the right way, or phonological rules that add other precedence
links to ensure that everything aligns as it does on the surface. I will leave this as an open
question.
3.2.2 Vowel Harmony in Akan
Beyond independence of some material, PROP also easily derives ?spreading? phenomena
(here used in a descriptive sense). Consider Akan (Kwa) [ATR] harmony. The general
pattern is for stems to be specified for [ATR] or not, which controls the form of both
prefixes (6) and suffixes (7).
(6) Akan prefix harmony
eat be called
1s mi-di mI-dI
2s wu-di wU-dI
3s o-di O-dI
1p ye-di yE-dI
3p wo-di wO-dI
(7) Akan suffix harmony
21
wie ?to finish?
a-wie-i ?the end?
tO ?to fall?
a-tO-I ?West?
The forms in (6) show two roots that minimally differ in that the root for ?eat? is underlyingly
+ATR and the root for ?be called? is underlyingly -ATR. The person agreement prefix agrees
in ?ATR with the root. The forms in (7) show that the same harmony affects suffixes,
demonstrated with the nominalizer.
This is easy to account for in PROP with roots specified for ?ATR. For a root like eat
(8) that is specified with {+ATR} between and %, any prefix inserted between and the
first segment will also be parallel to the {+ATR} value ((9)).
?
(8) di
{+ATR}
# d {+hi,-rd} %
(9) wu-di
{+ATR}
# d {+hi,-rd} %
w {+hi,+rd}
(10) a-wie-o
22
{+ATR}
# w {+hi,-rd} {-hi,-rd,-lo} %
{+lo,-ATR} {+hi,-rd}
The reason the above graphs work is that the {+ATR} feature, being specified only
as following and preceding %, is parallel to everything that also occurs between those}
symbols. In (9) we can see that there is a path from to % going via the {+ATR} node
and a completely separate path from to % going through the {+hi,+rd} segment of the
prefix. This gives us automatic bidirectional spreading.
Intuitively, the realization of this type of graph involves pronouncing a +ATR value
throughout the word that will surface whenever it does not conflict with other features, e.g.
those of the consonants. Motor planning is told to move the tongue root to produce +ATR
in an event that follows the start of the word and precedes the end of the word. Since the
two vowels are underlying underspecified for ATR the parallel {+ATR} node will surface
during those. One can imagine each stream as a part in a musical ensemble. The [+ATR] is
?played? throughout on one part, while the other stream ?plays? the other segments. This
rough analogy breaks down when it comes to resolving conflicts between multiple streams.
We will see how these are resolved.
It is worth noting that I am therefore defending a view of harmony patterns in line
with Lightner (1965), what he calls harmony as a property of root-morphemes. It is a
property of morphemes and their lexical specification that makes them cause harmony
phenomena, not directly a property of the co-occurence of segments and features involved.
In this chapter we will see examples of disharmony and harmony controlled by morphemes
lacking paraticipating segments that pose an problem to a theory of vowel harmony based
on segment co-occurence restrictions.
3.2.3 Siane Tone patterns
This simple type of spreading is more common with harmony patterns, but it is attested
for tone patterns in James? (1994) analysis of Siane (Trans-New-Guinea) (cited in Cahill
23
(2000)). In this language noun stems come with one of the tone patterns H, L, LH, HL,
or HLH and the generalization is that the first tone is realized on the first syllable and the
last one on the rest, including the suffixes. The exceptions are the case of HL words over
four syllables in which case the two first syllables carry H and the rest L. and the case of
bi-syllabic HLH words which seem to mostly surface HL-H rather than H-LH.
noun stem 1p.poss. defin erg gloss
H ku?la? ku?la?te? ku?la?ma? ku?la?ka?fo? ?dog?
H ke?tu?fu? ke?tu?fu?te? ke?tu?fu?ma? ke?tu?fu?ka?fo? ?saliva?
L me?ina? me?ina?te? me?ina?ma? me?ina?ka?fo? ?payment?
L ko?s??na? ? ko?s??na?ma? ? ?sky?
(11)
LH ma?fo? ma?fo?te? ma?fo?ma? ma?fo?ka?fo? ?taro?
LH k??l??fu? k??l??fu?te? k??l??fu?ma? k??l??fu?ka?fo? ?trap?
HL lo?no? lo?no?te? lo?no?ma? lo?no?ka?fo? ?work?
HL ma?fu?na? ma?fu?na?te? ma?fu?na?ma? ma?fu?na?ka?fo? ?owl?
HLH ke?fa? ke?fa?te? ke?fa?ma? ke?fa?ka?fo? ?meat?
The PROP analysis of this pattern combines the insights of Mende and Akan and starts
with a parallel stream of tones for each root?s pattern with the suffixes added in parallel to
those. The string of segments /mafokafo/ is being pronounced while the sequence of tone
/HL/ is also being pronounced.
(12) ma?fo?ka?fo?
L H
# m a f o %
k a f o
One may wonder why the tone melody tone is realized as it is with a low tone on one
syllable and a high tone on three syllables. That is, why doesn?t the graph in (12) predict
24
[ma?fo?ka?fo?], with a low tone on two syllables and a high tone on the other two as in the
HL case of [lo?no?ka?fo?]. After all, if two tones have to be pronounced during four syllables,
one could well think that they would get two tones each. However the formal system here
makes no such claim. All that the graph says is that a sequence of tones /LH/ must
be pronounced between the beginning and the end, and a sequence /mafokafo/ must be
pronounced between the beginning and the end, nothing else. It might be that we need
to formulate phonological rules that would add the required ordering relations, but ideally
there is nothing more to say about how that happens at the level of the phonology if it is
resolved by phonetics and motor planning.
In other words I contend that the choice between all configurations of a sequence of
/HL/ tones pronounced over four syllables is chosen for non-linguistic reasons in a motor-
planning module. There are problems, such as how to get the tones to align in the exact
way they do. For instance why is the HLH form ke?fa HL-H rather than H-LH ke?fa? The
question of how this may be done is a topic for further research. It is sufficient here to
derive the contrasts.
3.2.4 Finnish Transparent vowels and Turkish opaque vowels
One assumption I made at the beginning of this section is that parallel segments are con-
strained by phonetic compatibility: two parallel segments will not be pronounced simulta-
neously if their features are incompatible. For the purpose of this thesis this is simply the
impossibility of performing two gestures that cannot be peformed at the same time: if the
consonant holds features incompatible with tone or vowel specifications, then those tones
cannot be simultaneous to those segments.
However one very strict and simple use of this principle is in the case of transparent
vowels, vowels that are seemingly ignored by vowel harmony, where featural specifications
of two segments in parallel can be explicitly contradictory.
Consider Finnish backness harmony as described in van der Hulst and van de Weijer
(1995). Roots are segregated into front vs. back, such as va?rttina? ?spinningwheel? vs.
palttina ?linen cloth?, which will surface respectively with front affixes, va?rttina?-lla?-ni-ha?n,
?with spinning wheel, as you know?, or back affixes, palttina-lla-ni-han ?with linen cloth, as
25
you know?. The underlying forms of these roots would be as in (13) and (14), where /A/
stands for a low vowel underspecified for backness2.
(13) va?rttina?
-bk
# v A r t t i n A %
(14) palttina
+bk
# p A l t t i n A %
As expected the back feature will have ?scope? over suffixes and create the harmony
pattern:
(15) va?rttina?-lla?
-bk
# v A r t t i n A %
l l A
(16) palttina-lla
+bk
# p A l t t i n A %
l l A
Note that /i/ is unaffected by vowel harmony. This is easy to explain if we posit that
Finnish /i/ is underlyingly -back. Because the +back autosegment and the -back /i/ cannot
be coextensive, only one of them will surface at that point in time, here the segment?s for
2I am not concerned here with the issue of underspecification, which may easily allow one of the two
classes of Finnish words to be underspecified for backness and simplify the analysis.
26
a reason that will become clear.
Now consider the case of opaque vowels, vowels that not only do not harmonize, but
create their own domain of harmony. In the well known case of Turkish, vowels harmonize
for backness and roundness, as shown in (17) with the genitive suffix -in/-yn/-Wn/-un. The
plural suffix -ler/-lar however assimilates only in backness. It is always -Round, but it is
not transparent to roundness harmony; a genitive suffix following a plural suffix will surface
as -round, regardless of the root and of how it surfaces in the singular genitive, as in the
crucial case of jyz-yn vs. jyz-ler-in as opposed to *jyz-ler-yn.
nom.sg. nom. pl. gen. sg. gen. pl. gloss
ip ip-ler ip-in ip-ler-in ?rope?
(17) jyz jyz-ler jyz-yn jyz-ler-in ?face?,
kWz kWz-lar kWz-Wn kWz-lar-Wn ?girl?
pul pul-lar pul-un pul-lar-Wn, ?stamp?
The PROP analysis of the roots and genitives is straightforward given what we have seen so
far: the root must be specified to have parallel ? back and ? round features as in (18). The
genitive is then added to such forms to give (19), and the underspecified vowel is pronounced
with the values of the segment it is parallel to.
?
(18) jyz
{-bk,+rd}
# j {+hi} z %
(19) jyz-yn
{-bk,+rd}
# j {+hi} z %
[+hi] n
The plural introduces some complication: it contain a -round feature to ?protect? it from
27
harmony as in the Finnish case above, but this -round feature must also be parallel as its
roundness makes subsequent suffixes harmonize. It will therefore have the underlying form
?
in (20), with its [?round] feature scoping over any further suffix. If affixed to a root jyz
it will attach as in (21).
(20) -lAr
{-rd}
[ ? %] l {-hi} r %
(21) jyz-ler
{-bk,+rd}
# j {+hi} z %
{-rd}
l {-hi} r
Finally to this form we can affix the genitive as in (22).
(22) jyz-ler-in
{-bk,+rd}
# j {+hi} z %
{-rd}
l {-hi} r
{+hi} n
The graphs in (21) and (22) are starting to be complicated, but it is pretty straightfor-
ward: the [-bk,+rd] portion of the root emcompasses the whole form, and the [-rd] portion
of the suffix encompasses everything after the /l/ of -lAr. But now we reach an issue of
phonetic realization: at the point of pronouncing the {?hi} segment of the plural and the
[+hi] segment of the genitive, these segments are parallel to both the +rd of the root and
28
the ?rd of the suffix, so why do they surface as [-rd]?
I propose that it is a general fact of the phonetic realization of parallel contradictory
features that the ?inner? one always wins. More precisely: if all the segments parallel to A
are also parallel to B, but not vice versa, and A and B contain a feature with contradictory
values then for the segments that are parallel to B it is B that will be pronounced in parallel.
For instance in a configuration like (23), in which all the segments parallel to segment {+F}
are also parallel to segment [-F] but not vice versa, it is 4 {?F} that ?counts? during the
segments parallel to -F, namely /d/, thus it will surface as in (24).
(23)
+F
-F
a b c d e f g
(24)
[ a b+F c+F d?F e+F f+F g ]
Importantly, the case of transparent segments discussed above is just the extreme case of
this principle where there is no segment /d/ and the inner segment with a contrary feature
surfaces on its own as in the Finnish example in (16). We therefore unify the ?independence?
of transparent and opaque segments from harmony out of the same geometric principle.
Or seen in another way opaque segments are nothing more than segments with both the
property of having an ?inner? feature like a transparent segment, and the property of having
this feature stretch to one edge of the word like a ?spreading? feature.
Ideally we should hope to derive this principle of phonetic realization independently.
We will come back this in section 8.1.
The facts of Turkish described so far also straightforwardly allow for so-called ?half-
harmonizing? suffixes such as the progressive suffix as in (25) described in Clements et al.
29
(1982, p.231) and Nevins (2010, p.34), which is adequately accomplished with an affix such
as (26).
(25)
gjelj-ijor-um ?come-prog-1sg?
ko-ujor-um ?run-prog-1sg?
gu?lj-u?jor-um ?laugh-prog-1sg?
bak-1jor-um ?look-prog-1sg?
(26) -Ijor
{+rd,+bk}
[ ? %] {+hi} j {-hi} r %
This suffix will create a new harmonic domain to its right, but the first vowel is not
within that scope and will follow the parallel features of the root (or potentially previous
suffixes). This shows that although the PROP analysis makes vowel harmony a fact of the
morpheme rather than the segments involved, it is not so coarse as to allow only entire
morphemes to be harmonizing or not. PROP allows for flexibility in the representation of
what harmonizes and how.
3.2.5 Disharmony and Antiharmony
A natural consequence of the mechanics defined above is that the mechanism of vowel
harmony and that of transparent neutral vowel are independent. We therefore predict that a
root can trigger harmony while containing no vowel that participates in it. Disharmony and
antiharmony are well attested phenomena that are often relegated to a list of ?exceptions?
to the harmony.
For example in Turkish several roots borrowed from Arabic or French have front vowels
and take back suffixes or vice versa. (Lewis, 1967, p.17-18) gives multiple examples such as
fevk ?top?, fevk? ?top.acc?, with a front root vowel and back endings, and ya?r ?beloved?, ya?ri
?beloved.acc?, with a back root and front suffixes. In PROP they are simply represented as
30
in (27) and (28), with the root vowel containing a specification for ?bk that wins over the
parallel feature.
(27)
+bk
# f e v k %
(28)
-bk
# y a r %
Other well-known instances of disharmony is the case of roots with front vowels that
take back affixes in Hungarian. While some roots with /i/ or /e/ behave as one would
phonetically expect and take front sufixes like vi:z ?water? vi:z-ek ?waters?, some do the
opposite, e.g. hi:d ?bridge? hi:d-ak ?bridges?. The form of the affix is not predictable from
the surface.
It would be easy to dismiss these examples as ?exceptions? and ?non-native vocabulary?,
but this is not an account of them. These forms are still part of the language and used
productively by native speakers. They must have a representation that can combine with the
representations of the suffixes. In many theories this is ignored, but in PROP these forms can
be given an explicit underlying representation that will derive their behaviors.Phonology
needs to be powerful enough to encode this type of arbitrariness between roots and the
harmonic feature they impose. In PROP this is easily accounted for with a parallel affix.
A final note on disharmony is that PROP allows for artitrary disharmony in a lan-
guage with vowel harmony. In many languages there is a tendency for disharmonic stems
to take suffixes patterning with the final vowel. Thus e.g. the Hungarian root Sof?r
?chauffeur/driver? with one back and one front vowel takes back suffixes: Sof?r-?k ?chauf-
feurs/drivers?. But the opposite is also attested. in Tatar as described by Henry (2018),
consistently mixed stems take suffixes that consistently pattern with the initial vowel. We
31
therefore cannot draw a universal conclusion about the linear locality of vowel harmony
and phonological theory must be powerful enough to allow any patterns of disharmony
with regard to whether affixes match with the first or last vowel of a root, or with any of
them.
3.2.6 Underlying vs. harmonic rounding in Moloko
Another example of the independence of harmony and transparency comes from Moloko
and described by Friesen (2017, p.40). Moloko roots come in three varieties: neutral,
labialized, and palatalized, with a minimal triplet in (29) using Friesen?s notation where
o marks labializing morphemes and e marks palatalizing ones. Like many Central Chadic
languages, Moloko is commonly analyzed as containing a single underlying vowel /a/ with
unpredictable location, and epenthetic vowels with preditable locations. Labialization and
palatalization descriptively spread to other morphemes as in (30) and affect the output of
/a/, of the epenthetic vowels, and of some consonants.
(29) a. /kra/ [k@ra], ?dog?
b. /kra o/ [kwUrO], ?ten?
c. /kra e/ [kIrE]
(30) a. /na - z?/ [naza?], ?I take?
b. /na - zm o/ [nOzOm], ?I eat?
c. /na - s - j e/ [nESE], ?I drink?
This is very straightforward so far. This simply calls for roots like (31) and affixes like (32).
(31)
{?bk}
# k r a %
32
(32)
# {?bk}
[ ? %] j %
Labialization has a rounding effect on back consonants (velars asnd /h/), as shown with
/k/ in (29-b). But Moloko also has underlying labialized consonants, which can mismatch
with the melody of the root it is part of as in (33). There are therefore two source of
labialized consonants in Moloko: they can be underlying, or they can be the result of
harmony.
(33) a. /s l kw e/ [SIl? kw], ?broom?
b. /gw la/ [gwUla], ?son?
c. /hwa ?a/ [hwo?a], ?dregs?.
(34)
{?bk}
# s l kw %
There can therefore be forms in which an underlying labialized consonant persists despite
the root spreading palatalization to the rest of the word. Friesen cites the form [mI-sIkw?m-
E] (p.48), which has a labialized consonant and is otherwise palatalized throughout, except
for the local rounding effect of underlyingly labialized consonants on following vowels.
Moloko therefore militates against views of vowel harmony as fundamentally a fact
of interaction among segments. Most approaches to vowel harmony see the phenomena
as restrictions on surface co-occurrence among segment classes, or as segments giving or
copying features. But the facts of Moloko suggest otherwise: it is not a property of, for
instance, [gw] that it spreads or is a source of roundness, it is a property of roots that they
carry or don?t carry a round feature that spreads.
The forms in (34) are particularly problematic for search-and-copy approaches to har-
mony, because if harmony is triggered by a search from the underspecified segment to find
a labialization value, in these forms the first segment it will find leftward or rightward is
33
going to be labialized, but this will yield the wrong result because the roots are palatalized
or neutral. For instance the prefix part of the 1st person plural inclusive circumfix /ma-...-
ok/ surfaces as [mO-] or [mU-] in labializing contexts, such as in (35). This contrasts with
(36) in which the root does not trigger labialization and the prefix surfaces as [ma-]3. A
search-and-copy algorithm would have to say that the /a/ of /ma-/ seeks labialization to
its right so as to account for (35). But then that predicts that it should find it in (36) as
well. Moloko is therefore not straightforwardly analyzable in terms of search-and-copy.
(35) /ma - ka?- ako/
[mO?- kwO?- Okw]
1Pin+pvf - wait - 1Pin (p.42)
(36) ma?a? - hwU?- Ok
1Pin+pbl - destroy - 1Pin (p.227)
It also will not help to parametrize the search algorithm, e.g. to make it ignore conso-
nants and search for a vowel bearing a backness or rounding specification, because some of
the morphemes triggering harmony consist of only a consonant.
(37) a. /v e/ ?pass?
b. [v-E] pass[2s.ipm]-CL , ?pass!? (spend time)
c. [mI-v-ijE] nom-pass-CL, ?year? (lit. ?passing of time?) (p.131)
(38) a. /l o/ ?go?
b. [o-lo] ?he/she went? (p. 179)
c. [kU?-lO?-hO?m] go, 2P perfective (p.403)
(39) a. /-jo/ ?imp?
b. [ndolo-j] ?explode.imp? (p.180)
But while it is a problem for segment-oriented theories of harmony, root-based theories like
3For both (35) and (36), the perfective and possible moods are marked by the high tone and by the
high-low+length of the prefix respectively
34
PROP have no problem, roots may have a parallel harmonizing feature, and disharmonic
segments, and the two are not impediments to each other.
3.3 Plugging-in
The parallel graphs in the preceding section were all underlyingly parallel, i.e. the underly-
ing form of the root contained multiple streams. However we can define affixes that attach
in parallel to a root.
3.3.1 Parafixes
I will use the terms parafix to refer to an affix added onto a stem in such a way that its
segments are parallel to some or all the segments of the stem. The term has been used for
instance in analyses of Semitic templatic morphology along the lines of McCarthy (1981)
to refer to the morphological process that adds morphemes in parallel to CV templates. It
is important to keep in mind that in the analysis here there is nothing in the theory that
distinguishes the content of the affix itself or its affixation process that creates parafixation,
but it is useful to distinguish the geometrical pattern created by adding material in parallel
to other material.
For instance Roberts (1994, p.93-94), Akinlabi (1996), and Nevins (2010) discuss the
example of Kanembu in which the completive is +ATR and the incompletive is ?ATR.
(40) Kanembu from Nevins (2010)
gOn@kI gon2ki ?I took / I am taking?
dall@kI d2ll2ki ?I got up / I am getting up?
barrEn@kI b2ren2ki ?I cultivated / I am cultivating?
This can be accounted for in PROP with an affix like (41-a) attaching in parallel to
roots underspecified for [+ATR] as in (41-b) (where /O/,/E/,/I/ stand for segments under-
specified for ATR), giving graphs as in (41-c) with a similar geometry as the Akan example
above. We can see that affixes are in a way ?plugged? onto the graph of the stem.
35
(41) a. /#? {+ATR} ? %/
b. /#? g ? O ? n? E ? k ? I ? %/
{+ATR}
c.
# g O n E k I %
We saw in 2.2.0.2 that already for Raimy (2000) some affixes need to target segments other
than at the edges of the form, e.g. for infixation and partial reduplication, by anchoring
the affix to something other than # or %. As expected we can find cases where parafixes
also target non-edge segments.
An important class of phenomenon that this kind of plugging in can easily derive is
bounded spreading of certain features. Consider the regressive nasal spreading in Mixtec
that Piggott (1992) calls a pseudo-harmony, triggered by the second person inflection.
(42) Mixtec regressive nasal spreading from Piggot (1992)
ku?z?u? ?you are diligent?
k?iPv?i ?you will be drunk?
k?iP??i?i ?you will get angry?
kaPce? ta? ?you will sing?
koto?ndE?E? ?you will examine?
cikwePce? ?you will complain?
koPs?o? ?you will fall?
(43)
{nas}
x x x x
k u z? u
As shown in (42), the second person in Mixtec is marked by nasalization from the end
of the word to the last voiceless obstruent. A straightforward autosegmental analysis of this
pattern involves a second person suffix that spreads leftward until the a voiceless obstruent
as in (43).
36
This can be handled in PROP with a second person affix underlyingly set to attach
to voiceless obstruents as in (44). Note that the sticky-end here will seek all segments
?
containing the features -sonorant and -voice. As such when attaching to the root kuz?u
it will attach to the ends of the word, as well as to the /k/, thus the nas follows /k/
and precedes the end of the word, nasalizing everything in this span. But in the case
?
of cikwePce the resulting graph is more complicated, but the ordering relation is easy
to interpret: the {nas} segment follows multiple consonants, but in particular it follows
the last /c/ and therefore it will surface after it. We could perhaps devise a way for the
sticky end to pick out only the last such consonant, but this would lead to a more complex
representation for (44) and there is no evidence for it, so I will stick to (44) even though it
leads to the unexpected representation in (46).
(44) Mixtec 2nd person affix
# {nas} %
[-son,-voice]
(45) ku?z?u?
{nas}
# k u z? u %
(46) cikwePce?
{nas}
# c i k w e P c e %
These very basic examples show that the power of PROP is at least sufficient to account
for basic phonological patterns. The next section will turn to advantages of PROP over
more traditional autosegmental accounts.
37
3.3.2 Tone Donation
The examples so far have been very basic phonological patterns that are also very well
handled in autosegmental phonology. We will now turn to phenomena for which the PROP
analysis is, I think, conceptually superior: cases where tones seem to need both a sort of
independence from melodic content, and also some knowledge about linear order, giving
rise to call the partial-independence problem: autosegmental theory allows only complete
independence between autosegments or complete attachment. PROP on the other hand
flexibly allows for intermediate levels of independence.
A relatively common phenomenon of tone phonology is donator morphemes. This phe-
nomenon involves morphemes that contribute both a tone and segmental material, but the
tone gets realized not on the segments it came with, but elsewhere on the final form, thus
donating a tone to neighbours.
Consider KiYaka as described in Kidima (1991, p.19,35). Nouns that follow the class 7
prefix kya surface with a raised high tone on the stem4.
(47) KiYaka donating tone
?as for the as well? ?it?s of the ?
ndoongo pe? kya ndo?ongo ?needle?
ndoongo pe? kya ndoo?ngo ?palmwine?
zoba pe? kya zo?ba? ?idiot?
ngoombe pe? kya ngoo?mbe ?cow?
kat??ka? pe? kya ka?t??ka ?liver?
Before analysing this pattern it is worth bringing attention to a dangerous pitfall of
autosegmental phonology when trying to deal with tone donation. Consider the abstract
analysis in (48). It might look good at first, but it does not work: by autosegmental
assumptions the tone /T/ and the segments /ABC/ it is floating over should be unordered
with regard to each other. There is no sense in which /T/ could be to the right of /ABC/.
Illustrating /T/ slightly to the right of /ABC/ would be an abuse of notation.
4KiYaka has three phonetic tones: V = Low, V? = High, V? = Raised High (Kidima, 1991, 13-14).
38
(48) Bad autosegmental analysis of tone donation
rightward spreading
T T
A B C + X Y Z ? A B C X Y Z
A first lesson to draw here is a call back to the discussion in section 2.3.0.1 above:
there is a danger to letting some important relations like precedence remain implicit in the
representation, because then we might not realize when we are letting something back in
where it shouldn?t be.
But to the point at hand, (48) cannot be the autosegmental analysis. Something has to
force the floating tone to associate rightward.
Kidima?s analysis is with a process he calls H-Attraction (p.33) in (49). But it is not
clear that this analysis should be allowed in autosegmental phonology. It requires a notion
of floating tones being ordered with regard to material they are not associated with, which
is obvious in examples such as (50) from Kidima (1990).
(49) Kidima?s H-attraction rule
Associate a floating H to the first unlinked accented syllable to the right of its
domain.
(50) Example of H-attraction from Kidima (1990)
What I want to argue from this example is that an analysis of tone donation needs a way
to encode phonological material that is both relatively independent from other phonological
material and linearly ordered with regard to it, simultaneously. Autosegmental represen-
39
tations can only have one or the other: two phonological tiers are either independent and
unordered with regard to each other, or associated and ordered with regard to each other.
There is no halfway.
This is something that a PROP analysis does well. Consider the form in (51), which
would accomplish what (48) purported to account for. Here I intend the notation [# ? ]
to stand for a sticky-end seeking a segment that has the property of following # (in the
same way that traditional phonological rules use A B to refer to a segment following A
and preceding B). The advantage of this analysis is that it is possible to both maintain the
independence of /T/ with regard to /ABC/, as well as order the two of them so /T/ is right
of /ABC/.
(51) PROP version of (48)
T %
# A B C
[#? ]
With this kind of morpheme it is possible to account for the pattern in (47) as in (52), in
which I informally use ? to represented an accented segment, thus putting the H in parallel
to the first stressed segment5.
(52) KiYaka class 7 prefix
H [? ? ]
# k y a
[#? ]
An application of this type of tone donation can be see in Turkish to discuss is what
Clements et al. (1982, p.239) attribute to consonant-conditioned harmony. Some roots are
5For simplicity?s sake I omit here the fact that kya is taken by Kidima (p.19) to be a bi-morphemic
combination of a class 7 prefix ki- and a morpheme -a whose role is unknown.
40
found with front suffixes even though their final vowels are back as in (53) (compare with
regular [jatak]&[jata:g1], ?bed?).
(53)
nom.sg. acc.sg gloss
infiljak infilja?kji ?explosion?
idrak idra?kji ?perception?
ittifak ittifakji ?alliance?
In Clements et al.?s system, the only option they have is to attribute the front harmony
to a -back feature on /k/ that delinks word-finally. In PROP this is basically tone donation.
Roots have forms as in (54), and suffixes will be placed in parallel to the -back feature. There
is no need to worry about the k j& k alternation, as there is already a rule of Turkish that
makes /k/ agree in backness with the tautosyllabic vowel.
(54)
-bk
# i n f i l a k %
More complex phenomena of tone donation at long-distances are possible. And for this
we will analyze the case of Digo in more details.
3.3.3 Digo Verbal Tonology
Digo is a language with complicated word- and phrase-level tone phenomena. The following
analysis is based on the data from Kisseberth (1984), but the presentation does not go in the
exact same order and does not address the historical justification for parts of the analysis.
Digo possesses two main kinds of roots, some that are are underlyingly toneless and some
that have an underlying high tone. The two types can be exemplified with the infinitive
form marked with ku-. As is common in Bantu language all indicative verbal forms have a
final -a morpheme. The forms in (55) are toneless and the forms in (56) and (57) have an
41
underlying high tone6.
(55)
ku-changamuk-a ?to be cheerful?
ku-ambir-a ?to tell?
ku-dekez-a ?to spoil s.o.?
(56)
ku-furuku?t-a? ?to move restlessly?
ku-aru?k-a? ?to begin, start?
ku-bomo?r-a? ?to demolish?
(57)
ku-dundur??z-a ?to place in reserve?
ku-fur??z-a ?to apply heat?
ku-koro?g-a ?to stir?
The presence of a high tone can manifest itself in one of two ways at the surface as
seen in the difference between the rising-falling pattern in (57-a) vs. the high-low pattern
in (57-b). A good reason to treat the two patterns in (56) and (57) as manifestations of
the same tone ias that this difference is predictable: the high-low pattern occurs when the
final consonant of the root is a voiced obstruent (depressor consonant) and the rising-falling
pattern occurs elsewhere. We can also observe the underlying unity of the two patterns
for forms in which a suffix is added to the root and the final consonant is thus not from
the root. The derivational extension suffix -ir for instance can be added to toneless roots
without adding any new tone as in (58-a). When added to a high-toned root ending in
something other than a voiced obstruent the rising-falling pattern occurs shifted onto the
extension as in (58-b). Finally when added to a form ending in a voiced obstruent, the tone
is also shifted, but it now takes the form that we expect from a form ending in something
6For the rest of this section the morphemes that bring a High tone to the form are underlined
42
other than a voiced obstruent.
ku-vugur-a ?to untie?
(58) a.
ku-vugurir-a ?to untie for/with?
ku-fwin??k-a? ?to cover?
b.
ku-fwinik??r-a? ?to cover for/with?
ku-bundu?g-a ?to pound?
c.
ku-bundug??r-a? ?to pound for/with?
We can therefore conclude that all high-toned roots are underlyingly the same and a deriva-
tionally late effect causes the difference between the rising-falling and the high-low pattern
to arise.
For the PROP analysis, I posit that underlyingly high-toned roots come with a H tone
as in (59). Adding suffixes as in (60) and (61) puts them within the ?scope? of the high tone.
?
(59) fwinik
# f w i n i k %
H
(60) ku-fwinik-a
k u a
# f w i n i k %
H
(61) ku-fwinikir-a
k u i r a
# f w i n i k %
H
A process must then be responsible for narrowing down the H tone to the end of the
43
word so as to create the high-low vs. rising-falling patterns (as in the Siane case in (12)).
The details of this process do not matter much for the present discussion, but one possibility
is to take advantage of the fact that voiced obstruents in Digo can be argued to carry an
L tone, as is common throughout Bantu (depressor consonants). If this is the case, and
given a late process making tones that precede the end of the word precede the final vowel,
the difference between the two final patterns can be ascribed to the difference between the
schematic forms (62) and (63).
(62)
H
... V C a %
(63)
H
... V C a %
L
Pushing the idea that motor planning can bear part of the explanatory load, here is a
simple account of this final pattern that follows from event timing. In (62) H must precede
/a/. This can be done with the H pronounced with a peak on the consonant, which will
mostly surface as rising-falling on the neighbouring vowels as in (58)[b]. But in (63) the H
cannot be simultaneous with the consonant, as this consonant must already be simultaneous
to a L tone, and it cannot be pronounced any later as it must precede the final -a, so it
is planned to peak earlier on the vowel, resulting in the high-low pattern of (58)[c]. This
analysis is obviously very speculative. Again this is a promisory note, with the hope that
phonetics can do part of the work for us without having to totally specify the linear order
of segments.
The evidence that this process is late is that the final patterns can actually surface on
a following noun in Verb-Noun VPs. A complete analysis of full VPs would take us too far
astray.
44
(64)
ku-onye?s-a? ?to show?
n-jira ?path?
ku-onyes-a n-j??ra? ?to show the way?
One thing worth appreciating here is that PROP allows such a thing as an analysis that
is temporarily vague about the ordering of its material. A root can be introduced with an
H between the beginning and the end, i.e. anywhere in the form, and remain incompletely
specified until other affixes are added, after which a late process will narrow down the H tone
to the end of the word (as opposed to having the whole form surfacing with a high tone as in
the Mende and Siane examples discussed above). In a sense PROP brings underspecification
to ordering. It is a theory in which order can be underlying underspecified. We will cover
many examples of this idea in future chapters.
Digo also has object prefixes. The plural object prefixes come with a H tone that also
surfaces at the end of the word. In the case of underlingly toneless words these forms surface
with the same tone pattern as verbs whose roots have an underlying H tone as shown in
(65) with a toneless root.
(65)
ku-vugurir-a ?to untie for?
ku-ni-vugurir-a ?to untie for me?
ku-ku-vugurir-a ?to untie for you s.g?
ku-mu-vugurir-a ?to untie for him/her?
ku-u-vugur??r-a? ?to untie for us?
ku-a-vugur??r-a? ?to untie for you pl.?
(66) Digo 1pl. object
# a (#? )
H %
45
The affix in (66) will attach to the root and also contribute an H tone parallel to the
whole verbal complex. At the point in the derivation after affixing the plural the stem looks
like (67)7, very similar to the forms with a root H pictured above.
(67)
a
# v u g u r i r %
a H
Interestingly, when this affix is added onto a root that does have an underlying H tone,
the result is as one would expect from a word with a single of either of these tones. For
instance the root puput has a high tone, as we can see in (68-a-d), since we saw in (65)
that these object prefixes do not contribute a tone, so these tones must come from the root.
But we also saw in (65) that the u- and a- object prefixes do contribute a tone, and yet the
surface tonal shape of the word is unchanged.
(68)
a. ku-pupu?t-a? ?to beat?
b. ku-ni-pupu?t-a? ?to beat me?
c. ku-ku-pupu?t-a? ?to beat you sg.?
d. ku-mu-pupu?t-a? ?to beat him/her?
e. ku-u-pupu?t-a? ?to beat us?
f. ku-a-pupu?t-a? ?to beat you pl./them?
A way we can conceive of what is going on for the sake of the discussion is that the tone
contributed by the prefix is ?redundant?: it will surface when it is alone in the form, but
when added onto a graph that already contains a H tone it will not add to it.
This follows from the way the object affix has been specified in (66) and from how H
7This assumes that the suffix -a is already there at this point in the derivation, which is both preferable
here for for illustration purposes and also argued to be the general Bantu structure by Hyman (2009), Inkelas
and Downing (2015), and multiple previous work by Downing. But the analysis presented here is not affected
if -a is inserted late in the derivation
46
?
roots are encoded in (59). The root puput is as in (69). Once affixed with the verbal
suffix and the object prefix, there is a step in the derivation where the form looks like (70).
In this picture, the H on top of the image is the one contributed by the root. The one at
the bottom is the one contributed by the object prefix. We can see that they run parallel to
each other, which given the assumptions so far implies pronouncing them at the same time.
Reasonably, since they are the excact same feature, for the segments that are parallel to
both this is identical to having a single H tone in the form, hence we derive that multiple H
tones would have a ?redundant? behavior. And since both H?s precede the end of the word,
they will be equally targeted by the late process narrowing down the H tone to the end of
the word.
?
(69) puput
H
# p u p u t %
?
(70) 2pl.obj+ puput+mood
H
a
# p u p u t %
a H
There are other sources of H tones in Digo verbs. An important one is subject prefixes,
which appear outside of the tense prefix.
(71) Digo indicative verbal template
Subj.-Tense-(Obj.)-Root-a
(72)
47
a. ni-na-tsukur-a ?I am taking?
b. ni-na-mu-tsukur-a ?I am taking him/her?
c. a-na-tsuku?r-a? ?he/she is taking?
d. a-na-mu-tsuku?r-a? ?he/she is taking him/her?
?
As we can see in (72), tsukur is a toneless root and the singular third person subject
prefix a- (as well as the third person plural ma- as we will see in (74)) carries a high tone
that is realized as the now familiar final pattern, just like the first and second plural person
prefixes u- and a-. We can therefore anticipate the underlying form of the third person
subject prefixes to contain a similar donating H tone. However an interesting behavior
arises when these new prefixes are added to a form that already has a H. Consider (73)
which completes the paradigm in (72).
(73)
e. ni-na-a-tsuku?r-a? ?I am taking them?
f. a-na-a?-tsu?ku?r-a? ?he/she is taking them?
(74)
a. ni-na-pupu?t-a? ?I am beating?
b. u-na-pupu?t-a? ?you sg. am beating?
c. a-na-pu?pu?t-a? ?he/she am beating?
d. tu-na-pupu?t-a? ?we are beating?
e. mu-na-pupu?t-a? ?you pl. are beating?
f. ma-na-pu?pu?t-a? ?they are beating?
The form in (73-f) shows that when both the subject prefix and the object prefix con-
tribute a tone, all vowels between the tense prefix and the final vowel surface as H. Similarly
?
we know from (68) that puput has an underlying H that surfaces without any of the tone-
bearing prefixes, but (74) shows that with one of the third person prefixes the form also
surfaces with all vowels between the tense prefix and the final vowel as H. Note that it also
48
hides part of the final pattern, the final rising-falling sequence has lost its rising part as the
rest of the form prior to it is now high.
The tense prefix ka- also behaves this way. (75) shows ka- on root we know to be toneless
from (72) and (73). (76) shows what happens when ka- is prefixed to a root bearing a high
tone.
(75)
ni-ka-tsuku?r-a? ?I have carried?
u-ka-tsuku?r-a? ?you sg. have carried?
(76)
ku-kumbuk??r-a? ?to remember?
ni-ka-ku?mbu?k??r-a? ?I have remembered?
u-ka-ku?mbu?k??r-a? ?you sg. have remembered?
This new tone is therefore clearly not ?redundant? in the way I labelled the behavior of the
tone of the object prefix. The tone of this new prefix, to the contrary, supplements whatever
tone the stem already carries. Let us call this tone ?supplementary?. We can characterize
the behavior of this class of prefixes with ?supplementary? tones with underlying forms like
the following.
(77) Digo 3rd.sg. subject
# a [#? ]
H %
[H]
This form only minimally differs from (66) in that it has an additional sticky end that
seeks H tones if there are any. The result of this is that for a stem without any H tone,
49
adding (77) will create the familiar pattern, but when added to a form that does contain a
H of any origin, this new H has to precede it.
Consider the derivation of forms with a H tone from the root and one from a subject
?
prefix as in (74)[c]. It starts with the root of puput as in (69) to which the tense and
subject prefix are added, resulting in (78).
?
(78) 3s.subj+present+ puput+mood
a H
n a H
# p u p u t %
a
The graph in (78) crucially differs from (70) in that now the two H tones are not parallel
anymore: the H introduced by the subject pronoun precedes the one from the root. As a
result one H does not directly precede the end of the word. If the process restricting the
pattern of tones to the end of the word is sensitive to this difference (e.g. targeting H that
only precede % and nothing else) it follows that this H will not surface as one of the two
final patterns, rising-falling or high-low, and it is expected that it will be realized on a
greater portion of the word.
Simiarly the derivation of (73)[f] will start with the toneless root in (79), to which we
add the 3p prefix as in (80), and the tense and subject prefixes as in (81). As in (78) we
have a form where one of the H tone precedes the other, and hence will not be affected by
the process restricting it to the end of the word.
?
(79) tsukur
# t s u k u r %
?
(80) 3p.- tsukur-a
50
a H
# t s u k u r %
a
?
(81) 3s-pres.-3p- tsukur-a
a H
n a
a H
# t s u k u r %
a
The only thing missing from (78) and (81) is something to restrict the non-final H to
after the tense prefix. This could be as simple as a phonological rule adding a precedence
link from the tense prefix to the H tones of the word. A plausible way to obtain this is
to assume that the object prefix is somewhat separated and in that the subject prefix, the
root and the mood suffix form a natural unit syntactic unit. There could then be a silent
morpheme added that the non-final H can target to add a precedence link. Kisseberth
(p.129) does argue in favor of such a unit which he calls the verbal complex. In any case
this would manifest itself here as a precedence link from the tense affix 9or something near
it) to the tone added at some point in the derivation. I will not dwell into this aspect of
the Digo tonology.
More interesting is the right-hand boundary of the ?supplementary? tone. Although the
forms in (73) and (74) suggest that the ?supplementary? tone extends over the whole verbal
complex, the data in (82) shows that it is more complicated than this. Crucially the tone
does not extend to the right of voiced obstruents. To see this in (82-b), recall that in forms
above like (74) the ?supplementary? tone spreads to the penultimate vowel and hides the
51
rising part of the rising-falling final pattern, which does not happen in (82).
(82)
a. a-na-gur??r-a? ?he/she is buying for?
a-na-a?-gur??r-a? ?he/she is buying for them?
a-na-demur??r-a? ?he/she is scolding?
a-na-a?-demur??r-a? ?he/she is scolding them?
b. a-ka-e?ze?k-a? ?he/she has thatched?
a-ka-we?ze?k-a? ?he/she has enabled?
a-ka-su?ru?b??k-a? ?he/she is strong/firm?
a-ka-u?-to?go?r-a? ?he/she has praised us?
There is a very natural way to describe what is going on here: the ?supplementary?
tone of the tense ka- and the subject prefixes a- and ma- must precede voiced obstruents.
The tricky part is that is that this seems to be true only when this tone is ?supplementing?
another, not when it is the only tone of the word. E.g. in (83) the tone causes the regular
final pattern despite it following a voiced obstruent.
(83)
ku-togor-a ?to praise?
ni-na-togor-a ?I am praising?
u-na-togor-a ?you sg. are praising?
a-na-togo?r-a? ?he/she is praising?
ma-na-togo?r-a? ?they are praising?
Given the assumption above that voiced obstruents have a L tone I propose that a
phonological process like (84) is responsible for this, which adds a precedence link from an
H to voiced obstruents if this H precedes another. Thus the form built in (85-a), similar to
the form in (78), undergoes this process to give (85-b), with its ?supplementary? H restricted
52
to precede /z/, or more accurately .
(84) If an H precedes an H, make the former also precede all L?s in the form.
a H
k a H
(85) a. L
# e z e k %
a
a H
k a H
b. L
# e z e k %
a
Consider now the exceptional behavior of some monosyllabic roots. Kisseberth notes
that unlike polysyllables for which there are two behaviors, captured so far by positing H
roots and underspecified roots, there are three behaviors for monosyllables, whose difference
is visible when comparing the infinitive to the extended form. There are monosyllabic roots
with the regular unspecified pattern as in (86-a), roots with the regular H tone pattern as
in (86-b), and roots that are low-toned in isolation, but show the H tone pattern when the
extension is present as in (86-c).
(86) Digo monosyllabic verbal roots
a. ku-rim-a ku-rimir-a ?to cultivate?/?to cultivate for?
b. ku-ne?n-a? ku-nen??ra? ?to speak?/?to speak for?
c. ku-tsun-a ku-tsun??ra? ?to skin?/?to skin for/with?
One way to deal with this is to treat these cases as an instance of tone donation as KiYaka
in the previous section, except here roots are donating. So while the regularly-behaving
monosyllable roots have the form in (87), the roots whose H tone only appears on suffixes
have a form like (88).
53
(87)
H
# n e n %
(88)
H
# t s u n %
These forms, once suffixed with the extension -ir and the verbal suffix -a will surface
with the expected final pattern
(89)
H
# t s u n %
i r a
But without an extension the form will end up looking like (90). Given the reasonable
assumption that H cannot be pronounced without being parallel to some vowel or consonant,
the tone of a form like (90) will not be able to surface phonetically, since H must follow /n/
but precede /a/.
(90)
H
# t s u n %
k u a
And this concludes the analysis of Digo verbal tonology. We see that given PROP
assumptions it is possible to make sense of complicated tone patterns like those of Digo.
The analysis involves root which may contain an H from # to % or not, as well as donator
prefixes. These donator prefixes are of one of two kinds, adding either a tone in parallel
54
to tones already in the form, or adding them preceding other tones, giving rise to the
?redundant? and ?supplementary? patterns of behavior.
We can only truly see the benefits of this analysis if we compare it to previous ones. We
will therefore turn to the analysis of Kisseberth (1984).
3.3.4 Digo in Kisseberth (1984)
Kisseberth already offered an analysis of Digo in Autosegmental Phonology. We will very
quickly go over it to highlight the differences from PROP.
First, Kisseberth assumes that all tones on verb come floating and he posits a High Tone
Deletion rule deleting one H tone in what he defines as the verbal complex, comprised of
the root and subject prefixes, when there are two H tones. This accounts for what I have
called the ?redundant? vs. ?supplementary? behaviors: this rule neutralizes all the cases
where there is only one H tone on the root, one H tone on the object prefix, or both. As a
result a H tone on an object prefix does not add anything when there is already one on the
root. All these three types of forms as well as forms with only one H tone from a subject
prefix all neutralize after High Tone Displacement which attaches the rightmost floating H
to the Rightmost tone-bearing vowel as exemplified in (92).
(91) High Tone Deletion (copied from Kisseberth 1984, p.130)
(92)
55
From these forms Kisseberth derives the two forms of the final pattern, which for a
reminder are High-Low when the final consonant is an obstruent and Rising-Falling oth-
erwise. Starting from the forms above, Kisseberth posits first that there are boundary L
tones around the verb as in (93-a). At this point in the derivation these L tones spread
inward to all toneless vowels, and to at least one even if it is already high, yielding (93-b).
Then there is a rule of Leftward High Spread which spreads H one vowel to the left as in
(93-c).
(93)
a.
L H L
C V C V C V
b.
L H L
C V C V C V
c.
L H L
C V C V C V
We now have in (93-c) a Rising-Falling pair of syllables. This derives the most common
form of the final pattern. As for forms with a voiced obstruents, Kisseberth posits a rule of
High Tone Doubling beforehand which adds a new H tone when a final High toned vowel
is preceded by a voiced obstruent as in (94-a) where B stands for any voiced obstruent.
Then the spreading of the L boundary tones yields (94-b), and finally a rule of Final Fall
Simplification delinks a H tone from a final HL syllable if this H is not also attached to
56
another vowel. This yields the High-Low version of the final pattern.
(94)
a.
L H H L
C V C V B V
b.
L H H L
C V C V B V
c.
L H H L
=
C V C V B V
And finally the blocking effect of voiced obstruents when a second H tone spreads is
attributed to a Low Tone Insertion rule that gives a L tone to voiced obstruent, thus
blocking the spread.
This is a very straightforward and interesting analysis. There is however one thing to
note with which the PROP analysis I offered contrasts: all of Kisseberth?s rules above need
to apply only to verbs. Nouns do not undergo tone displacement or spread in the same
way. Kisseberth needs a theory in which phonological rules can be indexed for the syntactic
environment in which they take place, and directly refer to morphosyntactic structure like
the High Tone Deletion rule which refers to the verbal complex. This is obviously a problem
if the goal is a modular theory of phonology.
PROP in contrast manages to encapsulate all this to the phonology by putting all the
information distinguishing the behavior of different tones within the vocabulary items. This
is an indispensable quality if one believes in a fully modular theory in which the phonology
cannot reference the syntax.
This is made possible in PROP because of the increased representational freedom. There
57
are more ways to put information into the representation and as such it is possible to
attrubute the behaviors observed not to the syntactic context but the lexical items involved.
3.4 Summing up
The analyses in this paper brought us to recast a number of basic patterns and discover
a number of principles. The account of parallel features developed here re-conceptualizes
vowel harmony as a representational phenomenon involving features whose lexical entries
make them span multiple segments. We also now have the simple but powerfully general
nesting principle according to which competition among segments with incompatible fea-
tures will be won by the ?inner? one, which we saw at work as an explanation of both trans-
parent and opaque segments, and which we can hope to derive from more basic principles
of motor planning organization. We have a superior understanding of donator morphemes
now that the representation allows features to be simultaneously independent and ordered
with regard to each others, while autosegmental phonology allows only one or the other.
And finally we have a novel understanding of Bantu depressor consonants that carry low
tones and of how they may effect the phenomena we observe.
The suggestion of treating suprasegmental material as phonological material that is
simultaneous to the segmental material is suprisingly classical. It was the motivation for
Hockett?s 1954 coining of the term simulfix to convey the relation of intonational contours
to segmental material. And even before that Harris (1944) suggested to account for various
phenomena of phonology by breaking traditional segments and phonemes into simultaneous
components.
We will return to more tone phenomena as we discuss the interaction of parallel struc-
tures with reduplication in chapter 7.
3.5 PROP compared to its alternatives
It would be worthwhile to contrast the PROP analysis of long-distance phonological phe-
nomena developped in this chapter with its two main contenders: Autosegmental phonology
and Search-and-Copy. We have already seen a bit of the first comparison above in section
58
3.3.4 with regard to Kisseberth?s analysis of Digo, but more generally there are more con-
strasts to be made between PROP and its competitors.
In Autosegmental Phonology (Leben (1973), Goldsmith (1976)) vowel harmony and
tonal phenomena require an operation of spreading as in (95), which actively spreads the
association of a feature onto other segments. In a search-and-copy, vowel harmony requires
actively copying features from one segment to another as in the procedure taken from Nevins
(2010) in (96). Both of these analyses have some things in common.
(95)
(96) Harmonic Search-and-Copy procedure, in two steps: (? , ?, F)
a. Find: x = the closest ? to the recipient y in the direction ?
b. Copy: the value of F on x onto y, where x, y are segments, F is a feature, ? is
a predicate over segments.
First they treat both harmony and tone spreading as the outcome of a process. Lan-
guages must have a rule causing segments to either spread or copy features at a distance.
In contrast the PROP analysis in terms of parallelism presented here is representational
and passive. PROP attributes harmony to the representation and therefore to the static
details of vocabulary items and how they arrange themselves in word-formation. This is
interesting as it means that PROP maximizes the use of representation in the explanation,
as opposed to the existing approaches in terms of processes.
A second, more important difference is that PROP is unique in deriving harmony and
tone spreading directly from the fundamental elements of phonology. In PROP, there is
no extra stipulation granting to phonology the power to spread or copy features; here it
is a direct and unavoidable fact of phonology that the representation is free enough to
allow them. In Autosegmental Phonology and Search-and-copy, one can ask why it is that
phonology allows long-distance spreading or copying in the first place. It is a mystery why
phonology allows those things. Those possiblities feel tacked onto a system that could easily
exist without allowing long-distance phenomena. But in PROP, harmony derives from the
59
most basic ingredients of phonology: features and precedence left free to be organized in
any way. In PROP, forbidding vowel harmony would require extra stipulations, and not the
other way around. This, I think, is the most interesting aspect of PROP for harmony and
word tone.
It is worth noting at this point that there is a precedent in trying to incorporate Search-
and-copy with a Multiprecedence representation in the dissertation of David Shen (Shen,
2016). Unfortunately Shen does not discuss in depth how the complex structures of Mul-
tiprecedence would interact with Search-and-Copy. The thesis uses Search-and-copy to
handle sticky ends such that they can start from the edge of a stem and search left or right
for their attachment point, and then it discusses Search-and-copy vowel harmony without
any further reference to the representation. Multiprecedence and harmony are disconnected
topics of the dissertation with no overlap. Shen does not discuss the interesting issues that
would arise when using Search-and-Copy for vowel harmony in a Multiprecedence context,
e.g. search going in one direction and encountering a branching, or search being stuck in a
loop, or search starting from one segment, going along a loop, and finding itself. There is
therefore little to compare between Shen?s multiprecedence-friendly approach to harmony
and PROP beyond what I already said about Search-and-Copy in general.
60
Chapter 4
Affix position and Reduplicative size
Although not the primary focus of Raimy (2000), the multiprecedence proposal shows that
Multiprecedence can account for infixation in a satisfactory way.
The new representations proposed [...] have major implications for the under-
standing of what the phonological aspects of morphemes are and how morphemes
are concatenated. The notions of root, prefix, suffix, infix, etc. can be directly
encoded in the phonological material that is associated with a morpho-syntactic
feature. (Raimy, 2000, p.66)
The sticky-end, as an apparatus designed to select an attachment point, is ideally suited
to encode information about the precise locus of attachment of a morpheme, including within
a stem. The analysis captures two important theoretical goals. First the notion that there
are genuine infixes in the sense of Blevins (1999) and Yu (2003), meaning they are not
derived from inherent prefixes or suffixes and displaced by the phonology, and second the
notion that infixes are just a regular type of affix, without any special processes of their own.
In Multiprecedence an infix is like any other affix, except its sticky-ends happen to target
other things than the edges of the word. For example the Atayal Animate Actor focus in
(1) can be represented with the following infix attaching between the initial segment and
61
the segment following the initial segment.
(1) Atayal Animate Actor Focus (from Yu 2007, p.75)
root AAF gloss
qul qmul ?snatch?
kat kmat ?bite?
hNuP hmNuP ?soack?
(2) Atayal Animate Actor focus infix
[ ]
[#? ] m [#? ]?
PROP inherits all of those insights of Multiprecedence, but with even more freedom to
analyse other phenomena relating to the position and size of affixes, which we will cover in
this chapter.
4.1 Affix position in Tamazight Berber
Svenonius and Bye (2011, p.40) describe the data of Tamazight Berber in (3). While most
singular and gender agreement markers are prefixes, the first singular is a a suffix /-G/, and
while most plural agreement markers are suffixes, the first plural is a prefix /n-/.
(3)
Sg. Pl
1 Qum-G n-Qum ?I swam?; ?we swam?
3m i-Qum Qum-n ?he swam?; ?they swam?.
This is a problem for most models of morphology in which the linear order of morphemes
is decided prior to vocabulary insertion, and hence a consistent order among morphemes of
the same paradigm is expected. But this is unremarkable in PROP, because linear order
is not presumed to be fixed prior to vocabulary insertion, rather it is the underlying form
62
of the vocabulary item that encodes its position in the form of sticky-ends, morpheme by
morpheme. The four affixes in (3) are simply the following:
(4) 1.sg. affix
[ ? %] G %
(5) 3m.sg. affix
# i [#? ]
(6) 1.pl. affix
# n [#? ]
(7) 3m.pl affix
[ ? %] n %
In this respect the PROP analysis is in the spirit of the analysis of Svenonius and Bye
(2011). They also interpret this pattern with information within the UR, hence it would be
useful to compare the aspects of Svenonius and Bye?s proposal to PROP.
Their core proposal is a novel phonological machinery they call antitropal affixes. They
posit a new phonological symbol  that seeks non-alignment with a boundary, coupled with
a constraint Ident[antitropal] that penalizes morphemes aligned with said boundary. They
propose the following vocabulary items and constraint ranking for Berber,
(8) Tamazight 3m.sg. agreement (Svenonius and Bye, 2011)
i ]? < v, ? >
(9) Tamazight 1pl agreement (Svenonius and Bye, 2011)
n ]? < v, ?, Participant,Author, P l >
(10) n-Qum ?we swam (Svenonius and Bye, 2011)
63
Antitropality is more generally the core of Svenonius and Bye?s theory of morpheme
placement. It can lead to morepheme position reversal in Berber, but with Contiguity
lower ranked it also leads to infixation. In Svenonius and Bye?s system therefore there
are two forces involved in morpheme order: the order given by the syntax, and the order
emerging from the ranking of Antitropal with regard to other constraints for morphemes
containing .
While I agree with the move of putting affix order in the UR, it goes without saying that
the redundancy of Svenonius and Bye?s system can easily be avoided by rejecting that any
order is imposed by the syntax. If URs can contain information pertaining to their position,
we might as well go all the way and let that be the only determinant of position. This is
accomplished in PROP with the use of sticky-ends as the only machinery responsible for
ordering the segments of a morpheme with regard to another1.
It is interesting that  is defined negatively as non-alignment. Presumably the reason-
ing is to have a mechanism that does the minimum they need, namely only ban complete
prefixhood or complete suffixhood, to let the position be otherwise derived from the con-
1A consequence of this is that there is no principle of the grammar in PROP enforcing paradigmatic
uniformity in affix order. If a language has e.g. multiple case suffixes, it must be individually specified for
every case affix that it is a suffix and there is nothing in the grammar preventing a language from having
a mix of prefixes, suffixes, and infixes as case markers. I do not see it as a major problem for two reasons.
First there are cases of non-uniformity in affix order across paradigms. We saw the Tamazight Berber person
affixes in which the. Other examples abound. In the system of class affixes of Tiv, most classes are marked
with prefixes, except two that are marked with suffixes and three with circumfixes (Welmers, 2018, p.205-
207). De Wolf (2017, p.180) lists six other Benue-Congo languages with a mix of prefixes and suffixes in
their class marker system: Kom, Mam, Ukel, Duk, Dak, and Kag. Another example is the person markers
of multiple Muskogean languages in which the first person agent market is a prefix but all other persons
are suffixes; Cysouw (2003, p.11) lists Chickasaw, Alabama, Koasati, and Choctaw as having this pattern.
Cysouw also lists two Tequistlatequan languages with the same pattern of first person prefixes and suffixes
for other persons: Highland Chontal and Huameltultec. Yet another example is from Kilmeri in Foley (2017,
p.394) in which the modality system is mostly comprised of suffixes except for one prefix and one circumfix.
Given that the possibility of non-uniform affix order must definitely be allowed in the grammar, i see no
reason to try to make affix ordering uniformity a deep property of grammar. The tendency toward uniformity
may simply boil down to diachrony (e.g. the similar historical origin of similar affixes).
64
straint ranking, a natural OT move. However cross-linguistic surveys of infixation such as
Yu (2003) have showed that Prosodic Optimization does not account well for the data of
infixation, and it is more fruitfully analyzed in terms of affixes seeking a specific pivot in
the word. With this in mind we could easily modify Svenonius and Bye?s proposal by in-
venting a new symbol, say ?, which positively seeks a certain attachment point. Infixation
in Atayal described in the previous section could be handled as (11) where the affix seeks
contiguity with a certain consonant, and infixation in Tagalog described in chapter 2 could
be handled as (12) where the affix seeks contiguity with a vowel.
(11) Positively-defined Atayal Animate Actor Focus infix inspired by Svenonius and Bye
(2011)
/m ? C2/
(12) Positively-defined Tagalog um-infixation inspired by Svenonius and Bye (2011)
/um ? V1/
And with such a machinery needed for infixes, we also get prefixation and suffixation for
free:
(13) Positively-defined prefix un- inspired by Svenonius and Bye (2011)
/2n ? X1/
(14) Positively-defined suffix -able inspired by Svenonius and Bye (2011)
/Xlast ?@bl/
At this point it is obvious that we have essentially re-invented the sticky-end mechanism
through a different notation, by re-imagining the system of Svenonius and Bye (2011) stated
positively. The sticky-end-centric approach to affix position suggested here is not radical,
it simply involves taking ideas that are already around and pushing them to their logical
limit. In a sense, we can even compare the sticky-end system to the informal descriptive
notation of affixes with hyphens: at its core [#? ] is merely a formalization of the hyphen
in a prefix notated as /2n-/.
65
This should be interesting to all. With this kind of machinery one can offer accounts
in the lines of Svenonius and Bye (2011) without having to postulate a syntax-given order
at all. If a machinery is powerful enough to place a morpheme after the first segment?, it
shouldn?t be very difficult for it to place one before the first segment. Once we have accepted
that the UR of a vocabulary item can contribute to its position, which seems to be needed
for infixes according to Svenonius and Bye (2011), postulating a pre-vocabulary-insertion
order is redundant.
Using sticky-ends in the phonology is a matter of taking seriously the idea that mor-
phemes have phonologically-defined requirements as to their position and operationalizing
it. Svenonius and Bye (2011) did so to a degree with , and in this chapter we will discuss
how to go even further with sticky-ends.
4.2 Circumfixation in Georgian and Amatlan Zapotec
One peculiarity of affixation in PROP is the capacity to represent circumfixes qua circum-
fixes. The notion of circumfixes has long been challenged, in part because it does not fit
with the so-called concatenative ideal in the sense of Svenonius and Bye (2011), but some
strong cases of circumfixation whose two parts do not occur independently are mentioned in
Hall (2000, p.542): the Georgian comparative/superlative u-...-esi, e.g. lamazi, ?beautiful?,
u-lamaz-esi ?more/most beautiful?, and the Amatlan Zapotec negative na-...-t, e.g. top ?to
gather?, na-top-t ?to not gather?. These can be respectively handled in PROP with the
following affixes:
(15) Georgian comparative/superlative affix2
# u [#? ]
[ ? %] e s i %
2Note that this affix and the following one form a disconnected graph. PROP needs not make any
assumption about the connectiveness of URs.
66
(16) Amatlan Zapotec negative affix
# n a [#? ]
[ ? %] t %
Models of word-formation in which morpheme order is settled prior to vocabulary-
insertion struggle with circumfixes, as they have to assume that every affix is inherently a
prefix or a suffix. This has led to analyses in which circumfixes do not exist and all apparent
cases involve two morphemes, a prefix and a suffix independently found in the language (e.g.
Corbin 1987), but as argued e.g. by Anderson (2015) this is less convincing for cases like the
above where the initial and final part are not affixes independently found in the language,
raising the question of how the grammar conspires to force them to coocur. By dissociating
affix position from insersion PROP has no such limitation and does not need to make ad
hoc assumptions about attested word-formation processes that look like circumfixation.
This is possible in PROP because there is no requirement for a directed graph to be
connected. Here I have postulated disconnected graphs as the underlying forms of the
circumfixes of Georgian and Amatlan Zapotec. Disconnected graphs also readily account
for affixes comprised of an infixed part and either a suffixed or prefixed part (sometimes
called transfixes, parafixes, or polyaffixes) attested e.g. in Blevins? 1999 account of Leti.
This is yet another possibility that follows freely from the geometric possibilities of PROP
that would take extra stipulations to forbid from the theory.
4.3 Variable-position affixes in Afar
Fulmer (1997) discusses the variable position affixes in Afar. A number of Afar verbal affixes
can surface either as a prefix or as a suffix to the root depending on whether the root is
vowel- or consonant-initial. Words starting in a- behave as consonant-initial. The suffixes
67
-e? amd -a? are aspect markers3.
(17) Afar conjugation examples
1s 2s 3sf
ab-e? do ab-t-e? do ab-t-e? do
kal-e? prevent kal-t-e? prevent kal-t-e? prevent
robaaq-e? bounce(tr.) sug-t-e? had sug-t-e? had
ekk-e? become t-ekk-e? become t-ekk-e? do
ookom-e? win t-ookom-e? win t-ookom-e? win
3sm 1p
ab-e? do ab-n-e? do
be-e? take giin-n-e? pull
kallax-e? beg fan-n-e? want
y-erd-e? run n-ekk-e? become
y-oogoq-e? bury n-ookom-e? win
2p 3p
ab-t-e?-n?? do ab-a?-na? they did
mak-t-e?-n?? turn sool-e?-n?? stand
nak-t-e?-n?? drink milk nak-e?-n?? drink milk
t-ekk-e?-n?? become y-okm-e?-n?? eat
t-ookom-e?-n?? win y-ookom-e?-n?? win
In short, Afar has a 2nd person /t/, a (homophonous) 3rd feminine /t/, a 3rd masculine
/j/, and a plural /n/ (I will ignore the vowel, as it seems to be epenthetic and agree with
the preceding one and could be inserted later in the derivation). The immediately obvious
generalization of their location is that they are prefixed to vowel-initial roots and suffixed
consonant-initial (and [a]-initial) roots, with two caveats: i) /n/ gets ?second choice?, and
3Unfortunately although Fulner provides a lot of examples, because she is working with data from other
source she provides no complete paradigm that would allow for convenient comparison across the same verbs
in a single table, hence the format in multiple lists of representative examples summarizing the 14 lists in
Fulmer (1997, p.137-146)
68
if the initial position is occupied by one of the other affixes it behaves as if affixed to a
C-initial root, and ii) /j/ does not surface when one would expect it to be suffixed.
A less obvious detail is that there are two positions for post-posed affixes: one between
the root and the aspect marker, and one after the aspect marker. The generalization being
that /n/ occupies the latter position only when another marker is present (either prefixed
or in the earlier suffix-side position between the root and the aspect marker).
This can be accounted for in PROP as a parafix in the sense of chapter 3, this time
a parafix containing all the features of the relevant segment, except a +consonant feature
(which for brevity I will notate /t?C/). a full segment. I will assume that such a segment
cannot surface unless it is parallel to some +consonantal feature, an assumption reminiscent
of the autosegmental notion that floating segments un-associated to a CV tier do not surface.
This segment can only surface simultaneously to another segment with which it does not
conflict.
Combined with the plausible assumption that the V-initial forms, as well as the -e? suffix
start with (the PROP equivalent of) an empty C-slot, we can derive the first generalization
above from the structures involved. The 2s affix will be a parafix as in (18).
(18) Afar 2s affix
# t?C %
When added to a consonant-initial form as in (19), the only location where the /t/ can
surface is with the {C} of the aspect suffix /Ce?/ with which it does not conflict in any
feature. However when added to a V-initial form as in (20) there is also a {C} location at
the beginning of the form.
(19) kal-t-e?
t?C
# k a l %
C e?
69
(20) t-ekk-e?
t?C
# C e k k %
C e
This cannot be the full story, as something needs to be responsible for forcing /t/ into
the first {C} of rather than the second or both. Potentially it is simply a matter of positing
a phonological rule to the effect that /t/ precedes all {C}?s that are transitively preceded
by another {C}; alternatively some phonetic principle, universal or language-specific, forces
this graph to be realized such that /t/ is ?discharged? as early in the form as it can be.
Since the above is sufficient to handle the contrastive possibilities of Afar I contend that
the exact issue of the realization of these graphs is not an issue of PROP, but of phonetic
implementation.
The behavior of the plural /n/ is more complex. The first plural forms show that, like
/t/, /n/ can occupy either or both of these {C} positions when there is no other affix to
take it first, and the position of /t/ in the C-intial second plural shows that this second {C}
position is present in these forms, yet in V-initial second plurals the /n/ does not occupy
the seemingly free second position, occupying a third position after the aspect marker. This
can be accomplished if /n/ is set in parallel to the whole form just like /t/, but must also
be ordered with regard to /t/ or /j/, or ordered with regard to something ordered with
regard to /t/ or /j/.
(21) Afar plural
# n?C %
[ [[ ] ]]
? ?C ?
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This new sticky-end seeks a segment with the property of following a segment with the
property of preceding a segment with the property of being unspecified for Consonant4.
When attached to a form without another affix it will behave as in (22), namely just like
/t/ in (20). But when there is another affix, it will also follow anything that precedes
anything that follow that affix. In (23), since the only thing that follows /t/ is %, /n/ will
follow everything that precedes %, in this case /k/, /e?/, as well as /t/ itself, hence it will
surface as a suffix. If the epenthesis applies at this point whenever /n/ has not found a
{C}, we derive the correct form.
(22) n-ekk-e?
n?C
# C e k k %
C e
(23) t-ekk-e?-ni?
t?C n?C
# C e k k %
C e
There are some exceptions to this pattern: vowel-initial words that behave as consonant-
initial and take the suffixed forms, e.g. in-?t-e ?say-you-perfective? and iman-s-it-t-aa-?na
?believe-causative-benefactive-you-imperfect-plural? (Marus?ic?, 2003, p.6). These
forms as well as the /a/ forms have been argued to be a counterargument against the
tempting analysis of this pattern in terms of syllable optimization, with the forms appear-
ing as prefixes whenever doing so gives an onset to an otherwise onsetless syllable (Paster,
2009b,a). I agree with this assessment; there is no optimization in the PROP analysis
4Sensitivity to underspecification is a strong mechanics, but it is inessential to the analysis here and only
used for convenience. Anything that can identify the conjugation affixes will do, be it a lexical diacritic or
something else.
71
above. And as for the exceptional vowel-initial behaving as consonant-initial, these forms
can simply be stored without the initial empty-C; it is a fact one has to know about a form
in order to speak Afar. This would also account for /a/-initial forms
4.4 Unpredictable Infixation
This kind of arbitrariness is also found in various Siouan languages in which verbs unpre-
dictably take prefixes or infixes. Albright (2000) observes that in Lakhota, ?the position of
subject marking is to a certain extent unpredictable, and must be listed on a verb-by-verb
basis?. Conside the examples of the first person (-)wa- in (24).
(24)
3rd person 1st person gloss
lo?wan wa-lo?wan ?sing?
nu?we wa-nu?we ?swim?
ka?ge wa- ka?ge ?do/make?
u?npa wa-?u?npa ?lie down?
o?ta wa-o?ta ?be many?
ma?ni ma?-wa-ni ?walk?
aphe? a-wa?-phe ?hit?
hoxpe? ho-wa?-xpe ?cough?
ixa? i-wa?-xa ?smile?
o?mna o?-wa-mna ?smell?
As discussed by Rankin et al. (2003); Helmbrecht and Lehmann (2008a) there is a
diachronic generalization here, namely the infixing behavior come from reanalysis of pre-
fix+verb sequences as unanalysable roots, trapping some previous prefixes and forcing them
to be reanalyzed a prefixes, a common diachronic scenario in the evolution of infixes ac-
cording to Yu (2003, ch.4). But synchronically these are unpredictable and Albright argues
that infixing can apply to novel forms.
72
As argued for the related Siouan language Hoc?ek in Helmbrecht and Lehmann (2008b)
these affixes challenge our theories of infixation, which hold that the location of infixes is
phonologically defined. It was one of the main findings of Yu (2003) that all infixation could
be accounted for as set right before or right after a specific phonologically-defined position
in the stem such as ?first segment?, or ?stressed vowel?.
Something has got to give, and somehow this arbitrariness must be handled somewhere.
One solution would be to propose massive homophony between a prefix and one or more
infixes, each specified both for a phonologically-defined position and for the set of roots to
which it applies. The alternative ?simpler in my opinion? is to accept that the phonological
form of these roots contain some arbitrary diacritic which lacks a phonetic correlate but is
of the phonological type and can serve as a target for the location of affixes.
This can be done in PROP by assigning each verb a feature on one of its segments as
in (25), this feature will be the target of the infix in (26), placing itself between the [F]
73
segment and the segment preceding it, as in (27)
? ?
(25) nuwe, mani
# nF u w e %
# m a nF i %
(26) Lakhota 1st person affix
[ ? [+F ]] w a [+F]
(27) wa-nume, ma-wa-ni
w a
# nF u w e %
w a
# m a nF i %
The nature of feature F here is inessential to the analysis as long as such a feature
without direct phonetic correlate can be present in underlying forms and can be targeted
by sticky-ends. All analyses of this pattern will have to resort to positing some difference
between the URs of prefixing and suffixing affixes, or a morphological module containing a
list of all prefixing and suffixing forms. PROP allows us to have an analysis of the former
type without a special morphological module, in which a single form of the affix accounts
for both the prefixing and infixing behavior.
4.5 Free variation of reduplicant location in Tagalog
Ryan (2010) describes the case of the Tagalog Contemplated aspect, which surfaces as CV-
reduplication. In verbs with some sequences of one or more prefixes, it is claimed that the
74
reduplicant can freely vary in location. Ryan claims that Tagalog researchers are unanimous
that this does not lead to semantic differences, and that native speakers produce all the
different variants in speech (p.762). This cannot be a case of different syntactic orders
with vacuous scope difference, because Ryan points out that in both examples below the
Contemplated aspect scopes over the causative (p.763).
(28)
pa?:-pa-buks-a?n ?red-caus-open-LocativeTopic?
pa-bu?:-buks-a?n ?caus-red-open-LocativeTopic?
This can be accounted for in PROP if we assume the following: a sticky-end can inten-
sionally describes a property that describes multiple segments of the stem it attaches to,
but be specified to attach to a single one of them. I will represent this with a superscript
U on the sticky-end. This can create ambiguity in attachment point, leading to this type
of free variation. The Contemplated Aspect would have the underlying form in (29). The
leftmost sticky-end seeks something that follow an initial segment and connects it to an
initial segment.
(29) Tagalog Contemplated Aspect (preliminary version)
[[#? ]? ]U [#? ]U
The result is that when attached onto a prefixed form like (30)5, these sticky-ends have
more than one initial segment to choose from, resulting in the two possible structures (31)
and (32).
(30)
p a a n
# b u k s %
5Ryan (2010) confirms that the aspect scopes over the causative(p.763).
75
(31) pa-bu:-buks-an
p a a n
# b u k s %
(32) pa:-pa-buks-an
p a a n
# b u k s %
However this is insufficient. There are two segments that follow # and two segments
following a segment that follow #, thus 4 possibilities. The following two graphs should be
available if (35) is the actual form of the contemplated, because its two sticky ends can vary
independently, yielding also the two graphs (33) with reduplication of both prefixes which
is not cited as a grammatical alternative and (34) with a vacuous ?forward? link leading to
no pronounciation change, which is not cited as able to carry Contempated reading.
(33) *pabu:-pa-buks-an
p a a n
# b u k s %
(34) pa-buks-an (* with the intended Contemplated reading)
p a a n
# b u k s %
The essence of the problem here is that the sticky-ends as stated in (35) are independent,
but need to be have a stated dependency: the sticky-end [[# ? ] ? ]U cannot attach
to just any segment following a segment that follows #, it must specifically attach to a
segment of the stem that immediately follows the sticky-end [#? ]U .
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I propose to accomplish this with features on the sticky-end itself that can be referenced
by other sticky-ends. In (35) the sticky-end [# ? ]U finds a single segment following #
and assigns it [F], and the sticky end [[F ] ? ]U finds the segment preceding [F] so that
the morpheme as a whole adds a precedence link between the segment that follows [F] and
segment [F]. This affix will only generate the forms (31) and (32) above.
(35) Tagalog Contemplated Aspect (final version)
[[F ]? ]U [#? ]UF
This capacity to add features via sticky-ends can be employed with regular features to
derive cases in which morphemes affect the segments they attach to. For instance
4.6 Reduplicant size in Malagasy
Reduplication of variable size is attested in various languages. For instance Keenan and
Polinsky (1998) and Hannahs (2004) describe the facts of Malagasy in which, for forms with
ultimate or penultimate stress, the attenuative is formed by reduplication of the segments
from the stressed syllable to the end of the word as in (36). This simply requires an affix
as in (37) where [*] stands for a stressed segment. (37) adds a link from the last segment
to the segment before the stressed vowel.
(36)
le?hibe? ?big? le?hibe?-be? ?fairly big?
had??no ?forget? had??no-d??no ?forget a bit?
(37) Malagasy Attenuative (Penultimate or Antepunultimate stress)
[ ]
[ ? %] ? [?]
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The situation is a bit more complex in the case of forms with antepuenultimate stress as
in (38). Descriptively, C-initial forms appear as CVCV reduplication in which the second
copy has a ?fortified? initial consonant; while V-initial forms appear as VCVC reduplication.
(38)
fa?ntatra ?known? fa?ntapa?ntatra ?slightly known?
va?rotra ?selling? va?roba?rotra ?sort of selling?
a?loka ?shade? a?loka?loka ?somewhat shady?
e?votra ?bouncing back? e?votre?votra ?sort of bouncing back?
Although neither Keenan and Polinsky (1998) nor Hannahs (2004) see it this way,
this can be straightforwardly analyzed as CVCVC reduplication from the stressed sylla-
bles, followed by fortification of post-consonantal consonants, followed by deletion of pre-
consonantal consonants.
(39)
fa?ntatra e?votra
fantatr-fantatra evotr-evotra
fantatr-pantatra ????
fanta-pantatra ????
fantapantatra evotrevotra
This can be handled with the feature mechanics of the previous section that allows for
one sticky-end to be positioned relative to another. In (40) the rightmost sticky-end seeks a
stressed vowel, and the leftmost one will attach for segments away from it6. As follows from
the discussion in chapter 2, the lefmost sticky end refer to the property ofbeing a consonant
that follows a chain of preceding five nodes, the first of which contains F, the second of
6The sticky-end in (40) could be simplified with reference to syllables or feet. We will not discuss this
here.
78
which V, the third of which C, and so on.
(40) Malagasy Attenuative (with antepunultimate stress)
[ ] [ ]
[F ]? [V ]? [C]? [V ]? [C] ? [?]
F
The affix in (40) accounts for the reduplication of forms with antepenultimate stress
while the forms in (37) accounted for the penultimate and ultimate stress forms. Combining
the two will have to wait for chapter 5.
4.7 Unpredictable Reduplicant size in Woleaian
Paster (2006, p.131-132) cites data from Woleaian taken from Kennedy (2002). In Woleaian
the location of denotative marker is unpredictable: it is either reduplication of the final two
syllables or gemination of the initial consonant.
(41)
feragi ?spread? f feragi ?to be spread?
Nu?su?-ri ?snort it? NNu?su?-ri ?to snort?
pilegu?-w ?bundle it? ppilegu?-w ?to be bundled?
Bugo-si ?tie it? Bugo-Bugo ?to tie?
faNoso ?current? faNoso-Noso ?to have a little current?
file-ti ?stir it? file-file ?to stir?
Given that this is unpredictable, a solution similar to that used for Lakhota in (25) and
(26) must be used. Roots can come in two forms as in (42), which the affix in (43) will
reduplicate appropriately by always adding a path from segment [F] to segment [G] as in
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(44).
? ?
(42) feragi, faNoso
# fF,G e r a g i %
# f a NG o s oF %
(43) Woleaian denotative affix
[F] [G]
(44) fferagi, faNoso-Noso
# fF,G e r a g i %
# f a NG o s oF %
Multiple languages similarly have reduplication of unpredictable size and in unpre-
dictable locations. For example Rubino (2005) describes the plural formation in Pangasinan
in which the size of the reduplicant in unpredictable.
sg. pl. gloss
CV- too toto?to ?man?/?people?
-CV- am??go amim??go ?friend(s)?
CVC- ba?ley balba?ley ?town(s)?
CVCV- manok manomanok ?chicken(s)?
Ce- dueg derewendg ?water buffalo(es)?
Another example is from Akuntsu?. Aragon (2014) describes reduplication in this lan-
80
guage, which marks plurality in nouns and iterativity in verbs.
(45)
base form pl/iterative gloss
bawRo ba-bawRo ?woodpecker?/?many poodpeckers?
a?bi a?bi-bi ?to pull?/?to pull successively?
pi pi-pi ?foot?/?feet?
tSokin tSokin-in ?small?/?very small?
kop kop-kop ?ripe?/?very ripe?
kapa kapa-kapa ?to roll?/?to roll repeatedly?
We therefore have a number of examples of patterns where arbitrary information about
affixes needs to be stored somewhere and I propose that if this is done with diacritics then
PROP can easily account for everything. We will see more interesting examples of how this
interacts with core PROP principles in future chapters.
4.8 Conclusion
I showed in this chapter that PROP and the sticky-end mechanics are capable of han-
dling interesting cases of affixes with variable positions and reduplication with variable size.
Accounting for cases in which this position or size is phonologically predictable is straight-
forward and simply requires to cleverly design the underlying form of the affixes. Cases
that are not predictable require the root to carry some cover information that sticky-ends
can utilize to attach properly. Something like this is unavoidable: the information of which
forms behave in a certain way has to be somewhere, either in the underlying forms as I
propose here, or elsewhere in the grammar such as listed in an vocabulary insertion rule.
The solution defended here to put things within the underlying form has several ad-
vantages. It dispenses with the complexity involved in assuming a morphological module
capable storing lists of roots. It also concentrates the locus of morpheme-specific informa-
tion to the underlying form.
The mechanics of affix position here does allow for some amount of phonologically con-
81
ditioned affix position. This might be worrisome in light of Paster (2009b), who argues
against the existence of phonologically-conditioned affix position. But her argument is fo-
cused on opposing across-the-board re-orderings of the type predicted by Optimal-Theoretic
constraint orders in which phonological markedness constraints ranked above morpholog-
ical constraints (PM) drive re-orderings that resolve phonological markedness. Those
would also be hard to state in PROP. Paster (2009b) however does admit variable affix
position in the case of allomorphy, and in agreement with this assessment some machinery
and geometry to be devised for allomorphy in chapter 5 would be needed for most cases
of phonologically-conditioned affix order going beyond the complexity discussed in this sec-
tion, and we will therefore come back to this topic. It is worth noting that Paster (2009b)
explicitly admits one analysis using an accidentally homophonous pair of prefix and suffix
to account for the case of Afar discussed above in 4.3, so perhaps, if we hope to avoid this
type of redundancy, we need to admit a bit more phonologically-conditioned allomorphy
than she does, albeit more restrained than predicted by PM OT rankings.
We will come back to these issues as we explore additional capacities that PROP allows
us to handle representationally.
82
Chapter 5
Phonologically-Conditioned Allomorphy
Another set of phenomena that seems like it could be appropriately handled by the increased
representational power of PROP is allomorphy, particularly of the suppletive kind. This
chapter witll cover Phonologically-Conditioned Allomorphy (PCA) and the next one will
cover Lexically-/Morphologically-conditioned Alomorphy.
The terminology of allomorphy varies by traditions and in this chapter I will use the
term in a mostly descriptive sense to cover any changes between instances of a single mor-
pheme in the line of Hockett (1954), but restricted to the type that isn?t attributable to
regular phonological processes. Allomorphy of the regular type that can be attributed to
phonological rules will be covered in chapter 9. We will come back to terminology in 5.4
once the range of phenomena I propose to attribute to PROP is on the table.
5.1 Background: representing alternatives
There is a long tradition in Phonology of analyzing patterns of allomorphy in terms of one
underlying forms and some phonological processes. In a way that is the very impetus of
phonological analysis notably since Jakobson (1948) and Chomsky and Halle (1968): coming
up with a single underlying form per set of allomorphs and phonological rules applying to
them that produce the surface variants. Phonological analysis is in a way the process of
explaining morpheme alternations not in terms of morphology per se, but through a mix of
clever underlying forms and regular phonological processes.
New developments in phonological representation and machinery are often accompanied
by an increased capacity to encode some allomorphy in the phonology, through what I will
call Single-Underlying-Form (SUF) Allomorphy. For instance autosegmental phonology has
been used to analyze French liaison in terms of floating segments and pieces of a CV skeleton
allowing a segment to be pronounced or not based on context. The original analysis is due
83
to Clements and Keyser (1983), but many variations have been offered, discussed in Tranel
(1995). The following is a typical example.
(1) French Liaison
C V C V C V C V
p @ t i t + a m i
Scheer (2016) proposed that even more radical alternations could be analysed autoseg-
mentally. He discusses the case of Caddo, in which the simple future suffix surfaces as -PaP,
except after [P] where it surfaces as -waP, without any justification in the language for a
P>w process. Scheer points out that the additional representational power of autosegmen-
tal phonology allows for floating segments to be put in a UR and made to surface not by
rules changing a segment into another, but by simpler de-linking and re-linking processes.
I.e. some apparent cases of segment-to-segment processes could actually be processes of
re-linking to a floating segment that was underlyingly specified. The Caddo example could
therefore be accomplished with a floating /w/ in the underlying form as in (2-a). If we then
posit a rule delinking P after P, which is plausible as Caddo does not have geminate glottal
stops at the surface, then when this suffix is concatenated with a form ending in a glottal
stop as in (2-b) the glotal stop of (2-a) will delink and by autosegmental principles the
timing tier autosegment will automatically relink to the available /w/, forming the form
[waP] without any P>w process in the language. i will refer to this style of analysis as
Floating-Segment-Replacement.
(2) Analysis of Caddo in Scheer (2016)
a. X X X
P w a P
b. X X X X
+ ?
P P w a P
This style of proposal has launched a mini-industry, largely sustained by proponents of
84
CVCV phonology, focused on reanalysing cases commonly analysed as involving multiple
underlying forms as deriving from complex autosegmental representations (e.g. Pagliano
2003, ch.11, Barillot and Se?ge?ral 2005, Faust 2015, Barillot et al. 2018, Faust et al. 2018).
This style of analysis is entirely predicated on making full use of the representational pos-
sibilities of Autosegmental Phonology.
In parallel to this when Optimality Theory came about, its architecture, built around
selecting surface forms among candidates, was very well suited to explain PCA in terms
of choice among lexically-stored candidates. For instance Drachman et al. (1996) account
for the allomorphy in Greek deverbal action nominals between the suffixes -ma and -imo
by positing that the constraints are evaluated not against a single input, but against all
combinations produced by selecting one form among a set of allomorph in a tableau like
(3). This conceptualization of allomorphy is now standard in Optimality Theory, but in all
its simplicity it is a radical departure from everything that came before.
(3)
pyas-, {-ma, -imo} FtBin Parse2 Stem=PrWd NonFin
a. (pyas)-(ma?) ?!?
b. (pya?s)-ma ?!
c. (pya?s)-imo ?! ?
d. (pya?s-ma) ? ?!
e. pyas-(??mo) ? ?!
f. + (pya?s-i)mo ?
First it entails a very different notion of what a lexical entry is: a lexical entry is not a
phonological form anymore, it is not a string of segments; it is a list of strings of segments,
an object more abstract than a phonological form.
Second, like the autosegmental ideas above it places allomorph-selection in the phonol-
85
ogy. This stands in contrast with architectures like that posited only one year prior by
Russell (1995) in which allomorph selection from abstract morphemes takes its own mod-
ule.
(4) Optimality Theory Architecture from Russell (1995)
Similar SUF ideas existed even prior to Optimality Theory, such as in the work of Hud-
son (1974, 1975) and Hooper (1976)1. Hudson proposed that non-automatic phonological
alternations could be represented with underlying forms containing the alternatives. For
examples to account for the alternation of some Spanish verbs like contar&cuento Hudson
uses diagrams like (5-a), which a process like (5-b) would eventually resolve2. In this sys-
tem it is this representation of the alternatives that distinguish contar from non-alternating
?
verbs like montar&monto, which would be have the root / mont/, and amueblar&amueblo,
1Ultimately this type of analysis can be traced to Trubetzkoy?s (1929, 2001) ?Sur la Morphonologie?,
though not fully and explicitly worked out.
2Hudson was probably not intending for this notation to be taken literally as the underlying form, but
merely to summarize lexical relationships between different lexical items to choose from, but everything
in the way it interacts with phonological rules invites a literal interpretation where the bracketed form is
actually inputed whole into the phonology.
86
?
which would have the root / amwebl/.
(5)
??? ??o ?
a./k nt/
???w?? ?
??
?e ??
? o ?? ?? o / [-stress] ?
??
b.? ?? ?we? ?we elsewhere?
While OT?s representation required us to think of lexical storage as one degree more
abstracts, storing lists of phonological representations rather than phonological represen-
tations, Hudson?s diagrams suggest phonological representations themselves may be able
to contain parallel segments. This is probably not what Hudson had in mind: it seems
he considered the brackets to represent relationships between different lexical items within
the lexicon, and not literal non-string mental objects (although I fail to see how a rule like
(5) can apply to a relationship between lexical items). But we can take the notation as a
serious proposal requiring us to rethink the notion of a phonological representation, allow-
ing lexical items containing alternatives within themselves. This latter idea is more flexible
than the OT solution. Unlike OT?s representation of allomorphs, the alternation can be
confined to only the phonemes that actually alternate. For instance in (5) the alternation
is limited to the segments that actually vary: [o] vs. [we]. An OT equivalent would have to
posit an input to the phonology like {kont, kwent}, and in this representation the similarity
between, say, the [k] of kont and the [k] of kwent is accidental.
I will borrow some aspects of the logic of these SUF approaches to Allomorphy, partic-
ularly Hudson?s representation as it can be easily implemented in PROP.
5.2 Basic geometry
Fundamentally, suppletive allomorphy is about having multiple alternative forms that can-
not be accounted for by a regular phonological process. It is therefore characterizable as a
problem of selection among multiple memorized alternatives based on a context.
The geometric possibility granted by PROP allows for this to happen within the phonol-
87
ogy with representations such as (6). In (6), an allomorphic prefix contains separate parallel
paths, but in contrast to the cases of chapter 3 in which the expectations was for parallel
streams to be phonetically compatible and all attach, allomorphy results from the scenarios
in which (in the simple case) only one of the alternatives successfully attaches to a stem,
in which case only one of the alternatives is part of a complete path from # to %. There
is no expectation that the streams be compatible, since they never actually end up truly
in parallel in any finished graph, as (again, in the simple case) only one of them is actually
attached at both ends.
(6)
alternative 1 [environment A]
# alternative 2 [environment B]
alternative 3 [environment C]
5.3 Examples
5.3.1 Consonant/Vowel Sensitivity in Korean
First consider cases of phonologically conditioned allomorphy as in (7). In Korean the
nominative suffix is [i] after a consonant and [ka] after a vowel. This can all be handled
with technology we already have as in (8). The top sticky-end seeks a final consonant and
the bottom one seeks a final vowel. Assuming it only finds one of those at a time, the form
will contain only one path from # to %. The graphs of mom-i and kho-ka will look like (9)
88
and (10) respectively.
(7) Korean nominative allomorphy (Nevins, 2011, p.7)
mom -i ?body?
kho -ka ?nose?
(8) Korean nominative morpheme
[[+V ]? %] k a
%
[[+C]? %] i
(9)
k a
# m o m %
i
(10)
k a
# kh o %
i
5.3.2 Partial suppletion in English a/an
Additionally, just in like Hudson?s diagrams, PROP allows allomorphs to share segments
they have in common. For example the English a/an allomorphy can be handled with the
89
same machinery as the Korean case, except only one [a] is needed3.
(11) a/an
# a [#? [+C]]
n [#? [+V ]]
(12) a cat
a n
# k ? t %
(13) an eel
a n
# i l %
5.3.3 ? Approximant sensitivity in Swedish
Phonologically-conditioned allomorphy targeting specific features can also be defined in this
way. Consider the Swedish en/n allomorphy. Leaving aside some exceptions with [l] (see
Lo?fstedt 2010), the form -n is used for vowels and liquids, whereas -en is used for nasals,
fricatives, and stops. This can be described as sensitivity to ? Approximant. We can
therefore account for this behavior with sticky-ends sensitive to ? Approximant as in (15),
3I am assuming here that a and an do in fact have a vowel in common, which is probably not true in
varieties of English where /e/ and /2n/ may be more accurate. The example is mostly illustrative.
90
which will attach to the roots by: and gru:p as in (16) and (17), respectively.
(14) Swedish definite suffix allomorphy, data from Nevins (2011) and Lo?fstedt (2010)
indef. def. gloss
a. by: by:n ?village?
b. syk:el syk:eln ?bycicle?
c. pilgrim pilgrimen ?pilgrim?
d. i:s i:sen ?ice?
e. gru:p gru:pen ?hole?
(15) graph of en/n.
[[?Approx]? %] e
[[+Approx]? %] n %
(16) by:n
e n
# b y %
(17) gru:p
e n
# g r u p %
5.3.4 ?Nasal sensitivity in Nishnaabemwin
A similar pattern of harmony showing sensitivity to a specific feature is found in Nishnaabe-
mwin. Valentine (2001, p.221-223,227), Paster (2006, p.93) and Scheer (2016, p.353) discuss
the allomorphy in the 3rd person suffix in the VAI conjunct. This third person suffix has
91
the form -g following a nasal and -d elsewhere. This alternation does not appear to have
any phonological reason since sequences of [nd] are found elsewhere in the language.4
This pattern is readily accounted for as sensitivity to the feature ?nasal with a suffix
like the following:
(18)
[+nasal] g
%
[?nasal] d
5.3.5 Feature-level suppletion in Bari
Allomorphy in PROP can be stated at the level of alternating individual features rather
than entire segments. Paster (2006) discusses the Bari causative/reciprocative prefix. The
vowel of the prefix undergoes ATR harmony with the root, and is otherwise +high before
a root with a +low vowel and -high before a root with a -low vowel. Following Paster?s
notation in the following examples <@> is a low +ATR vowel and <a> is a low -ATR vowel.
4It is worth mentioning the phonetic outcome of this /-g/ which is never clearly summarized in one place
in any of the works cited above: all the /N+g%/ sequences formed by this allomorph apparently surface
as [N]. Valentine does mention a phonological process of assimilation followed by deletion (p.74) that causes
/n+g%/ sequences to surface as [N], but there is also scattered evidence that /m+g%/ also surface as [N]
as Valentine gives multiple examples of /m/ assimilating in place to following consonants, e.g. the suffix
/-m/ indexing an unspecified actor assimilating to?the third person marker (p.222), the theme suffix /-am/
assimilating to /s/ and /k/ (p.308), and the root waabam, ?see? to the VTI third person suffix /-d/ as
waaban-d-am (p.305).
92
(19) Bari causative/reciprocative
n@k ?to suck? tu-n@k ?to give suck?
Na ?to open? tU-Na ?to open with force?
rik ?to drive away? to-rik ?to pursue?
gwut ?to beat? to-gwut ?to beat each other?
rem ?to stab? to-rem ?to cause to stab; to stab each other?
mor ?to insult? to-mor ?to abuse violently; to insult each other?
mEt ?to see? tO-mEt ?to look at each other; to cause to see?
kOr ?to divide? tO-kOr ?to settle a dispute?
yIN ?to hear? tO-yIN ?to listen attentively; to attract attention?
kUr ?to till? tO-kUr ?to help each other with the tilling?
This can be handled with an affix like (20). The part of the prefix common to both
allomorphs, /t{+back,?low,+round}/, will invariably attach as a normal prefix, whereas
the choice between +high and -high will depend on the quality of the vowel. When this
attaches as in (21) the harmonic ?ATR value will come from the root in the way defined
in chapter 3 with a parallel path that prefixes are put in parallel to, and the height of the
vowel will depend from whether the +Low or the -Low sticky-end has successfully attached
(as the other is not part of a path from # to %.
(20) Bari causative/reciprocative prefix
{+hi} [ ? [+lo]]
# t {+Rd,+Bk,?Lo} [#? ]
{-hi} [ ? [?lo]]
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(21) tO-kUr
{+hi} {+ATR}
# r e m %
t
{+Rd,+Bk,?Lo}
{?hi}
5.3.6 Default allomorphs
Not all cases of phonologically-conditioned allomorphy involve complementary distributions
both sides of which are natural classes. For instance consider the distribution of the per-
fective in Kwamera, which Lindstrom and Lynch (1994) report as being 1n- before [-hi]
vowels and uv - before [+hi] vowels and consonants, e.g. r-uv-regi, 3sg.perf.hear, vs. r-1n-
atu, 3rd.perf.see5. Since high vowels and consonants are not a natural class, there is no
single sticky-end that can accommodate this pattern of allomorphy.
There are at least two ways to handle such cases. The way that does not require any
new machinery would be to give one allomorph a set of sticky-ends covering the relevant
natural classes as in (22). This would adequately account for all the data in a sort of ?brute
force? way, with at least one path from the prefix to the root whether that prefix starts with
a high vowel or a consonant. Although descriptively sufficient here, this option would prove
unable to handle productive affixes in the case of Morphologically Conditioned Allomorphy
5As observed already by Paster (2006, p.32), Linstrom & Lynch do not give any example of uv used
before a high vowel. More worryingly they also offer examples of 1n- before /u/ and of uv - before /a/. On
close analysis of the paper it seems that the latter are the result of mistaken glosses confusing the exponent
uv - of the perfective with the verb uv elsewhere glossed as ?move? or ?proceed?, but I have no explanation
for the former. Like Paster (2006), Boutin (2009), and Scheer (2016) I will assume that the claim is correct
here because this example is eminently simple and useful for the expository claim at hand and I find it
implausible that Lindstrom & Lynch would have made such an error.
94
in the next chapter where there is no set of phonological features to brute force upon.
(22) Brute force version with multiple sticky ends.
1 n [#? [?hi]]
#
u v [#? [+hi]]
[#? [+C]]
An alternative would be to design a mechanism that can accomplish the equivalent of
selecting ?defaults?, so that one sticky-end can be specified for its environment and another
represented as default to form a path only if the other sticky ends have not successfully
attached. One sticky-end needs to be defined for a specific environment and the other for
a more general one. The issue that immediately arises though is that in the case of the
more specific environment we predict both allomorphs attaching without an obvious way to
decide which path to follow. In fact if anything given the discussion in chapter 3 we would
predict both paths to be followed in parallel, contrary to fact.
There are a number of ways we could try to accomplish defaults with pure PROP
machinery by taking advanatage of sticky-ends or parallel structures. Here are a number of
sensible proposals:
One option would be to make it about sticky-ends and the segment they attach to, e.g.
forcing the de-linking of the default form in case the segment it attaches to is also attached to
the non-default sticky-end, namely making the sticky-ends mutually exclusive. This would
amount to making the Kwamera perfective?s [#? [?hi]] and [#? [+C]] incompatible. A
version of this would be to posit an Elsewhere Condition on attaching multiple sticky-ends
to the same segment that always favors the most specific one and blocks the others.
Another logical option would be to attribute the default behavior to the phonetic in-
compatibility between [1n] and [uv], forcing the articulators to choose one of the two. This
would amount to letting both versions of the prefix attach and let the choice be made later.
The argument against the generalizability of these two options is that not all allomorphs
?compete? for attachment to the same location in positions that make them parallel to each
95
other. For instance consider the Nakanai nominalizing affix as described by Paster (2006):
the form -il - is used before a stressed first vowel of the word which, given the regular
penultimate stress pattern of the language, means words of one or two syllables. In any
case where the stressed vowel is not the first vowel a suffix -al is used instead.
(23) Nakanai nominalizing affix
pe?ho ?die?
p-il-e?ho ?death?
vi-ku?e ?fight(v.)?
viku?e-la ?fight(n.)?
This is a case of PCA with a default, but crucially the infix -il - and the suffix -la are
not competing for attachment to the same location, nor are they being attached in parallel
as we can see in (24). There is no way to attribute this to a local effect of the sticky-ends
or to phonetic incompatibility. Whatever regulates de-linking or non-attachment must be
non-local.
(24) *p-il-eho-la
i l
# p e? h o %
l a
Of course any encoding of defaults will make the theory more complex, but with the
goal of being able to discuss more patterns of allomorphy I will here describe and use an
implementation with non-local dependencies between precedence links themselves. I have
strong hopes that this idea can eventually be superseded.
96
This dependency is such that after attachment, precedence links marked with 	 delink if
the ones from the same affix marked with ? have been successfully created. The Kwamera
perfective could be formulated as in (25), with a specific sticky-end seeking initial [-high]
segments whose precedence link is marked ? and a more general sticky-end seeking any
initial segment whose link is marked 	.
(25) Version with a ?/	 default
1 n [#? [?hi]]?
#
u v [#? ]
	
In the case of a consonant- or high-vowel-initial root the graph will be as (26) with an
unambiguous path through uv. However in the case of a non-high vowel both sticky ends
will attach and then the 	 path will delink as in (27), creating a single unambiguous path
through 1n.
(26) uv-regi
1 n
# r e g i %
	
u v
97
(27) 1n-atu
1 n
?
# a t u %
	
u v
	 delinking
1 n
?
# a t u %
u v
Similarly, the Nakanai nominative will look as in (28) (a single disconnected graph), and
will attach to a stress-initial form as in (29). ?/	 allomorphy lets us express this in PROP
as the attachment of -al being dependent on the non-attachment of -il -. I currently see no
other way to describe this pattern.
(28) Nakanai nominative
?
[#? ? V?] i l [V?]
[ ? %] a
	 l %
(29) p-il-eho
i l
?
# p e? h o %
	
l a
98
There are three reasons why I would rather talk of de-linking some precedence links
rather than about blocking them from linking in the first place. First, the latter option
would involve forcing an order of attachment over the sticky-ends which would be more
complicated. Second, some analyses below will require 	 on precedence links that are not
directly added by a sticky-end, hence preventing linking would not be enough.
And the third reason is that with this linking and de-linking there is a stage in the
derivation where there was indeed a link from the default to the root, and hence a path
through the graph going through the default affix. This could play a processing role in
explaining why the use of an ungrammatical default affix on an inappropriate root, e.g.
oxes for oxen, or catched for catch, remains parsable by a native speaker. In the current
proposal, there is a stage in the derivation of a non-default affix in which one path through
the graph does cross the default affix. Assuming that lexical parsing involves some amount of
identifying paths through graphs, it allows for these ungrammatical forms to be retrievable
by a native speaker even though they would never utter them.
There are also analyses that suggest that other operations may happen during this
intermediate stage in the derivation between linking and de-linking, perhaps even to the
point of bleeding the 	-delinking rule. We will see such an example in Catalan in 6.1.4.
99
Although we have now been forced to posit a new piece of machinery taking us further
from the PROP ideal, this Nakanai example illustrates a way in which the PROP analysis
is superior to other phonology-internal attempts at SUF allomorphy, discussed in 5.1. The
Hudson-Hooper model with brackets cannot handle alternatives that are not competing for
the same string location, and the classical OT analysis requires selecting an underlying order
between morphemes that makes it hard to even define allomorphs competing for different
locations6. The representational power of PROP that allows representations like (28) in
which both linear order and allomorph-choice to remain undetermined until after spell-out,
is uniquely well suited for this situation.
5.3.7 Non-sticky-end default in Russian and Tahitian
The use of ? and 	 does not have to be restricted to precedence links added via a sticky-
end. This is useful in cases of allomorphy relating to changes other than at the point of
contact between an affix and a root. Consider the Russian reflexive discussed in Paster
(2006, p.54), which is -sj after a vowel and -sja after a consonant. This could be done as in
(31) without the use of ? or 	.
(30) Russian reflexive
a kupaju-sj ?I bathe myself?
on kupajet-sja ?he bathes himself?
(31) Russian reflexive suffix (two /sj/ version)
[[+C]? %] sj a
%
[[+V ]? %] sj
6Versions of OT attributing the location of infixes to the representation, e.g. Svenonius and Bye?s 2011
mechanics of antitropism, would fare better. This, in my opinion, comes from the insight of attributing
affixation location to the representation, just like PROP does with sticky-ends. But even these require an
underlying concatenative order, which makes it a challenge to analyse the Bari affix which aligns leftward
in one case and rightward in the other.
100
However (31) is unsatisfying in at least one respect: it implies that the the /sj/ of -sja
is not the same as the /sj/ of -sj. This is definitely at least counter-intuitive, even though
it would result in a correct output. But the use of ? and 	 allows us to have a single /sj/
across both forms as in (32). The link from /a/ to % is not connected to any sticky-end,
but it will de-link if the sticky-end marked with a ? does connect, i.e. in vowel-final forms,
leaving no path through /a/.
(32) Russian reflexive suffix (one /sj/ version)
[[+C]? %]
sj %
? 	
[[+V ]? %] a
Again this same strategy can be applied to individual features. The Tahitian causative/
factitive, described in Paster (2006, p.39-40) has the form ha?a before labials and fa?a
elsewhere. Assuming that [h] is a segment underspecified for place and therefore the only
difference between [h] and [f] is absence vs. presence of a labial feature, the prefix can be
formulated as in (34). In this prefix, the precedence link leading to the labial feature will
de-link if the sticky-end finds an initial labial, making the fricative an [h].
(33) Tahitian causative/factitive
ha?a-veve ?appauvrir?
fa?a-tai?o ?faire lire?
(34) Tahitian causative/factitive prefix
lab
	 #? [+lab]?
# h a P a
#?
101
5.3.8 Opaque Allomorphy in Japanese
Japanese has a pattern of PCA that interacts with a phonological rule discussed in Nevins
(2011, p.18), Kubozono (2015, p.367-368, 373), and Hall et al. (2018). A number of Japanese
suffixes are phonologically conditioned by whether they follow a vowel or a consonant. For
example /(r)u/, sometimes glossed as non-past (Nevins, 2011), present (Kubozono, 2015),
or infinitive (Hall et al., 2018), appears as [-ru] after a vowel and [-u] after a consonant, and
the negative /(a)nai/ appears as [-nai] after a vowel and [-anai] after a consonant, as one
can see in the contrast between these affixes on roots /yom/ ?read? and /ne/ ?sleep?.
(35)
/yom/ ?read? /ne/ ?sleep? /iw/ ?say?
non-past yom-u ne-ru i-u
negative yom-anai ne-nai iw-anai
However this pattern of PCA interacts with a phonological process: /w/ deletes before
all non-low vowels, and yet the suffixes surface in their pre-consonantal forms despite ending
up in pre-vocalic position, as one can see for the non-past form of /iw/ in (35), which surfaces
as [i-u] and not *[i-ru].
The allomorphy itself is easy to handle in PROP with an affix like (36) attaching as in
(37).
(36)
[[C]? %] r
[[V ]? %] u %
(37) /iw + (r)u/
r u
# i w %
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Then if the phonological deletion is handled as in (38) through adding a path, this will
convert the graph in (37) into (39), which is what we want.
(38) w -deletion
X w [-lo] =? X w [-lo]
(39) i-u
r u
# i w %
The possibility of opaque allomorphy easily follows from PROP assumptions, as the
attachment of allomorphs deciding paths happen prior to phonological rules.
5.3.9 Non-Attaching Allomorphs
A final geometric possibly to discuss is the situation in which some allomorphs are phono-
logically-conditioned and the default is phonologically null. Consider the English verbalizer
-en, which attaches only to adjectives ending in obstruents: to redd-en, to moist-en, to
thicken-en, vs. to green, to dry , to thin (cf. *to green-en, *to dry-en , *to thin-en).
This can be handled with a suffix like (40). In the case of a word ending in an obstruent
this will attach without issue and form the structure of a simple suffix.
(40) English verbalizer -en
[[+obstr]? %] @ n %
103
(41) black-en
@ n
# b l ? k %
However in the case of a root ending in a sonorant the sticky-end will not find anything
to attach to and will therefore not be part of any path from # to % as in (42).
(42) green (v.)
@ n
# g r i n %
This analysis somewhat captures the spirit of Zwicky (1985) who proposed that situa-
tions like this did not need to be analyzed as contextual zero-allomorphs, but could simply
be analyzed as a lack of any allomorph meeting the structural description. This is similar in
that I do not posit any part of the morpheme in (40) to seek out the default case as zero, it
is a lack of attachment that causes the zero realization. However the analysis here contrast
with Zwicky?s in that where he posits a lack of morpheme, I posit that the verbalizer is in
fact there, except without any part of it that is traversable, and hence without a part that
will end up pronounced.
There are some complications to the generalization above. For instance there needs
to be exactly one final obstruent, and final /t/ doesn?t count as it deletes, e.g. soft-en
[sOf@n] (leading Booij (2012) to refer to this as a surface constraint, and thus evaluated after
t-deletion. This pattern may be better analyzed as (43).
(43)
[[?obstr]? [+obstr]] @ n %
But even this generalization has problems, e.g. to crisp-en and to wast-en are sometimes
attested.
104
Either way the logic of the discussion below is valid regardless of the details of the
generalization, as long as there is a set of environment taking -en and a set of environment
surfacing without an overt ending (which may not be the case).
5.3.9.1 Summary of PCA
The approach to allomorphy presented so far in this chapter is roughly a ?selection? model in
the sense of Bye (2007) and Paster (2006) in that it relies on allomorphs being specified for
their environment rather than on any optimization effects. However this is accomplished
without without the architectural implication that a morphological module in charge of
allomorph section has to precede the phonological module. ?Selection? here is performed
internally to the phonology, selection arising as a side effect of sticky-ends, not through
optimization. We will come back to this discussion at the end of this chapter.
5.4 Further Issues
With the range of allomorphy phenomena I suggest to analyse using SUF allomorphy in
PROP made explicit, I will address what the approach outlined here has to say with regard
to a number of theoretical issues.
5.4.1 Terminology: ?Allomorphy?, ?Suppletion?, ?Irregularity?
I have used ?allomorphy? in a vague descriptive sense here because most of the typical uses
of allomorphy-related terminology is founded on assumptions that poorly apply to the SUF
approach of this chapter.
105
For instance a mainstream use of the term ?allomorphy? defines it as cases in which
alternations in surface forms require multiple URs, in contrast to alternations that can be
attributed to a single UR and regular phonological processes applying to it (e.g. explicitly in
Matthews 1974, Lieber 1982, Zwicky 1985, Kiparsky 1996, Bonet and Harbour 2012, Faust
and Lampitelli 2016, and implicitly in many others) By this usage, the claim of this chapter
is that there is no such thing as allomorphy, a confusing claim in my opinion. But indeed
the goal of this chapter is to account for all allomorphy-in-the-wider-sense with a single
UR and phonology-internal processes applying to it, sometimes in the form of phonological
rules and sometimes with sticky-ends selecting among alternative. If allomorphy is having
multiple URs, the claim of this chapter is that there is no such thing as allomorphy as all
suppletion comes from SUFs.
This usage stands in stark contrast with the complete opposite usage of ?allomorphy? to
refer only to the result of phonological rules to the exclusion of any suppletive or conditioned
forms, as in the Language Files textbook (Dawson and Phelan, 2016), in which allomorphy
is illustrated with the example of the [m]&[n]&[N]&[?]&[l] negation prefix, and the [s]&[z]&[@z]
plural (p.181) and defined as ?a set of non-distinctive realizations of a particular morpheme
that have the same function and are phonetically similar? (p.690). Another example is
Fa?bregas and Scalise (2012) in which they claim that ?allomorphy in its traditional sense
requires the two forms to be derivable from the same phonological representation? (p.82).
Proponents of the allomophy=regular-phonology version tend to think of suppletion as a
word-formation process, whereas proponents of the allomorphy=different-URs use ?supple-
tion? as a more descriptive term for alternations that require memorizing more things. By
this usage that opposes allomorphy to suppletion, the claim of this chapter is arguably that
there is only allomorphy and suppletion does not exist.
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These two uses, however contradictory, are predicated on the same premise, namely
the existence of a deep architectural split between the mechanism that yields common
alternations describable over phonemes alone, and the ones that yield idiosyncratic and
sometimes major alternations in forms that require reference to specific morphemes. In
the SUF PROP model presented so far this split does not exist. All lexical items arrive
in the phonology and it is there that the phonological material attaches and undergoes
phonological processes, leaving some surface form to be pronounced. There is no deep
architectural divide, and the differences emerge from the interaction of the different items
that can be sent to the phonology and the rules that can happen to them while there.
A new terminology was recently suggested by Haspelmath (2019), who discusses how
the term ?morpheme? itself is subject to a similar ambiguity to ?allomorph?, with different
theories refering e.g. to the two forms of the plurals book-s and ox-en either as two ho-
mosemous morphemes expressing plural meaning, or as ?members? of the same morpheme
[Plural]. Haspelmath proposes to call alternants like -s and -en different morphs part of the
same morph set, whereas [z], [s], and [@z] are the same morph. But even in these new terms
intended to be neutral it is unclear how to phrase the claim of this chapter: we could adopt
the terminology as a surface description and frame this chapter as claiming that morph sets
are stored in a single UR. Or we could adopt the terminology as a theoretical claim and
frame it as claiming that all morph sets are singletons and all surface variants derive from
a single morph, including -en and -z.
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Yet another definition is found in Tranel (1992): he defines suppletion as ?the lexical
listing of more than one allomorph for a given morpheme?. But we are faced with the same
problem: is a complex underlying form containing both -en and -z a listing of multiple
allomorphs? There is in fact only one vocabulary item, but in another sense there is a
listing of multiple allomorphs, namely within that vocabulary item.
5.4.2 PROP vs. Hudson & Hooper
As mentioned at the beginning of this chapter, the intellectual predecessors of the ideas
presented here include the ideas of Hudson (1974, 1975), and Hooper (1976), as the PROP
analysis of allomorphy involves packing the variants of a form within a single UR. I therefore
must address some of the criticisms that have been levied against those ideas.
Though they do not explicitly cite Hudson or Hooper, Kenstowicz and Kisseberth (1979,
p.180-204) offer an extensive critique of ideas that are very recognizably theirs. We will
see that the critique is irrelevant to the proposal of this chapter. They largely attack the
use of alternants in the UR to handle what regular phonological rules handle in Generative
Phonology. E.g. they are attacking a theory of the English plural as in (44) supplemented
with statements such as ?chose [s] after a voiceless non-sibilant?. I.e. they are objecting to
the use of alternants to account for regular predictable alternations. They object that these
statements end up recapitulating the phonological and phonotactic generalizations of the
language. They also object that this approach fails to explain the existence of completely
general alternations affecting all instances of a certain segment in the same contexts.
(44)
????? ?? s????
k?t + ????? z?
?
???
1z?
These objections do not really affect the ideas presented here, as I am only concerned
with the unpredictable alternations, the case where regular phonology is not enough. I
agree with Kenstowicz and Kisseberth that abstraction in representation is required by the
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data.
Plus, although superficially similar when looking at the representation of alternation as
in (5) and (44), there is really little else in common between the theory of Hudson (1974,
1975), Hooper (1976) and the ideas of this chapter. Hudson and Hooper were motivated by
a desire for ?concreteness? in representation and were essentially opposed to levels of repre-
sentation that are not pronounceable due to abstract archiphonemes or due to violations of
the languages phonotactics prior to repair.
So while PROP allomorphy can be said to be similar to the ideas of Hudson and Hooper,
it does not share the same problems.
5.4.3 PROP vs. Subcategorization
Paster (2006) argues in favor of a subcategorization model for Phonologically-Conditioned
Suppletive Allomorphy (PSCA). She proposes that affixes come with subcategorizational
requirements, specifications of what the affix needs in order to surface. PSCA results from
the cases where different affixes with the same meaning have different subcategorizations.
This therefore embeds PSCA in a general theory of bound morphology and unifies it with
syntactic c-selection in a constructional framework.
Recall the Tahitian Causative in 5.3.7, which is haPa before a labial and faPa elsewhere.
Paster proposes that Tahitian has the following two constructions:
(45) Paster?s 2006 constructional subcategorization analysis of Tahitian (p.12)
This approach unifies all PSCA, including the optimizing type and the non-optimizing
type, in contrast to varieties of OT that handle the two differently.
I will not discuss Paster?s analysis, which is so radically different from anything discussed
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here that there is little communication to establish, however Paster derives the following
four predictions from her model:
(46) Predictions of Paster?s subcategorical model for PCSA (p.257)
1. PSCA is not always phonologically optimizing
2. PSCA is sensitive to phonological elements in underlying/input forms, not surface
forms
3. Phonological conditions on PCSA can come only from the ?inside?
4. Affix allomorphs occur adjacent to the phonological elements of stems that condition
their distribution
She substantiates these predictions with an extensive typological survey of PSCA, so it
would be useful to see whether PROP SUF allomorphy derives them too.
The first point is definitely predicted here. Allomorphy is performed by affixes that
seek phonological features with sticky-ends and there is nothing in the system constraining
these, so allomorphy is arbitrary and free to be non-optimizing.
The second prediction follows since phonological rules cannot happen in PROP between
a stem and an affix prior to attachment, and therefore the attachment responsible for
allomorphy cannot be sensitive to any phonological rule affecting the stem triggered by the
root. We have already discussed a case of opaque PCA above in 5.3.8. Wolf (2008, ch.3) .
The third prediction only partially follows from PROP, and that?s a good thing. Given
that attachment of an alternative or another is the determinant of allomorphy in PROP, it
follows that the main way for allomorphy to be realized is ?inner? lexical items conditioning
?outer? ones. However there are limited ways in which outer material can phonologically
condition the allomorphy of inner lexical items and those are possible in PROP. We will
discuss this in the next subsection.
And finally the linear-adjacency condition follows too since allomorphy in PROP is
decided upon attachment. In PROP the same mechanics that determines the attachment
point of an affix also determine its allomorphy. This non-stipulatively derives the prediction.
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This is an important one because a linear adjacency condition on allomorphy has been noted
by others, notably in Embick?s 2010 C1-LIN Theory which posits both a syntactic cyclic
condition on allomorphy and a linear adjacency condition. PROP has nothing to say about
the former, which may properly belong to syntax and the hypothesis of cyclic spell-out, but
the latter condition follows from PROP and much more satisfactorily so. Embick has to
resort to a stipulation of the linear adjacency fact which he has to state on an ordered tree
since he posits allomorphy to be decided prior to insertion. PROP on the other hand is
compatible with a non-linearized tree structure in syntax.
5.4.4 Outward-sensitive allomorphy, and root allomorphy
We saw in the last section that doing PCA with sticky-ends derives the prediction that
phonological conditioning can only come from the inside, based on the fact that it is usually
determined by sticky-ends attaching to a stem. But there is one family of exception to this
generalization and PROP also derives it.
I am referring to cases such as the Spanish kont kwent mentioned at the beginning of
the chapter. The form is sensitive to stress, taking the form with [we] when stressed forms
and the form with [o] when unstressed. Because Spanish stress is computed from the end
of the word, whether the root vowel is stressed or not is not known to the phonology by the
point in the derivation in which the root is spelled out. Bermu?dez-Otero (2013) gives the
paradigm in (47). Because the choice of allomorph in contador must be delayed until the
stress is assigned to the suffix -dor, it cannot be determined at vocabulary-intertion.
(47)
kont-a?-R ?count.inf?
kwe?nt-a ?count.3sg?
kont-a-Do?R ?counter?
?
In PROP this is relatively easy to account for. The root cont has the form in (48),
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inspired by the analysis of Hudson (1974, 1975).
?
(48) cont
we
# k n t %
o
Without going into the details of stress assignment in PROP (we will briefly come back
to stress in ch. 9) it suffices that the mechanism that assigns stress to the penultimate
vowel in forms with -[a] and to the final vowel in forms in -[aR], assigns the stress to both
?
alternants of the root cont as they are both in penultimate position.
(49) cuent-a
we? a
# k n t %
o?
Given a rule de-linking o?? X if this X follows another stressed vowel, we can obtain
the graph in (50) with an unambiguous path through [we?]. An opposite rule de-linking
unstressed we? X if this X follows another vowel will account for the cases with [o]7.
(50) cuent-a
we? a
# k n t %
o?
The advantage of PROP is again that we can only account for this pattern because
the choice between [kwent] and [kont] is not decided right away, but is delayed until later.
This type of allomorphy is not possible in a system where allomorphs must be decided at
7We will see a perhaps more elegant analysis of this allomorphy dispensing with de-linking in 9.3.4
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insertion.
This type of phenomenon is the reason all models positing immediate resolution of
allomorphy had to come up with ancillary assumptions to handle such cases of ?late al-
lomorphy?. This is why the traditional Generative account is a phonological solution in
the form of an archiphoneme like /O/, whose resolution is phonology-internal. And in
Distributed morphology the above would likely be handled with a re-adjustment rule, a
separate mechanism to introduce variants of a morpheme within the phonology. Both of
those solutions are attempts at getting around the fact that some cases of PCA are delayed
until after insertion. PROP on the other hand does not need any extra mechanism to do
that, as both variants are allowed to cohabit in the form for the entire derivation.
Although plausible for the kwent&kont case in Spanish, the phonological solution is
unlikely to generalize well to all similar cases. Italian has a rich set of such prosodically-
determined allomorphs as described in Wolf (2008, p.194): e.g. the root of the italian verb
rompere, ?to break?, surfaces as ru?pp- when stressed and romp- when unstressed. Multiple
roots are in the same boat including those of muovere ?to move? (mo?ss- vs. m(u)ov-),
prendere ?to take? (pre?s- vs. prend-), and andare (va?- vs. and-). No single archiphoneme
seems capable of deriving all of these changes.
This last example of andare makes the readjustment solution very unappealing too. An
alternation like [and]&[va?] is not the type of ?small? change that readjustment rules have usu-
ally been posited for, but a complete suppletion. If readjustment can convert [va] and [and]
into each other then it simply recapitulates all the power of allomorphy that DM attributes
to contextual insertion. Readjustment in DM has already been extensively criticized from
a DM-internal perspective for being uneconomical, redundant, and/or unconstrainedly de-
fined (Siddiqi 2006, 2009; Bermu?dez-Otero 2012, 2013; Haugen and Siddiqi 2013; Merchant
2015; Haugen 2016), so I will not belabor the point here.
But also importantly for PROP, cases of outward-sensitive PCA are very limited. Unlike
allomorphy caused by sticky-ends, which can target any phonological properties of what they
attach to, allomorphy of the kwent&kont type is limited to what can be formulated as a
regular rule manipulating the graph, and can only be sensitive to the outcome of regular
processes; it cannot retro-actively force the attachment of allomorphs that failedto attach.
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All the cases of outward-sensitive allomorphy I am aware of involve sensitivity to stress and
can be done in PROP in the manner described above for Spanish.
This analysis in terms of root allomorphy that is resolved late offers an answer to the
problem that forms the starting point of Bermu?dez-Otero (2013). Bermu?dez-Otero is con-
cerned with the problem of forms like *cuentado?r, in which the stress pattern can only be
determined after the insertion of the suffix -dor, which, assuming as DM does that category-
defining heads create a cycle, is in a separate cycle from the root. In DM since allomorphy
happens at insertion, it would have to be fully decided by the end of a cycle. However in
PROP there is no reason for such an order: insertion of both variants happens, and the
ultimate choice can be delayed. Contra Bermu?dez-Otero (2013, p.58), we have a root-driven
theory of morphology in which allomorphy is not answered ?in the first cycle?.
5.4.5 The gradability of suppletion
Mel?c?uk (1994) discussed what he termed the ?gradable? character of suppletion by observing
that many cases of suppletion seem partial. He points out the example of French p? vs.
puv- ?can, be able to?. There is an intuition that the [p] of both allomorphs are ?the same
[p]? in a sense, and we may seek to capture that in the theory. In a theory of suppletion
with multiple URs this would not be possible: the grammar would have a lexical item /p?/
and a lexical item /puv/ and the similarity between the first segment of each would be
(synchronically) a coincidence.
Mel?c?uk offers the possibility that this may be derived by a restricted rule ?>uv. Nowa-
days this possibility would be phrased as readjustment, which we discussed in the previous
section. Again, an advantage of PROP is that it can derive this pattern without resorting
to such machinery as lexically-specific rules that are often very powerful.
In PROP the gradability of suppletion follows directly from what suppletion is in the
theory: multiple alternatives within a phonological represntation. Since these alternatives
are stated within one lexical they can be stated at any level of precision the language
demands.
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5.4.6 PROP and surface optimization
One logical possibility that will inevitably cross the mind of many readers would be to
incorporate surface optimization into this PROP account of allomorphy. E.g. one may be
tempted to dispense with overly specific sticky-ends and with ?/	-defaults and let the final
path through the graph be resolved not by fiat, but by selection of a phonetically optimal
path.
For instance recall the korean PCA in 5.3.1, in which the nominative -ka is chosen after
vowels and -i after consonants. This could plausibly be reanalyzed with an affix like the
following, which contrasts with (8) in lacking sticky-ends seeking vowels or consonants.
(51) Korean nominative suffix without selection via sticky-ends
k a
[ ? %] i %
Seeking only a final segment, both alternatives will therefore attach to a root, as in (52),
which contrasts with (9) in having a path from the [m] of the root to the [k] of the suffix.
(52)
k a
# m o m %
i
The final step would be to posit that it is the graph in (52) that is passed onward, and
that it is a phonetic principle, e.g. a preference for C?V over C?C, that forces the surface
pronunciation to be mom-i and not *mom-ka. One could even expand to embedding PROP
into an OT grammar with constraints over paths or the like. This is indeed a logically
possible development, but I will not explore it further here, other than to point out my
main objections to this type of analysis.
Namely I think that, as Paster (2006) and Bye (2007) amply demonstrate with a wide
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range of examples, enough non-optimizing PCA patterns exist to justify the existence of
a subcategoriation mechanism by fiat, and any mechanism capable of handling arbitrary
subcategorization can handle the optimizing kind as well. I will not recapitulate all of Paster
and Bye?s examples here, rather I will describe a family of non-optimizing alternations
which, to my knowledge, has not been discussed in the suppletion literature.
Consider the case of Wayoro as described in Nogueira (2011, p.145-155). The causative
/transitiviser is [mo?-] before a vowel and [o?-] before a consonants.
(53)
causative/transitivized gloss of the bare form
mo?-a?mo?ja? ?dance?
mo?-e?ra? ?sleep?
mo?-1kara ?cry?
mo?-e1ka ?belch?
mo?-agopka ?warm up?
mo?-atoa ?bathe?
o?-kejtokwa ?laugh (pl.)?
o?-gwea ?move up?
o?-po:riatkara ?age (masc.)?
o?-kodZikara ?age (fem.)?
o?-pi:tokara ?rest?
o?-paga ?get drunk?
o?-parega ?improve/stay good?
o?-n??a? ?be ashamed?
o?-goa ?mature?
o?-ta?n?dZora ?get pregnant?
The introduction of an initial [m] does nothing to alleviate the hiatus formed in vowel-
initial words. As such it is not clear that any optimization story can be given for this data.
This type of V-/CV- prefix allomorphy is widely attested in South American languages, e.g.
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in Kanamari (Ishy 2018, p.76-77,164-165, and Anjos Gonc?alves da Silva 2011, p.118-120),
Further, enough cases of opaque PCA exist to discourage the applicability of constraints
on surface form. We have already discussed the case of Japanese. Moreover it is sufficient to
attribute the predominance of seemingly-optimizing PCA to the patterns of sound changes
in diachrony, there is no need to further attrbiute it to the grammar. The burden of proof
is therefore on those who want to argue in favor of a seemingly redundant optimization
mechanism.
5.4.7 Scheer (2016) and melody-sensitivity in PCA
The model of allomorphy described in this chapter allows for PCA to target any feature,
as no restriction was put on what features a sticky-end can seek. This goes against Scheer
(2016) who argues that PCA cannot be sensitive to melody, defined in his work as the
segment content, but can only be sensitive to prosody and sonority, suprasegmental material.
Scheer?s conceptual argument focuses on the problem for modularity if morphology can
see segmental features. Scheer sees his position as following Zwicky and Pullum?s (1986)
principle of phonology-free syntax, according to which syntax does not use phonological
information in its operations. This argument is mostly set in opposition to non-modular
OT approaches.
Now recall that modularity in general and domain specificity in particular hold
that vocabulary items that are processed by a given module cannot be read,
parsed or understood by another module. In the case of PCA, this means that
phonological vocabulary ?labial, occlusion and the like that occur below the
skeleton? cannot be taken into account by morphological computation, i.e.
allomorph selection. Nothing prevents the conditioning of allomorphy by other
pieces of phonological representations, though: PCA is free to take into account
the output of phonological computation: structure that occurs at and above the
skeleton. (Scheer, 2016, p.346)
Scheer examines the empirical data and confirms that nearly every case of PCA in the
records involve either the contrast between vowels and consonants as in the Korean case
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of 5.3.1 or stress and footing. Other cases largely seem analysable as targeting sonority,
e.g. the Swedish allomorphy analysed in 5.3.3 as sensitive to ?Approximant can be given a
generalization as sensitivity to ?liquids up? vs. ?nasals down? as in (55), and the Kwamera
allomorphy analyzed in 5.3.6 as targeting [-hi] with a delinking default can be given the
generalization of targetting ?mid vowels up? vs. ?high vowels down? as in (56).
(54) Korean nominative
? ??k?a ? ? ???i ?
low > mid > high > liquids > nasals > fricatives > affricates > stops
(55) Swedish Definite Suffix
? ???n ? ? ??e?n ?
low > mid > high > liquids > nasals > fricatives > affricates > stops
(56) Kwamera Perfective
? 1?n?? ? ? u?v?? ?
low > mid > high > liquids > nasals > fricatives > affricates > stops
(57) Nishnaabemwin 3rd conjunct
? ???d ? ? ???g ? ? ???d ?
low > mid > high > liquids > nasals > fricatives > affricates > stops
A complex pattern that can still be given a prosodic generalization is found in Ikpeng.
Campetela (2002, p.155) describes the allomorphy of the second person singular prefix,
which takes the form w- before [a], a- before [Ca-], and [o&O-] elsewhere, i.e. before vowels
other than [a] and before CV where V is not [a]. This can be accounted for by paying
attention to the sonority of the first two segments: o- if both segments are Mid vowels or
lower, w- if the first segment is Low, and a- if the second segment is Low.
And finally for cases that do not look like either prosody or sonority, Scheer proposes
that they all can be reanalyzed within the phonology. For instance the Tahitian allomorphy
described in 5.3.7 can be reanalyzed as long distance dissimilation8. And in cases where the
8Paster (2006, p.40) argues against a dissimilation analysis, but the argument is rather weak. There are
no comparable prefixes with /f/ in Tahitian that could confirm or disconfirm that this dissimilation is a
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alternations do not seem to be general phonological facts of the language, Scheer suggests
using the representational power of autosegmental phonology in the way described above
in (2) to accomplish moderate amounts of segment replacement within the phonology.
5.4.7.1 Conceptual Problems
A conceptual problem with Scheer?s argument is that I do not see how allomorphy based on
morphology seeing prosody and sonority is any better for modularity than allomorphy based
on seeing any other features. Scheer restricts his version of modularity to the vocabulary of
a module, understood as the symbols it can read as its input. Scheer takes the lexicon to
contain only segmental melody features, and hence only those are the input to the phonology.
Prosody and sonority, he claims, are computed on top of the melody and are different. But
why is that? Even if sonority is computed and never inputed, it is still computed within the
phonology. It is a set of symbols used by the phonological module during its computation.
For it to be visible by the morphology would require that it not only be a non-input, but that
it be an output from phonology to morphology. I fail to see why such a backward interface
is desirable in the architecture of language. Further, if there were information sent back
from phonology to morphosyntax, it is unclear why PCA would be the only manifestation of
it. It does predict the impossibility of labial-movement to spec-CP, but why do we not see
C-initial movement to spec-CP, penultimate-stress movement to spec-CP, or polysyllabic
movement to spec-CP? Or if this is about visibility by a morphological module distinct
from syntax, then why does Scheer invoke Zwicky and Pullum (1986) and the principle of
phonology-free syntax?
While prosody is computed, it is not clear that it is ever outputed from phonology. Pho-
netic evidence for the syllable, a long-desired goal of phoneticians, has failed to yield any-
thing (Ladefoged and Maddieson, 1996, p.282). Prosody has the character of a phonology-
internal scratchpad, used for the computation of other things, and then never sent anywhere
else. The idea that this most-proprietary set of phonological symbols is the only thing to
leak back to feed PCA is architecturally strange. Further, as argued by Carruthers (2006,
general phonological process, so Paster?s only argument is the existence of reduplicated forms with multiple
[f]?s pointing to the absence of a language-wide ban on [f...f] subsequences. This is insufficient however, as
it is well-attested that a phonological process can underapply in reduplicative contexts.
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p.59-60) the rejection of inaccessiblity of the internal computation of modules defeats the
purpose of dividing processing into sub-systems running different algorithms.
Another glaring problem with Scheer?s thesis is the mistaken equation of segmental
material with what is inputed and suprasegmental material with what is computed. Scheer?s
modularity argumentation justifies a split as to what can inform PCA by distinguishing
inputs to phonology from computed phonology, and the rest of his discussion attempts
to equate this split with the segmental vs. suprasegmental split. But these two splits
are not the same, and the clearest problem is tone. Although cases of tones that are
computable from the melody exist (e.g. the rule of Low Tone Insertion on voiced sonorants
in Digo employed above in 3.3.3 as well as by Kisseberth (1984)), tone needs to be stored
lexically in many languages, and therefore there is no getting around it being an input to
phonology. But there are well-attested cases of PCA sensitivity to such lexical tone patterns.
A relatively simple example comes from Hausa plurals as mentioned in Dimmendaal (1987,
p.202) and Carstairs-McCarthy (2001, p.115): for bi-syllabic roots the ones with High-Low
or Low-High tone patterns take -una, and the roots with a High-High pattern take -ye9.
Another example of PCA sensitive to lexical tone is the Ngizim previous reference marker
as described by Schuh (1977, p.32-33). This marker takes the form -wu? after a low-tone
monosyllable ending in a long vowel or diphthong, -?w after a/i/u, and -gu? elsewhere, mean-
ing after consonants, mid-vowels, and diphthongs. This implies some cases where the only
determinant is lexical tone (e.g. da?a-wu ?the town? vs. shu?u-gu? ?the shit?). There is no
sonority or prosody generalization to draw. Note further that Schuh describes two varieties
of Ngizim, one spoken by younger speakers behaving as described above (with final [k] as-
similating in voicing to -gu?), and one spoken by older speakers in which final roots with
/k/ lose it and behave as vowel-final.
Although these last two examples are not about segmental content, they are definitely
about input content, as those tonal melodies need to be pre-specified in the lexicon and are
not computed, hence it does not adhere to Scheer?s input-vs.-computed dichotomy.
Of course one could imagine a machinery of tone in which all tonal information is
computed from segmental melody. This would allow the lexical information to be carried
9As for tri-syllabic roots, both authors only say they ?tend? to take the suffix -ai, without more discussion.
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by lexical items in a non-suprasegmental way while also leaving everything suprasegmental
computed. But surely that would be both a hack and circular reasoning. There is no
independent justification for putting lexical tone on segments; in fact a lot of the justification
behind autosegmental phonology is that tones largely behave independently from segments
and are frequently best analyzed as underlyingly floating. A theory of tone in which floating
tones are derived from segment-internal tones seems like a step backward. It would also
lead to numerous problems, e.g. cases of affixes that have been analysed as floating tones
without any segments (e.g. Tiv in Odden 1995) would now need to be re-analyzed with
some segment for the tone to come out of.
While it may seem forced to propose this type of computation for tone which Scheer has
not proposed, there is a similar conceptual problem is the issue of how sonority information
becomes suprasegmental and available for PCA. Surely something that takes the segmental
information of ?Consonant, ?Approximant, ?Sonorant (or their Element Theory equiva-
lent, which is the framework in which Scheer writes) and recapitulates it above the skeleton
would be the same type of hack as I described for tone. But Scheer?s suggestion is more
indirect:
It is undisputed that syllable structure is a function of two and only two prop-
erties: the linear order of segments and their sonority. The sonority of segments
is thus legible from above the skeleton by simply looking at syllable structure.
(p.349)
Leaving aside the comment that this is undisputed10, the claim is straightforward.
Scheer does not claim that sonority itself is suprasegmental, rather he posits that sonority
informs syllabification, and this syllabification is then visible to PCA.
As an example he discusses an analysis of infixation in a specific variety of Tagalog in
which infix placement appears to depend on sonority. In this variety some people infix -um-
10Not even the existence of syllable structure is undisputed (Samuels, 2009, ch.3). But even if we focus
only on pro-syllable analyses, it is arguably indispensable to refer to other features. Consider the syllables
of Atlanta, as opposed to apply and occlude. The different syllabification behaviors of [Vt.lV] sequences, in
contrast to [V.klV] and [V.plV] in English will have to reference place of articulation in the blocking of [tl]
onsets. Despite Scheer?s claim that everyone agrees, the proposal that only linear order and sonority are
involved is a radical claim that does not seem capable to even describe all the English facts without a radical
departure from the traditional account of English syllables.
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after the first consonant in stop-liquid complex onsets, but after the whole onset if it is
stop-glide. Scheer proposes that if stop-liquid onsets are syllabified differently than stop-
glide sequences, e.g. as branching onsets vs. separate onsets, the generalization is statable
the syllable level:
(58) Scheer?s analysis of Tagalog sonority-controlled affix position
However while this style of analysis works very well in this case where the relevant
property is how sonority affects onsethood and how the position of an affix can be stated
relative to these onsets, I do not see how it generalizes to all the cases above. The problem is
that while sonority may very well inform syllabification, syllabification rarely carries all the
information about sonority. It simply does not follow from the fact that syllables are build
using sonority that sonority is legible from the syllable structure. There is no discussion
in Scheer (2016) of how this strategy can extend to the cases discussed above in Swedish,
Kwamera, or Nishnabemwin aside of dismissing them since their generalization is stateble
by reference to sonority.
Consider again the Nishnaabemwin facts discussed in 5.3.4. Recall that the conjunct
third person suffix is -g after a nasal and -d elsewhere. Scheer dismisses this example
since the generalization can be made on the basis of sonority, but he gives no indications
of how CVCV phonology can actually handle this example. It is unclear what property
of syllabification is supposed to make nasals, and nasals alone, syllabified differently from
other consonants in final position, both the more sonorous consonants and the less sonorous
ones. It is also unclear what exact form those nasal codas could take in Scheer?s system:
strict CV phonology?s only representational degrees of freedom are branching and empty
Cs or Vs, and since final /n/ in simple coda can?t be any more or less branching than any
other Nishnabemwin consonant then it must be an empty CV, or a lack thereof, somewhere
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that is causing the allomorphy. But if so then should we not expect more effects than
merely conditioning allomorphy? E.g. given that Nishnaabemwin stress treats the end of
the word specially, saving final vowels from deletion and counting from the final foot for
stress (Valentine, 2001, p.51-55), we might predict some effect of final /n/ on stress, but
those have not been reported and in fact sound to me very unnatural.
Similarly the Kwamera facts of 5.3.6 again: the perfective is 1n- before non-high vowels
and uv- before high vowels and consonants. The same question arises: what principle of
syllabification is supposed to syllabify initial high vowels differently from initial non-high
vowels?
All in all, Scheer?s proposal when it comes to sonority is too hand-wavy to be useful. It
is not enough to say that sonority can influence syllabification and that PCA can see that
to show that this is indeed a viable strategy. Scheer gives no examples or suggestions for
how to translate a sonority generalization into a CVCV syllabification-based analysis.
5.4.7.2 Empirical problems
There are also a small number of exceptions to Scheer?s generalization, examples of PCA
that do not seem to be reducible to prosody or sonority, or re-analysable as complexity in
an autosegmental representation.
Consider the Mehinaku genitive as described by Mori (2007, p.255-256) and de Carvalho
(2015, p.127). The genitive suffix of Class 1 nouns has four allomorphs: -le after final
[e], -ra after final [i], -?a after final [1], and -la after final [a] or [u]. Carvalho explicitly
claims that no single underlying form could derive these allomorphs given our knowledge of
Mehinaku phonology, and there are so many segments involved that there is no room in an
autosegmental representation for a Floating-Segment-Replacement strategy like that used
for Caddo above. The only Mehinaku CV sequences reported to be unattested are *?i, *l1,
*re, *r1 and *wu (Mori, 2009). This does not seem enough to account for all of the changes
even if all four consonants and three vowels were packed together in a string to fight over
the same CV. In contrast this pattern is easy to handle in PROP with a form like (59) with
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sticky-ends seeking specific vowels.
(59)
?
[e] l e
?
[i] r a
?
[1] ? a
[ ? %] l a	 %
A second example that does not fit Scheer?s prediction is from Menya (Papuan). White-
head (2004, p.75-76) mentions that many Menya verb stems have two forms: one ?basic?
form found before a consonant other than /q/ and a ?derived? form found before a vowel
or /q/. Whitehead is very explicit that these changes are idiosyncratic and do not reflect
general processes of Menya. Some of these alternations are relatively small changes, such
as pa?k & pa?s ?hit/kill?, ma & me ?get/have?, and others are completely suppletive such as
mi & nyua? ?birth?, p & sua? ?harvest?. Some examples in context are shown in (60). There
is no phonological consistency in the forms, e.g. ?tour? ending in [a?] in the basic form and
[i] in the derived form, but but ?birth? ending in [i] in the basic form, and [a?] in the derived
form, making any derivation based on regular phonological processes hopeless.
(60) Menya Root variations (Whitehead 2004, p.76)
Gloss Basic ?they?re going to ? Derived ?not- -ing? ?we?re going to ?
root -p-Nqa?-i root ma- -qa? -atu-Nqa?-i
-23p/irr-goal-ind neg- -dvzr 1p/irr-goal-ind
get/have ma mapNqe me ma?meqa? metuNque
tour ika? ika?pNqe iki mi?kiqa? ikituNque
act q qpNqe qiy maqiyqa? qiyatuNque
hit/kill pa?k pa?kpNqe pa?s mapa?sqa? pa?satuNque
birth mi mipNqe nyua? manyua?qa? nyuatuNque
harvest p ppNqe sua? masua?qa? suatuNque
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Another example is from Seri. Marlett (1981, p.58-62) describes the suppletion of the
Action/Oblique Nominalizer, which combines both morphological and phonological condi-
tioning. The form of this prefix can be described by following the following rules in this
order:
(61) Seri Action/Oblique Nominalizer prefix
1.before the verb /ap/, ?stand?: /Pi-/
(/i-Pi-ap/ 3P-NOM-?stand? = ?my standing?)
2.before a +low short V or C: ?
(/Pi-?-emen/, ?my winnowing it?)
3.before a passive: /P-/
(/Pi-P-a:P-kas?ni/, ?my being bitten?)
4.before a vowel that is +Low or +Back: /y-/
(/Pi-y-otx/, ?my arising?)
5.elsewhere: /P-/
(/Pi-P-ip/, ?my staightening it?)
There is a lot that could be said about this pattern of affix , but what is relevant to the
discussion at hand are steps 4 and 5: this is a case of PCA sensitive to vowel backness.
This means that for any non-passive verb starting with a non-low vowel, vowel backness
determines the y-/P- suppletion.
Seri has multiple very complex patterns of allomorphy, many of which boil down to
regular phonology, and a lot of care was given by Marlett (1981) to finding regular rules
able to derive these forms, so we can trust that regular Seri phonology is unlikely to be
able to derive this. A Floating-Segment-Replacement analysis seems hopeless in light
of the fact that sequences of [y] with front vowels and [P] with back vowels are appar-
ently allowed on the surface: e.g. [p-y-i:m], 1sS-dist-?sleep? (p.20), and [P-oko:-Po], 1P-
ObjectNonfutureNominalizer-?see/saw? (p.57).
Anjos Gonc?alves da Silva (2011, p.121-123) describes another example of melody-conditioned
allomorphy in the Katukina-Kanamari intransitivizing suffix. This suffix surfaces as -k after
/u/, -i after [-sonorant] consonants and any other vowel, and -hiK after [+nasal] segments
125
(non-nasal sonorants cannot occur in the coda, plus in this positions all non-sonorants
neutralize to [k^] and all nasals neutralize to [N]).
Another problem can be found in Zulu. Lanham (1953, p.148) and Posthumus (2006,
p.128) describe a prefix variously called the copulative or the identificative, which is ng-
before [a,e,o,u] and y- before [i]. There is no language-wide ban of ngi or ya/ye/yo/yu
sequences in the language. This sensitivity to /i/ vs. /u/ cannot be captured with sonority.
Nakanai also poses a challenge. Johnston et al. (1980, p.136 fn.2) mention that the
reciprocal/causative prefix has the form va- before vowels, [h] and [l], and vi- elsewhere.
Examples of word boundaries with [i] followed by [l] or vowels or [a] followed by consonants
other than [h], [l] are numerous in Johnston et al. (1980) (though admittedly not sequences
of [i-h]). Nakanai has another liquid [r] as well as fricatives [v] and [s] hence there is no
generalization of [l] and [h] to make in terms of sonority.
A number of additional examples involve small allomorphs or are not fully suppletive and
therefore I cannot rule out that my inability to imagine giving them a Floating-Segment-
Replacement treatment is due to my lack of imagination and not to a problem of the theory,
but in all cases the facts involved seem to be somewhat too complex to really be handled
in one autosegmental UR.
One such example is from Witsuwet?en. Hargus (2011, p.229-231) describes the sec-
ond person singular possessive prefix, which has the form nj- before vowels, nasals, [s],
and [z], and n- otherwise. Before a consonant the form nj- further epenthesizes a schwa,
nj@-. Vowels, nasals, and sibilants to the exclusion of other fricatives and [l] cannot be
captured in terms of sonority, and this cannot be surmised to a general phonological pro-
cess as e.g. [n]+vowel and [nz] sequences can occur at other morpheme boundaries with
the perfective (@)n-, e.g. [ni-n-in-ye] ?stay/stop?+cnj-perf-?sg. go? (p.781,813), [ho-n-zu]
areal+perf+?be good? (p.622).
Another case that looks difficult for Scheer comes from Garland and Garland (1975) and
their description of the future suffix in Koiali. The future is -si after /i/, and -i elsewhere,
e.g. hei-si ?I cut-fut? vs. ta-i ?go-fut?. Given that /s/ is found after other vowels (e.g. in
the suffix -seleve ?really? in the manner slot of the verb, eleg-eve-seleve-holi-holi-n-u ?see-
Pl.Obj.-really-not-not-sing-past?) deletion of /s/ after vowels other thant /i/ sounds like a
126
poor analysis. However I cannot find the data or information about Koiali phonological
processes to reject various other hypotheses such as [s] epenthesis in i i.
Another example is found in Movima. Haude (2006, p.64) describes the allomorphy of
the intensifier/phasal aspect marker morpheme which is /uk/ after /a/, /ajP/ after /u/,
and in free variation between the two elsewhere, i.e. after /i, e, o/. The sensitivity to
/i/ vs. /u/ cannot be accounted for via sonority or prosody alone. However the reason
I cannot fully dismiss a Floating-Segment-Replacement analysis here is that the phoneme
/jP/ seems to have a very limited distribution, ?usually after the vowel /a/? (Haude, 2006),
hence a derivation based on underlying /ajP/ with dissimilation of a to u after a followed
by delinking of /jP/ after u with re-attachment of a floating k is plausible.
Another difficult case of partially suppletive melody-controlled PCA is in Hawaiian.
Elbert and Pukui (2001, p.76) describes the Causative/Simulative prefix which has the
form ho- before a glottal stop followed by a long vowel, ho?- before a glottal stop followed by
a short vowel, ho?P before /i/, hoP before /e, a, o/ and sometimes /i, u/, and hoPo before any
consonant other than the glottal stop. Because all these changes involve length or segments
that are either present or absent I cannot fully dismiss a floating segment analysis in which
the /P/ and the second /o/ are floating and only attach in certain contexts, but such an
analysis would require ad hoc assumptions about P-initial words.
Also difficult is the allomorphy of the Muskogee Patient Agreement markers. Martin
(2011, p.168-171) gives the forms of the 1S, 2S, and 1P agreement markers as respectively
?a-, ?i-, and po- before consonants and short /i/ and a?a-, i?i-, and ipo- elsewhere. This
is further complicated by the behavior of the vowel-vowel sequences created by these al-
lomorphs. When the second vowel is /o/ or /o:/, the first gets deleted; when the second
vowel is short /i/ or /a/ this second vowel gets deleted; and when the second vowel is long
127
/i:/ or /a:/, this second vowel gets deleted and the first lengthens.
(62) Muskogee Patient agreement marker 1S prefix
/na:fk/ ?hit? [?a-na:fk-i:-s] ?he/she is hitting me?
/inokk-/ ?be/get sick? [?a-no?kk-i:0s] ?I am sick?
/otak-/ ?hug? [a?-o?ta:k-??s] ?he/she is hugging me?
/anoki?-/ ?love? [a?a-nok???-i:-s] ?he/she loves me?
/a:fa?k-/ ?be/get happy? [a?a-:fa??k-i:-s] ?I am happy?
/i:lisk-/ ?be/get sulky? [a?a-:l??sk-i:-s] ?I am sulky?
However an analysis of Muskogee based on prosody and sonority cannot be fully dis-
missed since the Muskogee vowel system is /i, o, a/, and hence short /i/ can be singled
out from other vowels through sonority and prosody alone, but again I do not see how
the sonority difference between /i/ and /a,o/ can be reflected at the syllable level in near-
minimal pairs like /inokk-/ vs. /amoki/. The forms with short /i/ would need to have
some difference at the CV level compared to /a/ and /o/ to drive the allomorphy, but /i/
and /a/ can?t be too different either since they behave the same in terms of vowel deletion
in contrast to /o/. I do not see how all this information can be packed autosegmentally
in a single UR, particularly not if it is meants to follow directly from CVCV-phonology?s
assumptions.
Another difficult example comes from a Tuvaluan coordinating conjunction described
by Besnier (2002, p.152-153) which has the form kae, except before initial [k] where it has
the form a. The natural Floating-Segment-Replacement analysis would involve dissimila-
tion causing delinking of the /k/ of kae, however a general delinking of /k/ before /k/ is
implausible in Tuvaluan given other examples of syntactically close [kV+k] sequences at the
surface. The preposition ki can occur before /k/-initial words, ki kaleve ?to toddy? (p.175)
and the negative marker seki that can occur before /k/-initial verbs, seki kkau ?neg join?
(p.573). But even if we accept this delinking of /k/ before /k/ across vowels, I do not see
how this would easily account for the dropped /e/. If anything in CVCV phonology the
delinking of a consonant should open up more vowel slots, this is the whole logic behind
128
CVCV phonology?s approach to compensatory lengthening, but here we have a case in which
a delinked consonant causes fewer vowels to surface.
One other problem is found in Aguaruna as described in Overall (2007, p.78). Mul-
tiple suffixes of the language have a ?short form? and a ?long form? with idiosyncratic
phonologically- or morphologically-conditioned distributions. One in particular is a loca-
tive/different-subject suffix, which has the long form -n?? after /i/ or /1/ and -?? elsewhere.
Complicating a phonological analysis, there are multiple examples of morpheme boundaries
between a vowel other than [i]/[1] and [n], contradicting a deletion analysis (e.g. with the
accusative -na: kamisa-na ?clothing-acc?, tayu-na ?oilbird-acc?). Further, vowel sequences
arising at morpheme boundaries, including [i-i] and [1-i], seem to be resolved with deletion,
not epenthesis (e.g. with the declarative -i : [puha?mi] </puhu-a-m1-i/ ?live-impvf-2-decl),
complicating an analysis with insertion or docking of a floating /n/.
Another allomorphy pattern that seems difficult to account for with only CVCV me-
chanics but that I cannot prove is impossible is found in Vitu as described in Van den Berg
and Bachet (2006, p.30-31). The nominalizing suffix has three forms: -aNa after /e/, -Na
after /a/ (and one exception in /i/, hani-Na ?food? from hani- ?eat?), and -a elsewhere, i.e.
after /i, o, u/ (Vitu does not allow closed syllables and all roots end in a vowel, p.12).
Van den Berg and Bachet point out that the choice of -Na over -a, can reasonably be at-
tributed the fact that [aa] sequences are not permitted in the language, but it is still a
challenge for a Floating-Segment-Replacement analysis as sequences of other vowels and [N]
are allowed, making a delinking hypothesis untenable (e.g. vari-Noro-ai ?sleep? (p.81) with
the circumfix vari-...ai inflecting intransitives for a plural subject; vari-kodo-Ni ?help each
other? (p.80) with vari- marking reciprocals on transisitive verbs). And even if the choice
of -Na is explained there remains -aNa after /e/ to explain.
Another difficult case is reported in Kosena by Doreen (1974, p.15-16). Kosena has a
set of prefixes which mark the possessor of certain nouns and the object of transitive verbs.
The 2nd person non-singular and the 1st person are respectively t-&tu-&tin-&ti- and s-&su-
&sin-&si-. t- and s- occur before /o/, /aa/, /i/ & /u/, tu- and su- before /w/, sin- and tin-
before /k/, and si- and ti- elsewhere. Both the sensitivity to mid vowels /e/ vs. /o/ and the
sensitivity to /k/ vs. other stops are a problem for an analysis based on sonority and the
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latter is also unlikely to be able to receive a Floating-Segment-Replacement phonological
analysis since the normal outcome of nasals followed by stops in Kosena is not deletion but
assimilation (p.9-12).
And finally a few more examples that seem to pose a serious problem, but where the
data or analysis in my sources is either doubtful or very scant.
One such case which might be complicated for Scheer is the French allomorphy of [?f]&[?]
?egg? in Swiggers (1985). Contrary to most prescriptive and descriptive sources saying that
varieties of French that still distinguish the two have [?f] in the singular and [?] in the plural,
Swigger claims the existence of speakers for whom the allomorphy does not in fact track
morphosyntax, but rather the presence of /z/ before it, giving the forms [lez?] ?the eggs?,
[d?z?] ?two eggs?, [siz?] ?six eggs?, and [diz?] ?ten eggs?, but [kat??f] ?four eggs?, [sE?k?f]
?five eggs?, [sEt?f] ?seven eggs?, [4it?f] ?eight eggs?. This pattern, if indeed it represents a
real variety of French, would be a problem for Scheer11. One caveat however is that I am
skeptical of the existence of this variety. The [?f]&[?] allomorphy, and plural allomorphies
in general, has been in flux in spoken French for centuries and finding people who use either
at different times is not difficult. It is very possible that Swiggers is reading too much into
what is really free variation or multi-dialectalism.
Another potentially difficult case with too little data to thoroughly trust is found in
Ikpeng according to Pacheco et al. (1997, p.39). Pacheco gives a table of the phonological
conditioning of possessive prefixes which claims that the third person possessive is e- before
the forms [-eren-], [-engru-] and [-mtag-], and i- before [-amto-], [-laglu-], [-lu-], and [-pun-].
This could be read to mean that the form is e- before non-low vowels and nasals, and i-
before low vowels and other consonants, but with such a poor sample of Ikpeng segments
and no discussion of the table in the main text, it is hard to know exactly what classes
of sounds are intended by Pacheco. The author?s further works, although showing explicit
11One alternative for Scheer would be to cpitalize on the fact that there is a commonality among all of these
[z]?s, namely they are all liaison [z] plausibly marking the plural. Hence one could conceive of this allomorphy
not as phonologically-conditioned by /z/, but morphologically-conditioned by the plural morpheme. This
analysis would not be without complication either as it raises the problem of why this [z] is not present in
other numerals. In isolation the presence of [z] could be given a lexical explanation in terms of some words
having a floating /z/ and others not, but if it is lexical then we lose the potential morphological explanation
of the allomorphy, hence the morphological analysis would require to put the complexity of whether /z/ is
present or not into the morphosyntax.
130
focus on the allomorphy of possessive prefixes, focuses entirely on the split between what
he calls Series I and Series II, which is irrelevant to e-/i- as both are Series II. Pache?co
et al. (2001) claims in a table that e- occurs before consonants followed by [e] or [a], which
contradicts the table of Pacheco et al. (1997). Pacheco (2007) has the allomorphy in tables
but never mentions it, focusing only on the Series I/II allomorphy. This ambiguity suggests
that either Pacheco retracted from his 1997 analysis or that he never had a solid analysis
of e-/i- in the first place.
All of these empirical challenges would need to be addressed for the proposal to have
a chance of being true, but the proposal as it is is too hand-wavy to even know how one
could go to analyze the above data.
5.4.7.3 Falsifiability Problem
However it remains true that cases of PCA unambiguously sensitive to melody are vanish-
ingly rare. Neither Paster (2006), Bye (2007), nor Nevins (2010) mention any clear case
in their surveys of PCA other than the ones Scheer has alternative accounts for like the
Tahitian example. Scheer?s claim therefore still appears to have some force as a very strong
typological tentency. Given, based on the empirical problems of the previous section, that
the problem likely is not architectural, it is plausible that external factors of diachrony or
learning could better explain it better.
However, one good reason why Scheer?s claim is so hard to find counter-examples for is
that ultimately it does not really prohibit that many features from participating in PCA: the
allowance of all sonority allows vowel height and consonant manner to influence PCA, so all
things said and done there are very few things left outside of the predicted typology: voicing,
place of articulation, and secondary features are pretty much the only features actually
predicted to be impossible triggers of allomorphy. And even when one finds one of those,
it is very difficult to completely reject a Floating-Segment-Replacement analysis, because
even with its limitations there is still a lot of room for allomorphs in an autosegmental
graph, and affixes overwhelmingly tend to be very short in all languages, and they tend to
be phonologically similar. Any reasonably short or similar set of suppletive allomorphs can
plausibly be fitted together in a string and set to compete over one or two floating CVs.
131
So the only thing that can fully falsify Scheer?s claim is a set of long fully suppletive
affixes, sensitive to place of articulation or secondary features. I suspect one of the reason
those are rare is simply that they cross-cut so many categories.
5.4.7.4 PROP remains modular
I agree with Scheer (2016) on the fact that standard theories of allomorphy require a mor-
phosyntactic module that reads phonological symbols, and they are therefore anti-modular.
I also agree with the argument against a morphosyntax that can see phonology. It is impor-
tant to maintain the Principle of Phonology-free syntax defended by Zwicky and Pullum
(1986). However the solution does not require us to segregate the symbols manipulated
by phonology into a set of melody input symbols that morphology cannot see and a set of
prosodic and sonority symbols that is allowed to leak back into morphosyntax. PROP offers
a different solution: no allomorphy happens outside of phonology whatsoever and vocabu-
lary insertion is done in a completely myopic way. Allomorphs are stored within a single
representation and phonology-internal organisation is responsible for selection. Vocabulary-
insertion does not need to see any phonological environments because there simply is no
conditioned insertion in PROP, there is only conditioned attachment within the phono-
logical module. This achieves the desired modularity without having to stipulate what can
be in URs and what can leak back to inform allomorphy.
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Chapter 6
Morphologically-Conditioned Allomorphy
Not all allomorphy is phonologically predictable. In some cases allomorphy is sensitive to
specific lexical items, as in Morphologically-Conditioned Allomorphy (MCA) or a subcase of
it Lexically-Conditioned Allomorphy. This can also be accomplished within the phonological
module using the PROP technology we have discussed so far.
This chapter is not intended to be a complete survey of the phenomenon of MCA. The
first few examples will exemplify the basic mechanics of how MCA could be handled in
PROP, but the main goal is to exemplify advantages of parallel structures for MCA in
handling some complicated allomorphy patterns.
6.1 Examples
6.1.1 Romanian stem-allomorphy determining the suffix
This first type of allomorphy is sort of intermediate in that the analysis below is essentially
a phononological conditioning analysis, but it appeals to unpredictable properties within
the root that we haven?t seen yet.
Nevins (2010) discusses the fact that Romanian k -final nouns come in two varieties:
with or without a tS -final allomorph. The plural suffix -i and the denominal suffix -i can
only be affixed to k -final nouns with a tS -final allomorph, otherwise the suffixes -uri and -a
are used respectively.
(1) Romanian k -final nouns
gloss sg. pl. denominal verb
bagel(s) kolak kolatS-i 1N-kolatS-i, ?to roll up?
?fire(s) fok fok-uri 1N-fok-a, ?to fire up?
133
This can be handled in PROP with roots containing both allomorphs like (2) and suffixes
seeking a [+hi] consonant like (3) (or any feature that captures palatals). The formed
optained in (4) will serialize as desired after 	-delinking.
?
(2) kolak
tS
# k o l a %
k
(3) Romanian plural suffix (incomplete)
[[+hi]? ?%] i
%
	
[ ? %] u r i
(4) kolatS-i
?
tS i
# k o l a %
	
k
	
u r i
However in the case of roots without this allomorphy in the root like (5), the form will
assemble as in (6).
?
(5) fok
# f o k %
134
(6) fok-uri
i
# f o k %
	
u r i
This simple example shows that some of the complexity of allomorphy can be handled
by packaging it into morphemes.
6.1.2 English Adjectivizer
Some cases of morphologically-sensitive suppletion are difficult to attribute to the phono-
logical content of roots, even with internal complexities like those assumed for Romanian
and Spanish above. For instance English adjectivizers are lexically-conditioned by the roots
they attach to without any way to characterize the alternation phonologically.
(7) English adjectivizers
hill hill-y
moutain mountain-ous
pole pol-ar
equator equator-ial
boy boy-ish
girl girl-y
Alps Alp-ine
Andes Ande-an
It might be tempting to dismiss this allomorphy by suggesting that -ous, -y, -ar, -ial, -ish
-ine, -an, -ic and other adjectivizers are not allomorphs but different vocabulary items with
their own semantic contribution. The choice of words in (7) is intented to argue against
this idea in the lines of Isitt (1983). Surely hills are hilly in the same way mountains are
mountainous, the poles are polar1 in the same way the equator is equatorial, boys are boyish
in the same way girls are girly, and the Alps are Alpine in the same way the Andes are
1As is well known, the -ar and -al variants are etymologically related and derive from dissimilation in
Latin. Examples of English neologisms that do not respect this dissimilation suggest this is not productive
in English, e.g. such as familial or dialectal. the use of ial vs. al is not productive either, as shown by pairs
such as equatorial, hence I will not discuss a phonological analysis of -ar
135
Andean. There is no semantic difference between these pairs, there is simply complementary
distribution, predictable from the lexical item, and hence allomorphy in the sense of Hockett
(1954, ?2.7). This is not to deny that some adjective heads are truly separate with their
own lexical entry and semantics, e.g. -able, but those are not in complementary distribution
with the suffixes above and they make a very distinct semantic contribution.
In Distributed Morphology this type of allomorphy is accomplished with exogenous lists
in the vocabulary-insertion module. The form -y would be inserted in the environment
? ? ?
of the roots in the set { hill, girl, mess,. . . }, -ous in the context of roots in the set
? ?
{ ?mountain, bulb, courage, . . . }, and so on. This requires dedicated machinery in the
vocabulary-insertion module.
In PROP we could seek to give each form phonological content capable of deriving the
correct form in the lines of the Romanian and Spanish analyses above, following the pro-
gram of Ulfsbjorninn (2016) and Barillot et al. (2018) to get rid of class-driven allomorphy
and reduce it to phonological allomorphy through full use of representation. However I
will not attempt here to give such an analysis to every case of apparent morphologically-
conditioned allomorphy as it would take us too far astray. I aim to discuss the patterns
of morphologically-conditioned allomorphy and what PROP can solve about them, not the
small details of selection. After all even in absence of diacritic-free analyses, we can account
for this kind of allomorphy in PROP as SUF using only the technology we have so far, with
alternatives in the underlying form and sticky-ends specifying which one attaches. The use
of diacritics in this chapter should therefore not be taken as a strong proposal in favor of
arbitrary features and a rejection of the class-eliminativist program. All that is needed is a
way to encode the selection within the underlying form, and we have all that is needed for
this: the arbitrary features we posited to account for Lakhota infixation in 4.4 and Wolea-
ian reduplication in 4.7, except this time encoding not the position of the affix, but which
alternant will attach at all. As such the roots will be stored as (8), and the adjectivizer
suffix has an underlying form in the ballpark of (9).
136
(8)
a. # h I lA %
b. # m aU n t I nB %
(9) English adjectivizer (incomplete)
[A] i
[B] @ s
[C] @ ?
[D] i @ l %
[F ] I S
[G] aI n
[H] @ n
...
A form like (9) will correctly attach to the forms in (8) because only one sticky-end will
137
find a segment bearing the correct feature as in (10) and (11).
(10) hill-y
# h I lA %
i
[B] @ s
[C] @ ?
[D] i @ l
[F ] I S
[G] aI n
[H] @ n
...
(11) mountain-ous
[A] i
# m aU n t I nB %
@ s
[C] @ ?
[D] i @ l
[F ] I S
[G] aI n
[H] @ n
...
There is nothing elegant in this analysis. The claim here is not that the PROP analysis
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above is aesthetically superior, but that it can be accomplished within the phonological
module using only the technology that was independently argued for to account for infix
position and PCA. A superior analysis would ascribe a specific phonological form to the
roots above
I would however contend that there is at least nothing less elegant about this analysis
compared to the alternatives. All theories need to account for this phenomenon through
some unpredictable mass of information that must be stored somewhere, and whether we put
that information in the form of lists in the vocabulary-insertion module (as in Distributed
Morphology) or as features on roots will multiple morpheme-internal alternatives, it will
look messy in the end. The advantages of SUF allomorphy are conceptual: in PROP there
is no need for powerful contextual insertion mechanisms in a vocabulary-insertion module,
allomorphy is done using only pieces of phonology that are independently justified. In
PROP allomorphy is done entirely after vocabulary-insertion within the phonology using
information stored on affixes.
There is also at least one weak other argument in favor of storing features relating to
morphological features on the root rather than as a list: intuitively it is much easier for
someone to tell of a specific root whether it is irregular than it is to list all irregular verbs,
or all the roots that take a specific allomorph. This is perhaps surprising in Distributed
Morphology because there should exist a list of all the roots that take each affix ready in
the vocabulary-insersion module, but not in the analysis described here. If the lexical class
of a root is information stored in the underlying form on a specific segment, then listing
all forms of the same class should be about as hard as listing all the roots with a specific
phonological feature, and that is indeed hard.
The rest of this section will discuss other phenomena that can be accounted for with an
SUF approach to MCA in PROP.
6.1.3 Allomorphy and Affix position in Nisga?a
The feature mechanics employed so far can account for cases in which there is simultane-
ously affixes with unpredictable-position and allomorphy at the same time. Sapir (1921,
p.62) describes the case of Nisga?a (Nass) in which there are four means of forming the
139
plural: prefixation, an?on ?hand?, ka-an?on ?hands?, wai ?paddle?, lu-wai ?paddles?; vocalic
change, gwula ?cloak?, gwila ?cloaks?; suffixation, waky ?brother?, waky-kw ?brothers?; and
reduplication, gyat ?person?, gyigyat ?people?.
In PROP, this requires us to use arbitrary features which serve double function indicating
both the choice of allomorph and its position. The roots would look like (12).
(12) Nisga?a Roots
a. # aK n o n %
b. # wL a i %
c. # gw iF l a %
d. # w a kyKW %
e. # gyR a t %
Finally an affix like (13) sensitive to those features will attach to the forms just as
140
desired, forming the words in (14) (ignoring all the parts dangling from # and %).
(13) Nisgha Plural affix2
# q a [K]
# l V [L]
[ ? [F ]] u [[F ]? ]
[KW] kw %
[R] [R]
(14)
k a
a. # aK n o n %
l V
b. # wL a i %
u
c. # gw iF l a %
kw
d. # w a kyKW %
e. # gyR a t %
2Tarpent (1983, p.130) notes that the prefixed allomorph is lV - which appears with different vowels
depending on the stem according to what she calls the Vowel Specification rule: [@] before [P], [a] before [C?],
[u] before Cw, ? before [l], and [i] elsewhere. It is not clear whether this assimilation is regular for Nisga?a
phonology or if it should be encoded as PCA, but as it is phrased as a rule I omit it from (14).
141
As we can see PROP has no difficulty accounting for all sorts of irregularities in the
location and form of allomorphs.
Note however that the vowel replacement in (14-c) is accomplished by adding a segment
parallel to another. This is perhaps a problem: I am assuming that this particular scenario
in which a morpheme introduced as segment in parallel to another it is not compatible
with, the added segment can circumvent the original one rather than add to it, which does
not follow from the assumptions we have proposed so far and therefore needs to be seen as
one more assumption of our system. This assumption was already used in multiprecedence,
within reduplication to account for fixed segmentism in which one copy has some internal
segments replaced by another (McClory and Raimy, 2007), and outside of it to account
for subtractive morphology (Gagnon and Piche?, 2007). I hope to be able to derive this
assumption from simpler axioms in future research.
All I can say about this assumption is that it captures the intuition of Hockett (1954,
?4.2) who leaned towards an analysis of took as a /t...k/ allomorph of take and an infixed
allomorph /u/ of /ed/, over analyses with portmeanteau morphemes, zero morphemes, or
a /u/</ej/ replacive process. This also captures the intuition behind the terminology of
Wallis (1956) who described replacive morphology as simulfixation (a slightly different usage
of the term than the one mentioned in chapter 3 due to Hocket) .
6.1.4 Lexically conditioned masculine marker in Catalan
Consider the masculine suffix in Catalan discussed by Nevins (2010). The affix has two
allomorphs: -u and -?, but verbs that normally take the null affix still surface with -u in
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the plural, where otherwise a sequence of two [s]?s would occur3.
(15) Catalan masculine
sg. pl. Gloss
a. gOt gOt-s ?glass(es)?
b. mos-u mos-u-s ?lad(s)?
c. gos gos-u-s ?dog(s)?
The masculine allomorphy of (15-a-b) can be accounted in PROP with roots like (16)
and a masculine affix like (17). The zero affix will attach to roots stored with a [Z] feature
that will de-link the /-u/, and otherwise only /-u/ will attach.
? ?
(16) gOt, mos
a. # g O tZ %
b. # m o s %
(17)
[ ? 	%] u
Z %[ ] ?
(18) gOt-?
u
	
# g O tZ %
?
3This is, at least, the commonly cited analysis. I see no reason a priori why this pattern could not be
accounted for with allomorphy in the plural affix, -us after /s/ and -s elsewhere leading to accidental partial
homophony with the masculine marker. I will however trust the common analysis that the [u] in gosus does
indeed mark the masculine rather than being part of the plural.
143
(19) mos-u
u
	
# m o s %
But to account for the behavior of (15)[c] we need two things. First we need a [Z]
feature so that the singular form can appear with the zero allomorph as in (20).
(20) gos-?
u
	
# g o sZ %
?
But in the plural the presence of the second /s/ must force the /u/ allomorph to surface.
After attaching the plural we get a form like (21) with the /s/ following all segments that
precede %. I propose a rule like (22) applying before 	-delinking. Multiple rules are
plausible, as long as it has the effect of delinking the link bearing ?. The resulting graph
is in (23), and 	-delinking does not apply, resulting in the desired surface form gos-u-s.
?
(21) gos+ u+ s
s
	 u
# g o sZ %
?
(22) If there is an /s/ that precedes another /s/, de-link any path from that first /s/ to
%.
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(23) gos-u-s
s
	 u
# g o sZ %
We will return to phonological operations affecting graphs in chapter 9.
6.1.5 Final Consonants in French Adjectives
French adjectives tend to have a C-final form in the feminine and a masculine form without
that final consonant. Adverbial forms with -ment are uniformly formed from the ?feminine?
allomorph. A traditional explanation of this fact makes use of a final consonant deletion
rule and a feminine suffix in the form of a vowel that bleeds the deletion before being deleted
in turn. Such a derivation would like like (25).
(24) French regular adjectives
f. m. adv. gloss
fos fo fosma? false,falsely
la?t la? la?tma? slow,slowly
?r?z ?r? ?r?zma? happy,happily
bla?S bla? bla?Sma? white,whitely
(25) Traditional derivation
f. m. adv.
UR fos+@ fos+? fos+@ma?
C>?/ % ? fo ?
@>? fos ? fosma?
SR fos fo fosma?
Booij (1997) remarks that this traditional explanation is insufficient to explain the whole
set of facts, in particular the fact that even in the case of irregular pairs it is the feminine
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form that is used for adjectives.
(26) French irregular adjectives
f. m. adv. gloss
bEl bo bElma? beautiful, beautifully
sES sEk sESma? dry, dryly
vjEj vj? vjEjma? old, oldly
The fact is therefore more appropriately viewed as selection for the ?feminine? form,
rather than as a regular derivation from a root. French Adjectives have two forms existing
independent of gender, and different contexts select one or the other. This type of fact
is what leads Booij to argue in favor of allomorphy operating over paradigm slots, and
to posit a morphomic level of generalizations that are neither lexical, nor syntactic, nor
phonological.
However the analysis of allomorphy we have used so far allows us to analyse the facts
of French adjectives entirely within the phonology with all the complexity limited to inside
the lexical items. One thing to note is that whether the final consonant of the feminine is
present in the masculine or not is unpredictable, as for every consonant that can drop in the
masculine an example can be found of an adjective where that same consonant is present in
both the feminine and the masculine as demonstrated in (27). The selection can therefore be
neither a phonological process nor a phonological conditioning without assumptions about
underlying forms as radical as what I am about to propose. The information for how to
derive the ?masculine? forms from the ?feminine? one must therefore be arbitrarily known
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for each root.
(27) Variable and invariable French adjectives
f. m. gloss
sEKtEn sEKtE? ?certain?
Zon Zon ?yellow?
vjolEt vjolE ?violet?
ipokKit ipokKit ?hypocrite?
gKa?d gKa? ?tall?
ymid ymid ?humid?
gKos gKo ?big?
mE?s mE?s ?thin?
gKiz gKi ?gray?
Koz Koz ?pink?
bla?S bla? ?white?
luS luS ?fishy, suspicious?
Za?tij Za?ti ?kind?
paKEj paKEj ?same?
lO?g lO? ?long?
bEg bEg ?stuttery?
leZEK leZe ?light?
fjEK fjEK ?proud?
I therefore propose that French adjectives come pre-specified with features marking the
end of each allomorph and different suffixes pick out one of those. A variable adjective
would have a form like (28), an invariable adjective would have a form like (29), and a
suppletive form would look like (30).
?
(28) fos
# f oM sF %
?
(29) Zon
# Z o nF ,M %
147
?
(30) sE(k/S)
SF
# s E %
kM
Affixes are simply sensitive to these features and will select them appropriately. The
feminine affix simply picks the segment bearing an [F ] features, and the masculine affix
picks the segment bearing an [M]. The adverbalizer also picks out the segment bearing [F ].
(31) French Feminine affix
[F ] %
(32) French Masculine affix
[M] %
(33) French adverbalizer
[F ] m a? %
A sample of complex forms follows.
(34) fos ?false? f.
# f oM sF %
148
(35) fo ?false? m.
# f oM sF %
(36) fosma? ?falsely?
m a?
# f oM sF %
(37) Zon ?yellow? f.
# Z o nF ,M %
(38) Zon ?yellow? m.
# Z o nF ,M %
(39) Zonma? ?yellowly?
m a?
# Z o nF ,M %
(40) sES ?dry? f.
S F
# s E %
kM
149
(41) sEk ?dry? m.
SF
# s E %
k M
(42) sESma? ?dryly?
SF m a?
# s E %
kM
This analysis shows some conceptual advantages of doing allomorphy with features on
the roots rather than with lists roots that participate in some process. If this were done
in Distributed Morphology the list of environments requiring to insert the ?feminine? or
?masculine? forms or to perform a readjustment rule would have to list the same list of roots
multiple times. But certain classes of segments recur throughout a language?s morphology,
making information storage in the root much more economical. The Feature [F ] in the
analysis above does not only serve as target for the feminine, it also serves as target for
the adverbalizer and in verbalization, thus performing double or triple duty. The feature
[M] also has other functions, as the ?masculine? is the form called for in adjective-noun
compounds, against expectations from agreement or the semantics of gender, e.g. grand-pe?re
[gKa?-pEK], ?grandfather?, but also grand-me?re [gKa?-mEK], ?grandmother?, and not *[gKa?d-
mEK]. The plausibility of these features on the UR is much reinforced if they are reused
multiple times in word-formation.
This entails that unlike analyses that take the two forms to be different affixes marked
for different gender, the theory proposed here suggests that the two forms are part of a single
morpheme unspecified for gender. In that it therefore resembles the analysis in Lamarche
(1996).
150
6.1.6 Hungarian bidirectionally-conditioned allomorphy in Plural Posses-
sives
Another way in which the fact that allomorphy is not fully settled at insertion can manifest
itself is by allowing for allomorphy to be conditioned by material inserted later in the
derivation, a pattern of allomorphy often termed outward sensitivity.
Embick (2010, p.44) discusses the case of the Hungarian plural when it co-occurs with
the possessive. The plural surfaces as [-Vk] in isolation, but as [-(j)ai] with the possessive.
(43)
sg. sg.-1sPoss pl. pl.-1sPoss gloss
ruha ruha?-m ruha?-k ruha-a?i-m ?dress?
kalap kalap-om kalap-ok kalap-jai-m ?hat?
ha?z ha?z-am- ha?z-ak ha?z-ai-m ?house?
In PROP the analysis of this phenomenon simply follows from defining each of the parts:
the plural needs to store both allomorphs, and the possessive needs to select one of these
allomorphs if it is available. The plural and 1s.poss look like (44) and (45) respectively4.
(44) Hungarian plural suffix
[ ? %] k %
aiF
4These graphs takes for granted that the harmonic vowel in the post-consonantal [-Vk], [-Vm] and the [j]
in [-jai] are epenthetic. Although I am not aware of any explicit claim to the matter, the former process has
an independent justification: Vago (1976, p.259-260) justifies an analysis with epenthesis breaking word-final
clusters e.g. /bokr/ >[bokor] ?shrub?, /tykr/ >[tyk?r].
In the worst case scenario, if neither of these epenthesis rules is justified and the alternations need to be
analysed as PCA based on V- vs. C-final selection, the graphs can be made to convey this, e.g. the plural
can instead be represented as the following:
[[V ]? %] k %
V
[[C]? %] j aiF
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(45) Hungarian 1s.poss
[ ? %]
	
m %
F ?[ ]
The plural therefore contains a regular [k] part and an [ai] that cannot be pronounced
unless something else finds its [F ] feature. And the possessive is normally a regular suffix
attaching after the last segment, unless it finds an [F ] feature. When the two affixes co-
occur we get the graph in (46). Again we must assume as in 6.1.3 above that the more
recently added links can circumvent others when put in parallel.
(46)
# r u h a % 	
?
k m
?
aiF
This analysis shows another advantage of delayed allomorph selection, namely it allows
for affixes inserted later in the derivation to influence allomorphy of material inserted earlier.
6.1.7 French preposition+article forms
Another example of morphemes added later in the derivation affecting the allomorphy of the
ones added prior to them comes from a well known phenomenon of French morphophonol-
ogy: the suppletive forms of some prepositions with definite articles. Descriptively, it causes
us to find du, au, des, and aux where *de le, *a? le, *de les, *a? les (respectively ?of the.m.sg.?,
?to the.m.sg.?, ?of the.pl?, ?to the.pl?) would be expected based on the independent preposi-
152
tions and articles.
(47)
preposition # f. V- f. C- m. V- m. C-
?sword? ?soup? ?donkey? ?dog?
? sg. l?e?pe?e la soupe l?a?ne le chien
pl. les e?pe?es les soupes les a?nes les chiens
a? ?to? sg. a? l?e?pe?e a? la soupe a? l?a?ne au chien
pl. aux e?pe?es aux soupes aux a?nes aux chiens
de ?to? sg. de l?e?pe?e de la soupe de l?a?ne du chien
pl. des e?pe?es des soupes des a?nes des chiens
The four forms in bold are where an interesting interaction between phonology and
allomorphy emerges. The masculine determiner le has an allomorph l? before vowels, and
the generalization is that sequences of a?/de and this determiner are replaced by au/du if
and only if the form le would be expected.
Zwicky (1987) explains the problem posed by these forms: if elision of le to l? is
phonological and the ?fusion? (in Zwicky?s terms) into du is morphological, then French
is demonstrating a phonological operation is taking precedence over a morphological one.
Embick (2007, 2010, p.63-) further points out that it is difficult even if both operations are
morphology-internal, as in Distributed morphology the Lowering responsible for the prepo-
sition going to the determiner is supposed to be an early morphological operation, and the
Article Cliticization is dependent on linearization which in his model should happen after
lowering.
This difficulty is what leads Bye and Svenonius (2010) and Svenonius (2012) to abandon
the strict modular and derivational assumptions of Zwicky and Embick and posit an analysis
in which constraints on minimizing exponence are ordered in the same constraint ranking
as phonological constraints. They propose competition taking place over a representation
containing multiple competitors for insertion, including ones differing in span. Candidates
for insertion are illustrated in (48) with squiggly lines connecting each morpheme to its
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insertion site. A constraint *Struct penalizing candidates with more exponents favors
the portmanteau spell-out of du over the individual spell-out of de and le, as in (48). The
blocking of du by de l? is analyzed as a case of the phonological constraint Onset ranked
above *Struct yielding (49).
(48) du parc (, p.)
a.
b.
(49) de l?ho?pital
a.
b.
This analysis is highly anti-modular, as it posits a single representation on which mor-
phosyntactic features and phonological material cohabit so as to be compared by a con-
straint ranking. The PROP analysis of this phenomenon is not in terms of portmanteau,
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but rather takes advantage of the representational power of directed graphs to have one
morpheme ?by-pass? another. The masculine determiner needs to look as in (50). The
prepositions de and a? look as in (51) and (52), respectively.
(50) French Masculine determiner
# l [ ? [V ]]
@F [ ? [C]]
(51) preposition de
	
@ #?
# d
y [[F ]? ]
?
(52) preposition a?
	
a #?
#
o [[F ]? ]
?
Here the du and au forms are taken to be allomorphs of the preposition. The replacement
of le is done with sensitivity to the feature [F ] on the schwa of le: the sticky-end linked
to /y/ always attaches to a segment following this schwa, and hence it causes the graph to
by-pass the le completely. But crucially, because the schwa only attaches to word-initial
consonants, the du and au morphemes will only find a segment following [F ] in C-initial
155
words, and hence the by-pass of the le will happen only in C-initial words, as desired.
(53) de l?a?ne
# A n %
a.
l @F
# A n %
	
b. d @ l @F
y
(54) du chien
# S j E? %
a.
l @F
# S j E? %
	
d @ l @b. F
y ?
# S j E? %
d @ l @c. F
y ?
This analysis offers an alternative to the two main theories used to analyze sequences
of syntactic terminals surfacing with a single morpheme: contextual zero-allomorphs and
portmeanteaux. Zero-allomorphs have always been treated with a lot of suspicion in mor-
phology. Hockett (1954, ?4.2) cleverly criticizes the analysis of took as an allomorph of
take with a zero-allomorph of /ed/ by pointing out that the same rules that allows such
an analysis would just as easily allow for took to be an allomorph of /ed/ accompanied
by a zero-allomorph of take. Matthews (1974, p.123) called analyses with zero-allomorphs
156
?desperate?.
Portmanteaux have often been received more favorably, but they require a system of
vocabulary insertion capable of handling variable size inputs, which adds complexity to the
vocabulary insertion system.
The PROP alternative here utilizes only the machinery elsewhere needed for phonology-
internal purposes while keeping the vocabulary-insertion in the form of a single mapping
from terminals to phonological URs without any comparison, competition, or context-
sensitivity needed. Morphemes can fail to show overt phonetic effects, not because they
are contextually zero, but because they were phonologically ?by-passed?.
157
Chapter 7
Interaction of parallel structures with
reduplication
In this section we will take for granted the parallel structures of the previous chapters
and discuss further interesting interactions with reduplication so as to fully tie the PROP
program into the Multiprecedence analysis of reduplication.
I will not offer a full-fledged ?linearization? or ?serialization? algorithm (now a misnomer,
as the final structure is no more taken to be linear or serial) in this thesis. I will simply
assume a few basic interactions between parallel structures. For instance I want to posit
that structures like (1) would be sent to the articulators as in (2). Essentially parallel
structures normally surface in both copies.
(1)
c
# a b e f %
d
(2)
c c
# a b e f a b e f %
d d
And I want to posit that (3) is resolved as in (4). Essentially reduplication is resolved
158
locally when it can, without interfering with parallel structures.
(3)
a b c d
# %
w x y z
(4)
a b c b c d
# %
w x y z
I also need to borrow an assumption for previous Multiprecedence analyses such as
McClory and Raimy (2007), namely that adding a parallel segment can result in replacement
in a single copy, as if the form traverses one arc in one copy and one in the second, such
that (5) surfaces as one of the forms in (6) (subject perhaps to parametrization). This is
similar to an assumption we had to make in ?6.1.3.
(5)
# a b c d e %
x
 abcde-axcde
OR
 axcde-abcde
And finally, and least intuitively, I posit that forms such as (6) are resolved as in (7). The
logic is simply that the X is not involved in the reduplication, and after the reduplication
is resolved X is left precededing both copies of what it was originally set to precede with
the net effect that it is restricted to the first. I will omit the redundant arc to the second
159
copy in the rest of this chapter.
(6)
x
# a b c d e %
(7)
x
# a b c d e a b c d e %
The rest of this chapter will discuss a number of cases in which reduplication interacts
with parallel material, or multiple lines of parallel material interact with each others.
7.1 Tuvan vowel and harmony overwrite in reduplication
Harrison and Raimy (2004) describe reduplication in Tuvan and give an account using
Multiprecedence. Tuvan has multiple reduplication patterns, but I want to focus on total
reduplication with vowel overwrite. This construction has the semantics of ?X or something
like X?. As seen in (8) the generalization is that the underlying vowel is overwritten with
[a] in the second copy, unless it is /a/, in which case the second copy gets [u]. The forms in
/a/ introduce some irrelevant complexity that I will not address. I take for granted that a
160
dissimilatory phonological rule prior to serialization can handle it.
(8) Tuvan total reduplication
simple form reduplicated form gloss
nom nom-nam ?book?
er er-ar ?male?
is is-as ?footprint?
o?g o?g-ag ?yurt?
su?t su?t-sat ?milk?
q1s q1s-qas ?girl?
xol xol-xas ?hand?
at at-ut ?name?
aar aar-uur ?heavy?
An interesting side effect of this reduplication pattern is how it affects Tuvan vowel
harmony. Tuvan has a backness and rounding harmony, and so in cases where a front vowel
is overwritten with [a] we have a change in backness. Disyllabic forms show that vowels
after this [a] pattern with back vowels. Unfortunately Harrison and Raimy (2004) do not
discuss harmony on suffixes.
(9)
simple form reduplicated form gloss
idik idik-ad1q ?boot?
inek inek-anaq ?cow?
nomdZuur nomdZuur-namdZ11r ?read?
Harrison and Raimy (2004) offer an analysis in terms of multiprecedence. They posit
that the precedence loop from the last to the first segment comes with a floating [a] which
overwrites the first vowel of the second copy, and that vowel harmony operates on that
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representation. Their analysis is copied in (10).
(10)
There are some issues with this analysis. Some are minor like the omission of the
effect of backness harmony on /k/>[q]. But a bigger issue is the idea of a precedence link
accompanied by a floating segment parallel to it. It is clever, but it certainly feels to me like
an abuse of notation. It treats the arrow as an object in the representation with respect to
which a segment can be parallel, rather than a notation for the organization itself. There
is certainly no way to represent this in the ordered pair notation I took as primary in ch.2.
But all these issues could be remedied. What I want to do instead is propose a full
PROP analysis, in which vowel harmony is not a separate operation, but -as proposed in
chapter 3- accomplished via parallel features. First consider a disyllabic root like (11),
where /I/, /E/, and /K/ are underspecified in backness and the first two also in rounding.
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/C/ is an empty consonant needed for the analysis to work.
?
(11) inek
{?bk,?rd}
# C I n E K %
The affix we are discussing must do three things to this root. First it must cause
reduplication, hence it will add a path from the last segment to the first segment. Second,
it must overwrite a vowel, so it must add a vowel in parallel to that of the root. Third,
it must add a new harmonic feature bundle {+bk,?rd} in parallel to the form. I posit a
single affix with the content in (12).
(12) Tuvan ?X or something like X? affix
{?rd,+bk} %
[#? ]U A [U ? V ? ]
[ ? %]
When affixed to (11) this will yield (13).
(13) idik-ad1q
{?bk,?rd}
{?rd,+bk}
A
# C I n E K %
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(13) will serialize as in (14).
(14) Serialization of (13)
{?rd,?bk}
{?rd,+bk} %
# C I n E K C
A n E K
Surface: [inekan1q]
This final form is exactly what we want. The Nesting Principle takes care that {?rd,+bk}
is realized on the second copy and beyond, leaving {?rd,?bk} only on the first copy, and
the overwriting vowel surfaces in the second copy.
7.2 Tone remaining on a single copy in Yao
Downing et al. (2005, p.3) describe the case of Yao verbal reduplication in which the iterative
is marked with total reduplication, but with the second copy lacking any tone. (15) gives
examples in the infinitive marked with ku-.
(15)
Infinitive Gloss to X repeatedly
ku-te?le?ka ?to cook? ku-te?le?ka-teleka
ku-wo?mbo?ka ?to save? ku-wo?mbo?ka-womboka
ku-su?lu?munda ?to sift? ku-su?lu?munda-sulumunda
This is straightforward if roots have the form in (16) with the high tone not reaching
the end, which doubly makes sense given that a) in trisyllabic forms the tone only extends
to the first two syllables, and b) the final -a is probably a suffix that Downing did not gloss
164
as such.
?
(16) cook
H
# t e l e k a %
The reduplicated form would get an arc as in (17) and serialized as in (18). I am here
assuming that since the H tone precedes /k/ and reduplication picks back up at a point
after the start of H, the tone will find itself on a single copy. A more detailed algorithm
would be necessary but this seems like the intuitive resolution to me.
(17)
H
# t e l e k a %
(18) Final form of (17)
H
# k a t e1 l e2 k a %
t e1 l e2
The resulting graph is what we want, with the H tone stretching only over the first copy
and the second one without tone.
7.3 Tone-overwrite and semi-parallelism in Hausa
Newman (1986) describes two types of affixes in Hausa: Tone Integrating affixes (TIA)
that overwrite the tone of the stem they attach to, and Tone Non-Integrating affixes (TNI)
whose tone does not affect the stem. For instance Hausa plurals are notated with a suffix
which also imposes a tonal melody onto the root as in (19). Following Newman?s notation
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I will represent a TIA?s overwriting tonal melody with the notation ...)T to indicate that
tone melody T overwrites that of the entire word.
(19)
Bare noun plural suffix plural form gloss
wa?k??il??i ai)LH wa?k??ila?i ?representative(s)
tsa?atsu?un??ya?a ooCii)H tsa?atsu?un??yo?oy??i ?folktale(s)
r??iga?a unaa)HL r??igu?na?a gown(s)
zo?omo?o aayee)HLH zo?oma?aye?e hare(s)
ra?ana?a aikuu)LH ra?ana?iku?u day(s)
ha?nka?aka?a ii)LH ha?nka?ak??i crow(s)
j??m1?na?a uu)LH j??m1?nu?u ostrich(es)
ya?atsa?a uu)H ya?atsu?u finger(s)
There is a lot going on in (19). I want to focus here on the tone overwrite, however a
proper and complete PROP treatment of these forms compliant with chapter 6 would have
to handle the massive lexically-conditioned allomorphy in a single underlying form. I will
here ignore this aspect, focusing on the tone and taking for granted that once that part
is clear it is straightforward but tedious to combine the multiple allomorphs into a single
lexical item.
We can posit roots like (20) and an affix like (21).
?
(20) wa?k??il??i
L H L
# w a k i i l i i %
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(21) plural affix (omitting allomorphy)
[C ? %] a i
%
[#? ] L H
(22) wa?k??ila?i
L H L
# w a k i i l i i %
a i
L H
The Nesting Principle takes care that the LH melody overwrites the LHL one.
7.4 Sye allomorphy in reduplication
Crowley (1998, p.77-84) and Inkelas and Zoll (2005) discuss an interesting phenomenon of
root allomorphy in Sye reduplication. Most roots come in two shapes, a ?basic form? and a
?modified form? (Crowley, 1998, p.77) (Stem1 and Stem2 respectively in the terminology of
Inkelas and Zoll (2005)). The amount of modification descriptively varies from root to root,
from exceptional invariant roots, to simply adding an ?accretive? n- on so-called weak roots,
to vowel replacements and other substantial alterations in so-called strong roots (23-a).
Although Crowley identifies multiple generalizations, he admits that the alternation cannot
be phonologically predictable as even some homophonous roots have different modified roots
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(23-b).
(23) Sye Stem allomorphy
basic root modified root gloss
a.
ahi ahi ?just do? (auxiliary)
aruvo naruvo ?sing?
omol amol ?fall?
ehri ahri ?break?
ve eve ?go?
vag ampag ?eat?
ocol agcol ?dig?
evcah ampcah ?defecate?
b.
owi nowi ?plant?
owi awi ?leave?
ehkar nehkar ?hold feast?
ehkar ahkar ?stare?
One of these two forms is selected in any given environment. For instance the basic root
is called upon by the distant past affix (24), whereas the modified root is called upon by the
future affix (25), where br and mr stand for ?basic root? and ?modified root? respectively.
The alternation between co- and c- is not a case of PCA but the regular outcome of vowel-
vowel sequences at morpheme boundaries (Crowley, 1998, p.32).
(24) a. y-aruvo
3sg:distpast-br:sing
b. y-ehri
3sg:distpast-br:break
c. y-ocol
3sg:distpast-br:dig
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(25) a. co-navuro
3sg:fut-mr:sing
b. c-ahri
3sg:fut-mr:break
c. c-agcol
3sg:fut-mr:break
So far this is straightforward to account for in PROP. Roots need to be stored with their
two forms and with features identifying the basic and modified forms.
?
(26) aruvo
nM
aB r u v o %
?
(27) ocol
aM
eB h r i %
?
(28) ocol
aM g
oB c o l %
Affixes in turn need to search for one or the other of the forms of the root. Examples
of complete forms are shown for y-aruvo and co-naruvo.
(29) 3sg:distpast prefix
# y [B]
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(30) 3sg:fut prefix
# c o [M]
(31) y-aruvo
nM
aB r u v o %
# y
(32) co-navuro
# c o nM
aB r u v o %
Sye also has reduplication with the meaning ?all over?. E.g. Crowley (1998) cites amon
?hide? > amonamon ?hide all over? (p.143). These reduplicated roots are also subject to
root modification, but crucially only the first copy is ever modified, e.g. cw-amol-omol,
3pl:fut-mr:fall-br:fall (p.79).
Inkelas and Zoll (2005) point out the problem that these forms pose for standard the-
ories of reduplication. Derivational theories built on copying segments from a base to a
reduplicant that assume allomorph selection is settled at vocabulary insertion cannot ex-
plain how the reduplicative process is able to retrieve segments from an allomorph of what
it tries to copy. For instance in cw-amol-omol, either /amol/ or /omol/ must have been
inserted at vocabulary insertion, and the copying process only has that to work with. It
cannot go back in time to retrieve the allomorph that didn?t get selected.
Constraint-based theories built around base-reduplicant identity constraints suffer from
an equivalent problem. Again in cw-amol-omol, either /amol/ or /omol/ must be the base,
and base-reduplicant identity cannot enforce correspondance between a reduplicant and
an allomorph of the base. That would involve going back in time to correspond with the
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allomorph that didn?t win.
Inkelas and Zoll (2005) suggest a model of reduplication based not on base-reduplicant
identity, but on independent spell-out of two roots subject to different cophonologies. Their
model radically rethinks reduplication in constraint-based theories. In traditional base-
reduplicant OT models, identity between the two copies is the result of base-reduplicant
identity constraints, and differences between the two copies are the result of markedness
constraints ranked above those base-reduplicant identity constraints. Inkelas and Zoll?s
Morphological Doubling Theory rather makes identity between copies a function of their
common underlying form, and divergence a function of different cophonologies. Crucially if
allomorphy is decided by the cophonology then reduplication with different allomorphs is
predicted.
One thing to note is they do not give explicit cophonologies for Sye. If one looks at
the table above, it should be clear that there is nothing phonological in common to all the
basic roots that distinguish them from the modified roots so the selection process could
not be done on the basis of surface optimization as OT is designed to handle. OT seems
ill-suited for this task; what is needed is a machinery to select arbitrary forms i arbitrary
morphological contexts. The only thing in common among each columns of the table is being
a basic root or a modified root, so the cophonology of, say, the 3sg:distpast must directly
refer to requiring a basic root. So Inkelas & Zoll are implicitly assuming a phonology that
can either recognize arbitrary classes of lexical items or can read their diacritics. This is
definitely at most no better than the PROP assumptions I have been making, with lexical
items seeking class features stored on roots.
But more interestingly, on top of a no-worse handle on the allomorphy, the PROP
analysis of the allomorphy under reduplication has the advantage of requiring no further
assumptions whatsoever. The reduplication adds a link from the segment preceding % to
the segment carrying [B], which is an unremarkable reduplication. The the prefix adds a
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link to the segments of the modified root, and the rest follows from serialization.
(33) derivation of cw-amol-omol
aM
a.
oB m o l %
aM
b.
oB m o l %
# c w aM
c.
oB m o l %
This is a neat consequence of PROP. From the point of view of word-formation in PROP
(and in the Multiprecedence from which PROP inherits reduplication) reduplication is not
a process of copying anything, it is not a process of pronouncing things twice, it is simply
a process of adding a path that happens to create a loop, e.g. from the last segment to the
first segment. The reduplication pattern can surface with different allomorphs sharing less
than all segments in the loop because duplicating segments isn?t a goal of reduplication at
all, only a side effect of the geometry, hence it does not fall for the problems that Inkelas
and Zoll (2005) point to. A path was added from the last segment to the first and the job
of word-formation is done. Whether that results in all of these segments being pronounced
twice or not is not the problem of word-formation.
With SUF allomorphy, it is simply natural that both allomorphs remain ?available? to
be used by other morphemes. If allomorphy is not fully settled at vocabulary insertion then
allomorphs can continue to interact with further affixes and phonological processes, just as
in this case in which some constructions cause two allomorphs to surface.
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7.5 Muskogean reduplication
Many Muskogean languages contain a complex non-local reduplicative pattern in which the
initial segments of the root are copied towards the end of the form. Consider these examples
from Muskogee in which, descriptively, the initial CV of the root is copied and infixed before
the final consonant of the root to form the pluractional of stative roots if said root ends in
k or y or in a cluster.
(34) Muskogee (copied from Riggle 2004)
Forms that end in singleton or geminate consonants other than k or y take the CV copy
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as a suffix + y and simplify the geminate (or do not allow reduplication).
(35) Muskogee (from Martin 2011, p.205)
ma?:h-i: ma:hmay-??: ?tall?
como:tt-ita? como:tco:y-ita? ?to hop / to be bouncing?
cami:ss-ita? cami:sca:y-ita? ?to dodge / to be seesawing?
hola?:tt-i: hola:thoy-??: ?blue?
ho?nn-i: honhoy-??: ?heavy?
nika:tt-ita? nika:tni:y-ita? ?to nod?
This type of non-local reduplication does have a straightforward account in Raimy?s
2000 system. It suffices to add the right arcs in the right places to make the copy of some
segments surface anywhere, as in (36).
(36)
# l i k a c k %
But there might be more to say about this pattern. One thing to note is that this
pattern of location right before k or y or the last segment of a cluster and suffixed otherwise
is exactly paralleled by the infix -ho- which is another marker of the dual/plural, mostly
for for a different set of verbs: verbs of position or movement1.
(37) Muskogee -ho- (from Martin 2011, p.200)
ay-??ta ahoy-ita? ?to go?
ta:sk-ita? ta:shok-??ta ?to jump?
hoyan-ita? hoyanhoy-??ta ?to pass?
at-??ta athoy-??ta ?to come?
oss-ita? oshoy-??ta ?to go out?
Under an analysis in the style of Raimy (2000), the fact that these two affixes with
similar semantics are placed in the same location is an accident. While I do not think this
would be a major problem to have a this small amount of repetition in the grammar, I
1The constant semantic of -ho- is nonsingularity; verbs of position or movement can distinguish singular-
dual-triplural, in which case -ho- marks the dual. But if a root does not have a triplural form, then the form
with -ho- also conveys plural.
174
would like to suggest a way the two could be unified using PROP.
I propose that the inititial CV of roots is set in parallel to the rest and realize with an
empty CV on the root as in (38). In the normal case this will be pronounced just as if it
were linear. The reduplicated form would be as in (39).
?
(38) likacw
l i
# C V k a c w %
(39) likac-li-k-
l i
# C V k a c k %
C V {Dorsal}
The idea in (39) is that the plural involves reduplicating the initial CV while also
adding an empty CV towards the end of the form. The reduplicated li would have to be
pronounced where it is compatible, which would put one copy towards the beginning and
one copy towards the end. The underspecified {Dorsal} feature is simply there to ensure
that when there is no final dorsal a default y will surface, whereas when there is a final
dorsal then {Dorsal} will be compatible with it and nothing will need to be added.
Forms with -ho- in turn lack the underlying parallel stream but still take the CV{Dorsal}
parafix as well as a ho parafix which will surface on it.
(40) ta:s-ho-k-
h o
# t a s k %
C V {Dorsal}
If the the CV{Dorsal} part is its own affix and -ho- vs. reduplication (decided via
175
morphologically-conditioned allomorphy) is another then this unifies the complex placement
of these two forms. The CV{Dorsal} affix is set to follow non-dorsal segments and precede
the end of the word.
7.6 Reduplication with a ?weakened? copy as partial redupli-
cation
Many languages have patterns of reduplication in which one copy is phonologically ?weak-
ened? in a variety of ways. These effects have been largely compiled and studied in Opti-
mality under the rubric of The Emergence of The Unmarked (TETU). The most common
manifestations of these are cases where one copy either lacks some structure such as codas
as in (41) or contains a fixed segment characterizable in OT terms as ?unmarked? as in (42).
(41) Nootka (from McCarthy and Prince 1994, p. 10)
Pu- Pu-?i:? ?hunting it?
c?i- c?ims-i:? ?hunting bear?
(42) Tu?batulabal (from McCarthy and Prince 1994, p. 29)
P1-p1t1ta ?to turn over?
Po- tomo?ka ?to stumblea??
Pa- kami? ?to catch it?
Pa- maSa ?to cover it?
Pe- Pela ?to jump?
These were straightforwardly handled in Raimy (2000) as either partial reduplication
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(43) or fixed segmentism (44).
(43) Nootka2
# c? i m s i ? %
(44) Tu?batulabal
# p 1 t 1 t a %
P
However there is another case that would not be so easily accounted for in the model
of Raimy (2000): these are cases where one copy?s segments ?simplify? compared to the
underlying form. Consider continuative reduplication in Nuxalk CC- and CVC- stems in
(45).
(45) Nuxalk dorsal neutralization in reduplication (from Newman (1971) unless marked
otherwise)
root/stem cont. gloss
? ?
nik- nixnik ?cut? ?1.2
skw- sixsikw ?untie? ?2.11
sxw- sixsixw ?burn? ?2.11
cakw- caxcakw ?be long? ?2.12
sikw- sixsikw ?pull? ?2.12
kixw- kixkixw ?gnaw? ?2.12
tux- tuxtux ?unwind? ?2.13
niqa?Xm nixniqa?Xm ?have cramps? (Carlson, 1997, p.33)
tiiXm tixtiiXm ?hit? (Angermeyer, 2003, p.22, citing Nater 1984)
2For simplicity here I treat -c?ims-i:? as an undivided root, but it is manifestedly a verbal root with an
incorporated noun, which would needlessly introduce a lot of complexity in this discussion.
177
As Newman discusses (fn.6) this pattern of CVx- reduplication only (though not always)
occurs when the second consonant is a dorsal, and as such it seems natural to derive this
[x] from the underlying dorsal. Some of the explanation may have to do with regular
phonology, as several processes delete secondary features in Nuxalk, but it does not seem
to be a general fact of Nuxalk that dorsals neutralize in this context, as some dorsals that
?
are not neutralized into [x] can be found in CV C contexts, e.g. Piknaaxw-i ?crab.dim?
? ?
(<kinaxw ?crab?) (Bagemihl, 1991, p.598), Pix-ukwp lx ?repetitive-stalk? (Bagemihl, 1991,
"
p.604), Pakwna ?? (Bagemihl, 1991, fn.40). I therefore take for granted that maybe not all
but some part of this neutralization is specific to continuative reduplication.
This would be a bit of a challenge for Raimy (2000). The phonological rule neutralizing
all dorsals into [x] would have to be ordered either before or after serialization. If it happened
before serialization in (46), we would expect both copies to undergo the neutralization,
contrary to facts. If it happened after serialization we would have to target only the first
kw in (47), but with the PROP assumptions so far we have lost the information that this
kw is the outcome of reduplication, and there is no way to target it without making the rule
apply to all dorsals in similar contexts, and I have shown it does not.
(46)
# s i kw %
# s i x %
*sixsix
(47)
# s i kw s i kw %
This is an insufficiency of the model of Raimy (2000). While the model is powerful
enough to handle some cases of over- and under-application in reduplication, it can only
178
account for cases where the over- and under-application cause both copies to be identical,
because the only mechanics for this in Raimy (2000) is for the rule to apply prior to serial-
ization. All rules applying after serialization will display normal application. A process like
the Nuxalk one above that is dependent on reduplication without yielding identical copies
is not doable with Raimy?s (2000) methods.
However PROP can account for the above case if we make some assumptions about the
underlying form of these dorsals: if their dorsality is separate and parallel to their secondary
features, we can have the reduplicative affix pick only the former without the latter. Adding
the assumption that the ?default? dorsal in the language is a velar fricative (an assumption
also implicitly present in OT analyses of this data such as Carlson (1997)) we derive the
data above.
?
(48) sikw
Dorsal
# s i %
+round
(49) sixsikw
Dorsal
# s i %
+round
=? si{Dorsal}sikw
=? sixsikw
This analysis is essentially extending the idea of partial reduplication to other kinds of
partiality than substrings, namely by picking a portion that does not contain all underlyingly
parallel features.
With this analysis it is also very straightforward to account for the stems that do not
undergo this neutralization. They are simply stored without the split posited above. E.g.
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sx- >sixsx- (Newman, 1971, ?2.12). In this respect there are no ?exceptions? in PROP, there
? ? ?
are only different inputs.
(50)
# s i x? %
Patterns of reduplication-specific neutralization are relatively common. Many are men-
tioned in Rose (1999) and they would all receive a similar PROP analysis to the Nuxalk
one above.
In (49), the realization of the reduplication is taken to be through only the Dorsal part
in the first copy, and through both the Dorsal and +round parts in the second, but another
logical possibility would be to only go through the +round part in the second copy, seeing
as the Dorsal part is already traversed.
I would like to posit that both of these realizations are possible, based on language-
specific parametrizaion, as the opposite scenario can also be observed. Struijke (2002), in
the context of OT, discusses a few patterns of reduplication in which both copies differ from
the unreduplicated form. This is descriptively the scenario in which some part of the input
has some features surfacing only in the first copy and other features surfacing only in the
second copy.
(51) Tohono O?odham
y@nt y@n-yat-m?u:t ?gnawings of a large animal?
q@ns q@n-qas-m?u:t ?chips?
In PROP this can simply be seen as an underlying form like (52) reduplicating as in
(53). The pronunciation of (52) with [nt], given that [n] and [t] cannot be simultaneous,
is a simple assumption that we can derive either as a phonological rule adding an arrow
from n to t in this context, or from a principle, either language-specific or generic to motor
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planning, that [nt] is a ?better? realization of unordered n and t than [tn].
(52) y@nt-
n
# y @ %
t
(53) y@n-yat-
n
# y @ %
a t
So as we can see, one property of PROP is that it allows for elements to be independent
enough that they are separable by some affixes such as the reduplicative affixes above.
It is important to acknowledge at this point that I am deriving contradictory effects
from the same representation. The same topology is posited to result in one weakened
copy in Nuxalk but in two weakened copies in Tohono O?odham, with the pronunciation
somehow choosing differently whether to re-traverse the upper node that was traversed in
the first copy. This is a problem with the vagueness, indeterminacy, and speculativeness of
my linking hypothesis with regard to the pronunciation of graphs. It might not be plausible
that the motor-planning of these graphs be parametrizable on a language-specific basis.
Further research will have to take place and it is very possible, in fact very likely, that not
all the analyses I have proposed are simultaneously tenable.
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Chapter 8
Using and learning graphs
In this chapter we will discuss all issues of implementation, acquisition, and neuroscience
that I have found to be relevant to the PROP program.
8.1 Phonetic implementation
Many assumptions about Phonetic implementation have been made in this thesis. I will
spell out the assumptions the PROP analyses require so far and attempt to justify them.
An assumption made by researchers who have worked with Multiprecedence represen-
tations involving loops has been that the representation, however non-linear it gets in the
course of word-formation, must be linear to be sent to the phonetics which can only deal
with strings (e.g. Samuels and Boeckx 2009 for an explicit statement to the effect.) The
core reasoning seems to be that while mental representations can be a-temporal abstract
structures, physical realizations must occur one at a time and that requires a string to
pronounce.
But multiple gestures can be done at the same time. A pianist can move their hands
in parallel with very different movements and therefore using very different articulatory
commands. It would seem difficult to me to account for the behavior of pianists linerarly
without attributing to them the capacity to have separate articulators receiving separate
commands in parallel. There must be a level of representation in which the input to artic-
ulators is not flat, and it is not therefore logically necessary that the output of phonology
be flat either. A weaker assumption would be to allow representations with either serial or
parallel commands to be interpretable, i.e. anything without loops. The acyclic graphs of
ch.7 are what we want.
One issue that must be addressed in more details is the phonetic behavior of repre-
sentations with contradictory parallel features. A central principle of this thesis is that
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contradictory features can be set in parallel in the representation sent to phonetics, with
the assumption that they will be resolved by the Nesting Principle. In this section I will
examine the existing precedents and circumstancial evidence in favor of it, but I cannot
conclusively argue that it is independently justified.
First, the assumption of simultaneous contradictory features was proposed first by Smith
(2018b) couched in Articulatory Phonology in which she posits complete gesture overlap
between features to account for vowel harmony with transparent vowels. Smith represents
vowel harmony in terms of a single feature spanning the whole word, with transparent seg-
ments specified with a contradictory feature and winning. Her diagram in (1) is something
that could very well have figured in ch.3.
I propose that in the Gestural Harmony Model, transparent segments are not
neutral to harmony, but instead that they are overlapped by a harmonizing
gesture. Transparent segments, then, are just a special type of undergoer. In
this model, transparency to harmony is the result of the concurrent activation
of a harmonizing gesture and a gesture that is antagonistic to it. Two gestures
are antagonistic if they have directly opposing target articulatory states that
strive to pull an active articulator in opposite directions. (Smith, 2018b, p.195)
(1) Schematic representation of transparency in the Gestural Harmony Model (Smith,
2018b, p.197)
The similarity ends there however, as Smith does not propose a general principle resolv-
ing those conflicts, but rather a feature-by-feature gestural strength deciding the winner of
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the conflict in case of incompatible overlaps, and capable of gradient blending. It would be
possible to modify the PROP account of this thesis to replace the Nesting Principle with
Smith-type strength specification, but I will not explore the possiblity here.
8.1.1 Nesting Principle
We made the major assumption in chapter 3 that if two features are parallel but one of
them is so-to-speak ?nested? into the other, the inner one wins. This was crucial to deriving
vowel harmony facts in Turkish and Finnish.
Proving this fact however is beyond my abilities. All I hope to do in this section is
provide two analogs that make it plausible to me that the nesting principle might be a deep
fact about the organization of motor commands, namely that a motor plan can include
contradictory specifications, and that when one is nested within another a gesture or state
can be interrupted and resume afterward.
Consider first an example from music. Sheet music for wind instruments often contains
breath marks over the staff indicating when to breathe, as in (2). Breathing is not meant to
interrupt the rhythm, and as such it must happen during the duration one of of the notes.
By convention the note immediately prior to the mark is played slightly shorter to allow for
the breathing.
(2)
With the intuitive assumption that the sheet music is representative of the musician?s
mental representation of the song, as opposed to the musician actually representing the
sixth measure of above as containing a shorter fourth note and a silence, then there is a
level of representation in which they represent both the notes and the breathing. Zooming
in on the sixth and seventh measure for instance, the musician would represent eight quarter
notes and one breathing period during the fourth of those. The muscle commands to the
diaphragm would require something like (3). And crucially where blowing out conflicts with
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breathing in, the command embedded in the other one wins.
(3)
We therefore have an example that seems at least analogous to the nesting principle in
phonology: a mental representation containing contradictory commands in which the nested
command wins1.
For a second example, it is worth noting that what I am suggesting is the production
analog of a well understood process in perception. In vision for instance the perceptual
systems typically infers continuity in the case of occlusion as in (4).
(4) Visual occlusion
Analogous auditory versions of this exist too, with perceived continuity where a sound
appears ?hidden? behind another. See O?Callaghan (2008) for a recent overview.
Crucially, the nesting principle proposal is the inverse of occlusion completion in per-
ception. Abstractly perception is able to perform as in (5) with a discontinuity in the signal
interpreted as continuous in the percept. The claim here is that production is able to do as
1It is not logically necessary that the Nesting Principle is the operative principle here. This is simply
illustrative of the possibility of resolving contradictory commands of a representation by performing a single
one of the two.
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in (6), with a continuity in the motor commands realized with a discontinuous output.
(5) Abstract illustration of occlusion completion in percetion
(6) Abstract illustration of interrupted parallel commands in production
Other aspects of Auditory Scene Analysis are relevant to PROP and we will come back
to them in section 8.2.
8.1.2 Resuming gestures
An assumption of the model of harmony with parallel contradictory features is that there
is such a thing as resuming a gesture, as distinct from starting a new instance of the same
gesture, maybe not at the phonetic level, but at least in the planning.
There are also other domains of Phonetics where features are best analyzed as inter-
rupted and resumed. Consider the glottalized tones of Vietnamese for instance as in the
lower right diagram in (7). Glottalization, variably realized as a glottal stop or as creaki-
ness, interrupts a vowel?s voicing, which then resumes. It would seem inadequate to analyze
this phonetic [VPV] sequence as such; it is rather universally treated as a single vowel, in-
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terrupted by glotalization, which then resumes with modal voice.
(7) Tone and phonation in Vietnamese (Brunelle and Kirby, 2016)
This type of vowel glottalization exists beyond South East Asia, e.g. the [+glottal clo-
sure] vowels of !Xo?o? (Bradfield, 2014, p.11), or the so-called rearticulated vowels of multiple
Mayan languages (Bennett, 2016).
Another relevant phonetic finding is that of Heid and Hawkins (2000) and Kochetov and
Neufeld (2013) with regard to long-distance coarticulation. They found that coarticulation
caused by [r] vs. [l] vs. [h] is detectable even 4 syllables away, e.g. on the word ?heard?
[h3d] in We heard it might be (a) ram/lamb/ham. Interestingly they found that sometimes
the closer word might is not influenced because of stress. This is long-distance [r] and [l]
coarticulation that crosses a word that is itself resistant to it. This has all the hallmark of
an [r] or [l] gesture starting early and being interrupted by a stressed word before resuming.
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8.2 Acquiring the parallel features of vowel harmony
In section 8.1 I have suggested that the Nesting principle may be the production analog of
the gap-filling principle in perception. Just as in vision an interrupted object whose ends are
sufficiently aligned is perceived as continuous, in audition an interrupted auditory object is
also perceived as continuous if it is interrupted. This fact of perception may have important
implications for the acquisition of vowel harmony. In general it has been taken for granted
that segments are perceived in isolation and any correlation between them due to phonology
must be observed and then explained by a phonological process. Thus for instance vowel
harmony would be harder to learn than the lack thereof, as learning it implies noticing the
correlation between the segments of a word along one or more feature and abducing a rule
from it. But this may not be true: if a discontinuous feature is perceived as continuous
by the low-level perceptual system, it may be that we have had it backward all along: it
is vowel harmony that is easy to learn, since the continuity of the harmonizing features is
directly perceived. Rather it might be the reverse, concluding from similar segments which
could be the product of a single continuous feature that they must be different entities, that
is hard.
To give a concrete example, consider a Finnish front word like tyhma?-sta?, ?stupid-ILL.?.
A traditional account would have the form parsed by the learner first as as a string of
segments as in (8). Then, on this representation, after being exposed to enough words, the
learner may notice the correlation between all Back features of Finnish words and posit a
rule of vowel harmony.
(8) Segmental parse of tyhma?-sta?
????? ???+cor???????????bk????
?
????
?
????????+lab???
????
? ?
? ?? ?? ?? ?
? ?? ?? voi?? ??
???bk??????????+cor??????????+cor???????????bk?????
?????voi????????+hi????? ?????+nas?????????+lo???????????voi?????????voi????????+lo?... ???... ... ... ... ... ?? ... ?? ... ?
But if gap-filling in auditory scene analysis plays a big role, it may be that tyhma?-sta?
gets immediately parsed as containing a continuous -back feature, going at least from the
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first vowel to the last, as an automatic perceptual fact, the representation may be more like
(9), or simply (10). Under this account, harmony does not require much analysis on the
part of the child; it is instead almost a given of auditory cognition. The learner would still
have to figure out that -sta? is a suffix, but that is true in any model.
(9)
(10)
-bk
# t Y h m A s t A %
The idea that children might learn by features rather than starting from segments and
that they have very non-surface-like assumptions about the organization of those feature
are two very unorthodox hypotheses, but I do not think that there is any a priori reason to
reject them. Why should the child segment speech into a flat representation if phonology is
freer than this? Why should initial analyses of speech be very surface-like if we know that
general audition itself is not completely faithful to the signal?
This of course opens up many more questions about children?s and adult?s representa-
tions of all features that could be perceived as continuous but obstructed. Consider a word
like splash with, on the surface, a strident at the beginning and one at the end. Could this
189
form be parsed as (11) with a continuous strident feature throughout the form?
(11)
+str
??????
? ? ?
+cor ?
? ?
??? ????? +cor ?????
# ????+cont????
p a
? l ?????+cont? ????
%
+ant ant?
This may seem strange at first, but a parse such as (11), at least at some initial stage
of acquisition may capture diacronic metathesis that Blevins and Garrett (2004, p.127-128)
attribute to the decoupling of sibilant noise from the rest of the speech stream. They cite
Ilokano saait ?weep? vs Aklanon taais as a pair of cognates that may originate in this way
from a long distance metathesis. Under the view presented here this sound change may boil
down to a speaker starting from a parallel analysis in the lines of (11) and resolving it in a
different way from the speakers of this learner?s input.
There is additional data from the field of Auditory Scene Analysis in favor of auditory
segmentation into multiple streams. Warren et al. (1969) played their subjects a repeated
sequence of a high tone, broadband noise, and a low tone, or a high tone, a hiss, a tlow
tone, and a buzz, each 200ms long, which as they observe is much longer than typical
phone length. Even though the subjects were fully able to identify the three or four sounds
involved, they had trouble telling the order in which they played. They conclude that
perception of linear order is more difficult than intuitively expected.
The interpretation of this experiment by Bregman (1994) is that some sounds are too
different to be parsed as a single stream and are parsed into different parallel streams that
are not ordered in time. Similarly souns in the same category but with abrubt transitions
also tend to be parsed as separate streams as O?Callaghan (2008) discusses for tones.
(12)
190
In light of such results the idea that some features like tone, nasality or specific formants
perceptually clash against others in a way that incites or even forces the child to initially
parse them as separate streams is a very plausible hypothesis. Again, language-independent
perceptual facts support that the initial parse may not be a segmental parse in the style
of (8). This is a somewhat different take-away from Auditory Scene analysis than the one
of Reiss (2007, p.67) who posits that the contribution of auditory perception to linguistics
is that speech gets parsed into its own stream, thus giving the learner a single string to
learn from decoupled from non-linguistic noise. Here I posit that even the input to speech
perception may consist of multiple streams.
If this is correct, contrary to segment-oriented bottom-up intuition, vowel harmony is not
hard to learn; it is basically not learned. Rather non-harmonic languages with misleadingly
harmonic words like Spanish banana are the actual challenge, as the learner must realize
that all these [a]?s are multiple objects, not a single partially obstructed one. This is like
being forced to learn that there are actually two pale grey objects in (4).
This tendency for the learner to assume continuity by default would also explain the
very common fact of OCP at the tone level: languages that are best analyzed as having
separate tone melodies from the segments overwhelmingly (but not universally, see Odden
1986) do not allow for multiple consecutive instances of the same underlying tone, *HH,
*LL, regardless of what they allow on the surface. If the acquisition of these patterns
involves parsing the tones into their own perceptual stream, then multiple consecutive
surface H tones will seem continuous by default, which could very well drive the cross-
linguistic rarity. The typological fact would therefore boil down to a non-linguistic fact of
how general audition necessarily deals with tones that are to be interpreted as parallel to
the segmental tier, and the OCP for tone thus does not need to be its own phonological
principle.
191
The idea of taking advantage of the inherent perceptual independence of some phonetic
features is a departure from the existing segment-oriented algorithms that have been offered
for the learning of harmony patterns and non-concatenative morphology. For example the
research program formalizing vowel harmony in terms of tier-based strictly local constraints
(Heinz et al., 2011; Akse?nova et al., 2016; Akse?nova, 2017; Akse?nova and Deshmukh, 2018;
McMullin et al., 2019) starts from strings and then constructs tiers onto which the gener-
alizations of vowel harmony and other long-distance restriction are to be stated. Similarly
Fullwood (2018) seeks to model the segmentation of Semitic non-concatenative morphology
in terms of a Bayesian learner testing the most parsimonious segmentation of a string of
segment into possibly discontinuous morphemes. Both of these models have in common
that they take a segmented string as an input and parse them into subsequences that are
themselves strings of segments. I propose that these assumptions are wrong: the input to
the child?s learning process is not a string, but a set of relatively independent streams, and
the ouput is not tiers of full segments, but tiers of sparse features. Fullwood improves on
her model by adding certain biases such as a bias for discontinuous morphemes that are
fully consonantal or fully vocalic, but this too may be in the percept. This bias does not
need to be a learning bias if it is a perceptual bias.
8.3 Planning parallel articulations
Ever since Lashley (1951), speech has been considered part of what he called the problem
of serial order in behavior. Models of speech production have mostly focused on accounting
for the fast serial organization of speech, developing rich models of speech production that
can account for real-time segment-to-segment speech production. For example Guenther
(2016, ch.7) discusses how feedforward neural nets can achieve rapid transitions between
segments, treating the problem of very fast transitions in speech as the main issue. Nothing
is said on the problem of coordination or simultaneity.
PROP changes the problem of speech as it does not require all speech to consist of quickly
serially-ordered segments. Some instructions may be organized in parallel and overlap in
time. This does not make speech not a problem of serial behavior, but it does suggest
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that it may be less serial than commonly thought. Contrary to segments changing every
few milliseconds in a single stream, we can imagine multiple streams with relatively slower
changes overall. This view is not fully novel, as it is shared with Articulatory Phonology?s
conception of a gestural score.
Of course some utterances will actually require rapid alternations, but in the extreme
these utterances will be tongue twisters, and those do get harder to articulate.
The one aspect of simultaneous motor planning that has been somewhat studied in
neuroscience is prosody, but the research must be treated with caution as the research
tends to treat linguistic prosody as closer to affective prosody than to non-prosodic linguistic
articulation, and sometimes seems to lump all prosody together. Within linguistic prosody
it tends to treat intonation, suprasegmental features, and laryngeal features as essentially
co-extensive phenomena. And within linguistic intonation studies are mostly restricted to
focus intonation (e.g. Mayer et al. 2002), which is different in so many ways from the more
phonological intonation that it would be surprising if its processing was not different2.
8.4 Alignment as a coordination problem
One aspect that PROP does not seek to explain when contrasted with Autosegmental
Phonology is the overwhelming commonality of one-to-one alignment in the realization of
parallel phonological structures. Autosegmental phonology attempts to explain it within
the phonology through an association convention.
I would like to suggest that this does not need to be explained phonology-internally.
There are limitations on the temporal coupling of movements. Heuer (1996) mentions the
difficulty of simultaneously tracing a circle and a triangle in the air, other than by forcing
a temporal alignment such as one revolution of the circle for every side of the triangle. The
details of the difficulty of maintaining different rhythms of movement has been studies for
instance by Klapp (1979, 1981); Klapp et al. (1985). Keele et al. (1985) further argued
that perception and motor production share a common timing mechanism, and thus the
2Focus intonation is not clearly based in rules anywhere similar to those of phonological intonation.
A major strangeness about focus is its universal or nearly universal phonetic realization, making it very
unlike other syntactic features. Its conditioning also taps into information, discourse, conversation, and
communicative pressures in ways that do not resemble phonology.
193
limitation on timing would affect both perception and production.
194
Chapter 9
Further Phenomena, Analyses,
Observations, and Suggestions
In this chapter we will briefly cover a number of theoretical and analytical questions that
either deserve some attention or for which PROP provides a novel insight, but which will
not be discussed in depth and deserve to be the subject of further research.
9.1 Regular Phonological Processes
The PROP model discussed so far does not replace regular phonology, and thus we still
seem to need something to acheive the effect of normal segment-changing phonology but on
graphs. This is a matter that was already discussed in Raimy (2000) so we will start with
a discussion of his proposal.
9.1.1 Phonological Processes on Graphs in Raimy (2000)
Raimy (2000) discussed the matter of phonological rules applying on multiprecedence graphs
to discuss the descriptive advantage that this offers to explain various phenomena of over-
and underapplication in reduplication and infixation. I will only summarize two of Raimy?s
examples here from Akan and Sundanese.
Consider the case of the interaction between reduplication and palatalization in Akan
discussed in Raimy (2000, p.18-23). Dorsal phonemes are palatalized before non-low front
vowels i/Ior e/E.
195
(1)
tCE *kE ?divide?
d?e *ge ?receive?
4i *wi ?nibble?
?? *hi ?border?
?4?n *NwIn ?weave?
The only exception to the generalization that dorsal segments do not appear before
non-low front vowels is in some reduplicated forms in CI- in which the consonant is not
palatalized.
(2)
kI-kaP *tC?-kaP *tC?-tCaP ?bite?
hI-hawP *c?-hawP *??-?awP ?trouble?
However this ban on palatalization is not a property of the construction itself, since
when the first consonant of the ?base? is a non-low front vowel the palatalization does take
place.
(3)
d??-d?e *gI-ge ?receive?
tC4i-tC4eP *kwi-kwe ?cut?
Raimy?s (2000) analysis, which I will adopt here, is only statable on a multiprecedence
representation of the reduplicated form. Raimy?s insight is to point out that on a graph,
there are multiple ways that classical phonological rules could be stated. E.g. consider a
rule that palatalizes /g/ when it precedes /i/. It seems intuitive that the rule should apply
to a form like (4). But what about (5) with /g/ followed by one /i/ and one /a/ vs. (6) in
which /g/ is followed by two /i/?s?
(4)
g i
196
(5)
i
g
a
(6)
i
g
i
Raimy?s suggestion is to posit a Uniformity Parameter on rules. Rules can be para-
metrized to apply either a) when all segments match the environment (so for our palatal-
ization rule, only (4) and (6) would undergo palatalization), or b) when at least one segment
matches the environment (so for the same palatalization rule, all three of representations
above, (4), (5), and (6), would undergo palatalization).
So returning to Akan, given that the forms of [kI-kaP] and [d??-d?e] would look like (7),
the crucial difference is that in (7-b) the /g/ precedes only non-low front vowels, whereas in
(7-a) the /k/ precedes a mix of non-low front vowels and other vowels. Hence if the Akan
palatalization rule is set with its Uniformity Parameter on, it will apply in (7-b) and not
(7-a), and it will apply in non-branching forms like (1), deriving all the facts.
(7)
a.
# k a P %
I
b.
# g I %
I
An example of the Uniformity Parameter set to off is found in the interaction between
197
infixation and nasalization in Sundanese discussed in Raimy (2000, p.71-74). Sundanese
has a nasalization process in which nasal vowels cause nasalization of vowels to their right,
with /h/ and /P/ transparent to the process, but blocked by supralaryngeal non-nasal
consonants.
(8)
ma?ro ?to halve?
ma?ne?h ?you?
ma?ndi ?to bath?
mi?a?sih ?to love?
kuma?ha? ?how??
?a?ho?ken ?to inform?
beNha?r ?to be rich?
However an exception to the generalization that oral consonants block nasalization is
the infix -ar- (or -al- when an /r/ follows), which lets nasalization through (aside of a local
de-nasalization of vowels immediately following an oral vowel). In (9) the nasalized vowels
after the infix go against the generalization that /r/ blocks the spread of nasalization.
(9)
mo?e?ken m-a?r-oe?k@n ?to dry?
?a?u?r ?-a?l-au?r ?to say?
n?iP?is n-a?r-iP?is ?to cool oneself?
?a?ho? ?-a?r-aho? ?to know?
Raimy?s answer is to look at the multiprecedence form of infixation. E.g. the form [n-
a?r-iP?is] would have the form in (10) prior to the application of the phonological rule. Even
though on the surface the /r/ intervenes between /n/ and the two /i/?s, at this point in the
derivation there is a path from /n/ to the vowels that bypasses the infix. If the nasalization
process applies on this representation, and crucially if the Uniformity Parameter is off,
meaning nasalization will happen as long as there is at least one preceding nasal segment,
then the first /i/ will nasalize and spread nasalization to the right (and will subsequently
198
de-nasalize due to the /r/). This derives the overapplication effect.
(10)
a r
# n i P i s %
I will maintain this analysis, but I will avoid the language of Uniformity Parameter and
?
convert the proposal into the notion of properties I introduced in ch.2 using the symbols ?
?
and ? , giving rise to properties defined as in (11) and (12), which respectively read as ?has
at least one preceding segment containing +F and +G? and ?has only following segments
?? ?containing +F and +G?. Crucially, and ? are not novel phonological relations, they
are a notation summarizing a first order property over graph relations.
?
(11) [[+F,+G]? ] ? ?uu? ({+F,+G} ? u)
?
(12) [ ? [+F, +G]] ? ?u ?u({+F,+G} ? u)
These properties can be used in rules as in (13) and (14)1, in which the context stands for
properties that A must have in order for the rule to apply. A rule may contain multiple
such properties as in (15).
?
(13) A > B/[[+F,+G]? ]
?
(14) A > B/[ ? [+F, +G]]
? ?
(15) A>B/[[+F,+G]? ] & [ ? [+F, +G]]
? ?
Note that this same notation can be used in sticky-ends. The ? / ? system allows us
?
to define different types of sticky-ends: [ ? [+F ]] which seeks any segment that precedes
?
some [+F ] segment, vs. [ ? [+F ]] which seeks segments only followed by [+F ] segments.
We will see this difference in use in the next section.
1I will avoid the use of arrows to represent change in phonological rules since the arrow is already used
for precedence.
199
9.1.2 Phonological processes on Graphs in PROP
With a way to do phonology, we can discuss a number of phonological phenomena whose
analyses become better understood thanks to the graph representation of the form.
9.1.2.1 Overapplication in Brazilian Portuguese
As discussed by Ferreira (2005), Bachrach and Nevins (2008) and Rolle (2018), Brazilian
Portuguese has a process of l-vocalization by which /l/ becomes [i] before /s/. This process
affects l-final forms in the plural as in (16-a). The diminutive singular form with -zinho in
(16-b) is not affected, showing that /z/ does not trigger the phonological change. But the
diminutive plural jornaizhinos does undergo l-vocalization, despite the distance.
(16)
sg. pl.
a. jornal jornais ?newspaper?
b. jornalzinho jornaizinhos ?newspaper.DIM?
This can be straightforwardly given an explanation in PROP. The plural is set to follow
any segment that precedes the end of the word, as in the UR in (17). When added to the bare
root it will create the form in (18) which naturally satisfies the condition of l-vocalization.
(17) Brazilian Portuguese plural suffix
?
[ ? %] s %
?
(18) jornal+-s
s
# Z o r n a l %
200
However when appended to the form with the diminutive as in (19)2, the plural will find
two segments that precede the end of the word, and thus will attach as in (20), in which
/l/ does precede /s/.
?
(19) jornal+-zinho
z i nh o
# Z o r n a l %
?
(20) jornal+-zinho+-s
s
z i nh o
# Z o r n a l %
Assuming that l -vocalization is defined as in (21), the rule will indeed find that the /l/
of (20) has the property of having at least one following segment that is /s/, and therefore
the rule will apply.
?
(21) l > s / [ ? s]
We therefore derive this form of overapplication across a morpheme from the allowed
combinations of the Uniformity Parameter in sticky-ends and rules. The Brazilian Por-
tuguese case can only happen because both the sticky-end and the rule are defined existen-
tially.
This analysis dispenses with the invocation of Paradigmatic or Trans-paradigmatic
Output-Output constraints that have been proposed to account for this kind of fact (e.g.
Ferreira (2005), Rolle (2018)). It is replaced with the representational possibility that seg-
2I oversimplify a bit as -zinho is presumably two morphemes, a diminutive -zinh and a masculine mor-
pheme -o, but it does not affect the analysis.
201
ments may covertly be related by a precedence link even though they surface apart from
each others, and that this link can make them local for the purpose of phonological rules.
Brazilian Portuguese has other suffixes across which l -vocalization does not take place,
most notably the augmentative -za?o. jornalza?o becomes jornalzo?es in the plural and not
*jornaizo?es. As noted by Bachrach and Nevins (2008) however, the augmentative has
different properties, such as changing the gender of roots, and thus may have different
structure, e.g. as the head of a compound. Importantly the account of l -vocalization in
this section does not entail that it should occur across all suffixes; what it entails is that
suffixes that block l -vocalization must have a different structure than (20) at the point in
the derivation where l -vocalization happens. Possibilities include not being a suffix at all,
like in the compound analysis of -za?o, or having triggered serialization to happen before
l -vocalization.
Rolle (2018) describes other cases of phonological processes taking place across affixes,
such as CiBemba spirantization taking place across the benefactive derivational suffix. This
is therefore not idiosyncratic to Brazilian Portuguese, it is simply a representational possi-
bility available to phonological systems.
9.1.2.2 Quebec French laxing harmony
Some varieties of Quebec French have a process of vowel harmony as described in Poliquin
(2006). I will focus here on what Poliquin calls Across-the-board (ATB). There are three
phonological processes that interact in Quebec French: High-vowel laxing, laxing harmony,
and pre-voiced-fricative tensing.
With high vowel laxing, high vowels becomes lax in final closed syllables. This is visible
202
in the vocabulary in general (22-a) as well as in morpheme alternations (22-b).
(22) High-vowel laxing
a.
li ?bed? e.lIt ?elite?
kKy ?raw? aK.bYst ?bush?
de.gu ?disgust? e.gUt ?drain?
b.
be.ni ?blessed.masc? be.nIt ?blessed.fem?
p?.tsi ?small.masc? p?.tsIt ?small.fem?
de.by ?start? (noun) de.bYt ?start.imperative?
a.Zu ?add-on? (noun) a.ZUt ?add.imperative?
In some varieties, this laxing gives rise to a laxing harmony. High vowels in previous
syllables become lax, even in open syllables.
(23) Laxness harmony3
No harmony ATB gloss
Zy.Ki.dzIk ZY.KI.dzIk ?judicial?
si.Ki.lIk sI.KI.lIk ?cyrillic?
ny.tKi.tsIf nY.tKI.tsIf ?nutritional?
dzi.si.plIn dzI.sI.plIn ?discipline?
li.mu.zIn lI.mU.zIn ?limousine?
A traditional analysis of this phenomenon would involve a two step process: first inser-
tion of a lax feature4 in the final vowel, followed by spreading or copying of the feature to
previous segments. In PROP on the other hand laxing and laxing harmony can be made
3I am skipping Poliquin?s category of Non-local harmony as it is not relevant to our purposes here and
there are reasons to believe it is misanalysed, see e.g. Cuerrier and Reiss
4I will not discuss here the exact details of the phonetics of the QF tense-lax contrast, as it is poorly
understood. Dalton (2011) suggests that it has nothing to do with advance or retraction of the tongue root.
I will therefore use ?tense? and ?lax? features with the hope that further phonetic study could inform us of
the appropriate features to use.
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into one single process that adds a lax feature in parallel to the entire word.
(24) QF Laxing rule5
When a +hi segment precedes a final vowel, add Lax from # to %.
# {lax}
=?
[+hi] C % [+hi] C %
So a word would enter the derivation with high vowels underspecified for tense/lax and
the rule (24) would apply.
(25) juridique ?juridical?
a.
# Z y K i d i k %
b.
{lax}
# Z y K i d i k %
This is interesting since contrary to all the cases of harmony discussed in chapter 3, this
is not a parallel feature introduced by a morpheme, but by a phonological rule. However
other than this detail there is no reason to assume that there is anything else crucially
different between the resulting harmony patterns.
The final process to discuss is a process of tensing that counteracts laxing. High vowels
5We have not yet discussed the representation of syllables, so this is stated as targetting C-final words.
A separate rule would be required for CC-final and CCC-final ones.
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are tensed and lengthened before /v, z, Z, K/.
(26)
gKi:v ?thrush (bird)?
e.gli:z ?church?
tsi:Z ?stem?
e.kKi:K ?to write?
This can be handled with a new rule.
(27) Pre-voiced-fricative tensing rule6
When a [+hi] segment x precedes a [+voi, +cont, -son] segment y, add +tense from x to y.
X [+hi] [+voi,+cont,?son] X [+hi] [+voi,+cont,?son]
=?
{tense}
Importantly when in apparent conflict, where a high vowel precedes a voiced fricative
and also follows high vowels that could be affected by harmonythe result is both tensing of
the final pre-voiced-fricative vowel and harmony over the previous high vowels, e.g. in the
word /misiv/ ?letter?, the result is [mIsi:v] with a harmonized first vowel and a tensed final
vowel.
This can be accounted for in a traditional analysis, however it involves a number of
analytical assumptions that have always been contentious. Laxing and harmony must be
crucially ordered before tensing which counter-bleeds them such that the vowels are first
laxed, and then the laxing of the last vowel is undone by tensing. This analysis involves
opacity and a duke-of-york gambit.
6I will not discuss the lengthening part of this process.
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UR /misiv/
Laxing misIv
Harmony mIsIv
Tensing mIsi:v
SR [mIsi:v]
The PROP analysis on the other hand follows from previous assumptions without any
extrinsic ordering or duke-of-york gambit. The surface form follows from the assumption
about nesting features from chapter 3.
(28) missive ?letter?
Lax
# m I s I v %
Tense
The Laxing rule adds a lax feature from the begining to the end as independently
justified for harmony, and the tensing rule adds a smaller tense feature over the final vowel
as independently justified for tensing. From nesting assumptions it follows that the final
vowel will be realized as tense and only the first vowel will be realized as lax. The seemingly
counterbleeding-like and duke-of-york-like outcome is the simplest possible outcome of the
two processes.
We now have the tools to account for harmony patterns introduced by phonological
rules and we see that they follow the same generalizations we have established before.
9.2 Regular alternations as partial overlap
In addition to the regular phonology on graphs as defined in the previous section, there are
also new possibilities opened up by PROP to account for some phonological alternations. I
will suggest here that some regular alternations that would traditionally be analysed with
the help of rules may have a representational account.
One analytical advantage of non-linear phonology has been in attributing assimilatory
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processes to geometrically simple spreading rules.
(29) Autosegmental assimilation
+F
w + x y z
These processes can be given an equivalent PROP analysis by reframing the phenomenon
in terms of putting morphemes partially in parallel to others, except the phenomenon is
now purely representational and reliant not on an explicit assimilatory process, but on an
explicit representation within the individual morphemes. The general logic would look as
in (30), with a root surfacing with an initial [+F, +C] that is underlyingly split into two.
If a prefix is specified to precede C, but is not given any sticky-end that will pick out the
parallel {+F}, the result will be a partial prefix that is placed in parallel to {+F} which,
based on the assumptions of chapter 3 entails that this {+F} will stretch over the duration
of w and C if it is phonetically compatible.
(30) Partially-parallel affixation
+F
# x y z %
C
Partial prefixation of w-
+F
# x y z %
w C
To take a concrete example, consider place assimilation of the prefix in- in intolerable,
impossible, i[N]capable, etc. If we assume that English roots underlyingly separate the place
feature from the other consonantal features as in (31), and the prefix in- is underlyingly as
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in (32), assimilation will follow representationally.
?
(31) possible
{+lab,?cont}
# A s I b l %
{+C,?son,?voi, ...}
(32) in-
[+C]
# I {+son}
[+V ]
When (32) is affixed to (31) it gives the structure in (33) with the +son parallel to the
+lab,-cont. With the extra minor assumption that English phonology fills in non-continuant
sonorants as +nasal we have the assimilation taken care of by the fact that in- was put in
parallel to the Place and continuancy features of the root-initial consonant.
(33) im-possible
{+lab,?cont}
# A s I b l %
{+C,?son,?voi, ...}
I {+son}
[+V ]
The assumption that the prefix consonant is not inherently +nasal helps account for
assimilation with /r/ and /l/ in irregular and illegal. The only constancy of the consonant
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of the prefix in- is its being a sonorant.
(34) il-legal
{+cor,+cont,+lat}
# i g @ l %
{+C,+son,+voi, ...}
I {+son}
[+V ]
In the V-initial case, we simply a default insertion rule, or for underspecified consonants
to surface as coronal by default.
9.3 Metathesis & Coalescence
Synchronic metathesis is an interesting type of phonological process in that it is complicated
to state on strings. But a theory in which precedence can be directly manipulated this is
much more straightforward. For instance if A and B phonologically metathesize we could
posit a rule of the form in (35). This was first suggested by Halle (2008) (in a different
notation, as pointed out by Samuels (2010)) but it has the effect of causing metathesis of
A and B by directly overwriting the order in which they must be traversed.
(35)
X A B Y =? X A B Y
However I would like to suggest that metathesis phenomena have more to do with
resolving parallel structures than active reversal in the phonology. And conversely I will
propose that coalescence may be the reverse operation, putting segments in parallel.
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9.3.1 Faroese
Consider an example of metathesis from Buckley (2011). In Faroese some words surface
with [ks] sequences in the context of a following [t] and with [sk] sequences otherwise.
(36)
msculine neuter
fEsk-Ur fEks-t ?fresh?
rask-Ur raks-t ?energetic?
dansk-Ur daN ks-t ?Danish?
Buckley like everyone else analyses this as a reversal of /sk/>[ks]. That is he takes one
order to be underlying and another to be derived. With strings this is the only possibility,
as everything need to be ordered throughout the derivation.
But with PROP there is a new option, namely the two segments could be underlyingly
unspecified for order.
?
(37) fesk ? /feks?
s
# f E %
k
From this underlyingly underspecified order the two surface orders would be derived
contextually. This can be done in a number of ways, e.g. via a specific phonological rule
adding a link from /k/ to /s/ in the context of a /t/, or from a language-specific phonetic
convention7, or maybe even from something universal about motor planning?s preference for
the order of certain events when their order is unspecified. Either way this allows for order
alternations without operations of order reversal: rather than starting from an order and
derive the other, we can start from no order and derive both. This is desirable because for
phonology on strings, operations capable of reordering segments are a big departure from the
7I will use this vague term to refer to anything not-strictly-linguistic that may be part of a speaker?s
knowledge when it comes to the usage of language.
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rest of operations needed for rule-based phonology and inherently add a lot of complexity
to the power of phonological rules. As Blevins and Garrett (2004) put it ?the reordering
of sounds in metathesis has required extensions of otherwise highly restrictive phonological
formalisms?. With PROP we may entirely dispense with re-ordering and therefore with re-
ordering operations. Variable order in phonology is a very straightforward consequence of
a representation in which things may be momentarily unordered with regard to each other.
Typologically, there do not seem to exist any case of synchronic metathesis that ex-
changes segments more than two places away (Canfield, 2016, p.38). If metathesis derives
from such local lack of ordering we derive why that is the case. Metathesis in this PROP
analysis is due to local underspecification for order.
9.3.2 Rotuman
Of course the patterns of metathesis can involve a bit more complexity than the examples
above. Consider Rotuman as described and analyzed in Besnier (1987). Rotuman verbs have
two forms, known traditionally as the Complete and Incomplete. The pattern is complicated,
but the gist of it from a descriptive point of view is that the Incomplete is always predictable
from the Complete and can be formed from it by reversing the last CV and applying a
number of consistent rules to the resulting VV sequences as in (38-a). Notably, if the
resulting VV sequence would be two identical vowels the result is a single vowel (38-b)
(despite Rotuman allowing long vowels). And sometimes the two vowels coalesce as in
(38-c). As the details of the phonological processes affecting VVs are unimportant here, I
will refer the reader who wants to know more to Besnier, particularly to Tables 1-3 which
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summarize all the VV outcomes.
(38) Rotuman metathesis
a. Complete Incomplete
hepa hyap ?broad?
fika fyOk ?number?
tife tyOf ?pearl shell?
b. hanuju hanuj ?tale?
toto tot ?blood?
c. forOsi for?s ?to spread out?
hose h?s ?oar?
fuli fu?l ?deaf?
The crucial alternation under Besnier?s analysis is therefore between -V1CV2 and -
V1V2C with some extra phonology happening in the latter forms.
I would like to suggest a PROP analysis which is very close to Besnier?s but crucially
involves underlying parallel structure and puts V1 and V2 in parallel rather than in order.
Specifically I would like to suggest that Rotuman forms underlyingly end as in (39).
(39) Underlying forms
V2
# ... V1 C %
Forming the Complete and Incomplete from this underlying form boils down to adding
one arrow, from C to V2 (40) or from V2 to C (41), respectively.
(40) Complete
V2
# ... V1 C %
(41) Incomplete
V2
# ... V1 C %
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The form in (40) naturally creates an unambiguous V1CV2 sequence in the Complete.
The Incomplete on the other hand puts V1 and V2 in parallel. This form immediately
accounts for all cases where V1=V2 as in (38)[b]. These forms simply send a redundant
representation to motor planning with two elements commanding to pronounce the same
vowel in the same span. This explains why those sequences even need to be resolved when
rotuman allows long vowels.
Cases of coalescence can be accounted for with explicit rules, but they can also be
thought of a another strategy for the motor systems to deal with conflicting commands,
namely gestural blending produced by averaging the two commands reminiscent of Smith
(2018a,b, 2019). Even for the ones surfacing as glide-vowel sequences, there is some ex-
perimental evidence that complex nuclei may be analyzed as synchronous vowels (Marin,
2005).
Some amount of arbitrariness may have to exist to resolve some sequences, as there
remains some asymetries, e.g. -aCe forms alternate with -EC while -eCa forms alternate
with -yaC, so we cannot rely on a consistent resolution of parallel /e/ and /a/. This could
require an explicit phonological rule, e.g. it would suffice to have a phonological rule that
adds a link from /e/ to /a/ if they both precede the same segment and /a/ also precedes
%. Or it could be that the surface segments are not all underlyingly identical: if the V2
that surfaces as /e/ is -lo,-hi and the V1 that surfaces as /e/ is -bk,-lo,-hi then the apparent
symmetry of -aCe and -eCa in the Incomplete is broken.
Importantly the Incomplete form in does more than putting V1 and V2 in parallel, it
puts V2 in parallel to the whole form. This is desired for polysyllabic forms in which the
incomplete affects all vowels as long as they are /u/ or /o/.
(42)
sukuni su?ku?n ?to pierce?
kukulufi ku?ku?lu?f ?tree sp.?
Popoti Po?po?t ?to follow?
Besnier?s analysis in contrast requires a separate harmony rule that is morphologically
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conditioned to only applies in this morphological context, a rather undesirable state of affair
from the point of view of an independent phonology. In the PROP analysis this derives
from the geometry.
Rotuman reduplication is also straightforwardly accounted for with the representations
posited above. In reduplicated Incomplete forms, the effect of V2 affects both copies, even
in cases where harmony is not expected. This follows from the representation if we add a
reduplicative loop as in (43), because there is a single V1 that is equally affected by the
coalescence rules prior to serialization of the loop.
(43) Reduplicated forms
Root (in linear representation) Red. Complete Red. Incomplete
/pore/ popore po?po?r ?suddenly?
/mami/ mOmi mEmEm ?disgustingly sweet?
/furuki/ furfuruki fu?rfu?ru?k ?pimple?
(44) popore
e
# p o r %
e
# p o p o r %
(45) po?po?r
e
# p o r %
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e
# p o p o r %
9.3.3 Indonesian
I have assumed in the previous section on Rotuman that coalescence amounts to seg-
ments coming to be in parallel. This fits particularly well with the analysis of vowels
harmony in PROP given the data of Rotuman in which coalescence and some amount of
morphologically-triggered vowel harmony seem to go together.
However Raimy (2000) already had an analysis of coalescence in terms of two nodes
becoming one and inheriting all the precedence links that went in and out of either segment.
for example in his analysis of Chumash, in which /l/ coalesces with coronals, Raimy posits
an operation like (46) where the dashed lines surround the /l/ and /t/ that become a single
/t/. As is visible in (46-b) the resulting /t/ combines all the arrows going in or out of either
of the input segments.
(46) Chumash /l/+ [coronal] coalescence (copied from Raimy 2000, p.27)
There are many languages where Raimy shows that this analysis derives complicated
effects in reduplication in which a coalesced segment affects both copies in reduplication.
For example Indonesian has a few prefixes whose behavior descriptively involve assimilation
and coalescence, including the active prefix /m@N -/, which in modern Indonesian marks
active verbs. Descriptively the /N/ of the prefix usually disappears, assimilates to the
following segment or defaults to /N/, but in the case of voiceless stops the result is a nasal
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of the same place of articulation as the voiceless stop.
(47) Indonesian active prefix (from McCarthy and Cohn 1998)
root prefix+root gloss
a. b,d,g,c,j bantu m@mbantu ?help?
b. m,n,N masak m@masak ?cook?
nomor m@nomor ?number?
N@ri m@N@ri ?horrified/ing?
c. l,r,w,y latih m@latih ?practice?
d. p,t,s,k potoN m@motoN ?cut?
tulis m@nulis ?write?
kata m@Nata ?word/say?
e. vowels, h isi m@Nisi ?fill?
atur m@Natur ?arrange?
hargai m@Nhargai ?value?
So far this is not a problem for the parallelization story. It is straightforward to specify
an affix so as to attach like (48).
(48)
m @ {+nas}
# p o t o N %
However the interaction of this prefix and its coalescence with the intensive/repetitive
reduplication lends itself slightly better to Raimy?s version of coalescence. As shown in (49)
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that the coalesced segment appears in both copies.
(49) Indonesian intensive/repetitive (from Raimy 2000, p.99)
root intensive/repetitive gloss
potoN m@-motoN-motoN ?cut?
tulis m@-nulis-nulis ?write?
For raimy this is easy to account for as in (50). Coalescence happens prior to serialization
and the resulting segment inherits from the original /p/ to be in the reduplicated loop.
(50)
This is not an immediate effect of adding reduplication to the form with parallel structure
above as in (51). Given the assumptions of ?7.6 and the similarity with the Sye pattern in
?7.4 we would precisely expect this form to surface as *m@motoN-potoN, the exact form that
Raimy?s analysis is meant to rule out.
(51) *m@motoN-potoN
m @ {+nas}
# p o t o N %
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We could imagine that the reduplication morpheme could be specified to add two back
arrows, one to /p/ and one to /{+Nas}, but since there isn?t much structurally in common
between those two nodes of the graph this reduplicative affix would need to be rather
convoluted, and then we lose the nice natural explanation that Raimy offers in terms of
coalescence feeding serialization.
There are multiple ways out of this that would preserve Raimy?s insight in PROP. A
simple one would be to posit that there are two processes that can lead to what we call
coalescence: Raimy?s node conflation idea and the parallelization we have been exploring.
Another possibility would be to modify/expand Raimy?s coalescence to apply to parallel
structures. Consider an operation that could take parallel structures and combine them into
a single segment.
(52) Parallel Coalescence
This would allow us to adapt Raimy?s analysis with coalescence feeding the resolution
of reduplication into a PROP format by applying Parallel Coalescence to the structure in
(51), yielding (53).
(53)
m @
# m o t o N %
One possible value for this operation is for the readers who may find the PROP analysis
interesting but are not on board with parallel structure in the output of phonology, as this
218
could help derive strings from the parallel streams we have posited.
(54)
9.3.4 Spanish root allomorphy
In chapter 6 I proposed an account of the Spanish kwent-/kOnt suppletion based on an
underlying root like (55) with the two options [we] and [o] fully separate. But in light of
this section?s analyses of metathesis and coalescence, I propose we could instead posit (56).
?
(55) cont (according to ch. 6)
we
# k n t %
o
?
(56) cont (updated)
u
# k n t %
e
With this form, the allomorphy would not consist of de-linking either the upper path
when stressed or the lower path when unstressed; it would rather consist of adding an arc
that orders the /u/ before the /e/ to yield [we] when stressed, or leaving the two in parallel
to coalesce into [O] when unstressed. This additive phonological rule dispenses with the
need for the precedence-relation-deleting rule we had to posit in that chapter.
9.4 Complex segments
We have seen already seen in chapter 3 how complex forms in the phonology could consist
of simultaneous components set in parallel and sent as such to the phonetics to performed
simultaneously by the articulators or heard simultaneously in perception such that a surface
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segment {+rd,+hi} may have the following form in phonology.
(57) Possible phonological form giving rise to surface {+rd,+hi}.
[+rd]
# %
[+hi]
It is easy to see how PROP may be useful to describe complex segments like doubly
articulated consonants and contour segments qua complex segments as in (58) and (59),
respectively. These analyses simply make use of the representations made available for free
in PROP
>
(58) Possible representation giving rise to [gb]
g
X Y
b
>
(59) Possible representation giving rise to [ai]
V
X Y
a I
A specific analysis of complex segments that can be adapted to PROP is the unique
and highly insightful analysis of Taa clicks in Bradfield (2014). Bradfield argues that Taa
clicks are ?concurent clusters?, clusters of segments that occur partially in parallel in time.
I will not go over the arguments for this view based on synchronic phonology, learnability,
and laboratory phonology and only describe the analysis.
Bradfield introduces a new notation (X?Y) signifying that X is concurrent with Y.
Bradfield proposes to decompose Taa clicks into ?Pure click phonemes? /? | ! { }/ and
220
?accompaniement phonemes? / h h ? ? / which combine with other non-
? ? ? ? ?
click consonants to generate the wide variety of Taa clicks through concurrent clusters.
For instance Bradfield proposes that !qh is underlyingly (!? qh). This is a concurrent
string of one click phoneme /!/ combined with a concurrent string of two phonemes, the
accompaniement / / and the non-click phoneme /qh/.
This organization of phonemes is interesting: it involves some features being in parallel
to others that are linearly ordered. This would be difficult to encode in most systems, hence
why Bradfield had to resort to inventing his new ?-notation. But it is very straightforward
to represent in PROP as in (60) using Bradfield?s symbols, or (61) featurally.
(60) Taa (!? qh) symbolically
!
X Y
qh
(61) Taa (!? qh) featurally
[+ant,+cor,?hi,+bk,?del.rel.]
X Y
[?voi,?nas,?spr.gl.,?glot.cl.] [?ant,?cor,?hi,?lo,+bk,?voi,+spr.gl.,?glot.cl.]
PROP therefore provides a way to represent Bradfield?s analysis of !Xo?o? clicks that
maintains his analysis in terms of concurrency vs. sequence, a distinction that follows
naturally from PROP.
Another type of complex segments is affricates. We could posit a PROP representation
such as (62). The pronunciation of this structure would surface as a contour as a necessary
result of the impossibility to pronounce both segments simultaneously. It is not necessary for
the two parallel nodes to be fully specified segments, it is sufficient that they contain some
incompatible features like ?continuant and +continuant (or ?continuant and +strident
221
k
k
k
k
k
k k k k k k k k
? ?
following Clements (1999)).
>
(62) Possible representation giving rise to [tS]
t
X Y
S
The question that needs to be asked then is how would motor planning deal with such
incompatible commands scheduled between the same pair of commands X and Y. It does not
>
seem that there is any optionality in the order of the [t] and [S] portions of an affricate [tS]. A
speculative but reasonable assumption would be that when nothing else determines the order
of two segments their relative will be left to whatever is easiest to schedule for phonetics.
If the muscle movements of a stop are faster to prepare than the muscle movements of
a fricative ?a reasonable claim since a fricative requires a more delicate aperture of the
constrictor? this might be all we need to say. This is fundamentally a scheduling conflict:
two segments are competing for use of the articulator, and motor planning is in charge or
deciding which one can go first. If we imagine that the decision is made on the basis of the
time to process the segment by scheduling the faster segments before the slower ones, we
might derive the facts of affricates.
However empirical facts about other complex segments do not lend themselves to such
an analysis. Glottalized consonants for instance would lend themselves to an analysis in
terms of a consonant with a parallel glottal stop, but it appears that the timing between the
glottal and suprasegmental events can vary from language to language and can even be allo-
phonically determined within a language. Howe and Pulleyblank (2001) describe Yolumne
and Kwak?wala whose glottalized sonorants are post-glottalized in codas but pre-glottalized
in other contexts, compared to Sm? algyak, Montana Salish, and Lai whose glottalized sono-
rants are always pre-glottalized. It therefore seems to be the case that if glottalized segments
are to be analyzed as parallel complex segments then, unless a universal phonological con-
ditioning can be found for all pre- vs. post-glottalized consontants, it seems that sometimes
the parallel complex segments are under-determined by the fully parallel notation above
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and must be handled by language-specific rules or conventions.
9.5 Ineffability and paradigmatic gaps
An interesting phenomenon of morphology is that of ineffability or paradigmatic gaps, slots
in the paradigms of a language where no combination of a root with any affix is acceptable
to native speakers. This phenomenon is already puzzling at first sight in light of Language
as a productive system, but further inquiry also shows multiple difficulties relating to the
acquirability of a gap in light of the problem of negative evidence, or to the nature of how
it is that one can know of a gap.
A classic example (dabrowska2001learning, Gorman and Yang (2019) is that of Polish
masculine genitives. Polish has two forms of the masculine genitive suffixes which are not
phonologically predictable: -a and -u, but some roots cannot take these suffixes. Some
roots like balon cannot take either suffix, and cannot be used in the genitive whatsoever.
This contrasts with indeclinable roots like guru which also cannot take either suffix, but
can surface without either in the genitive.
(63)
nom. gen. gloss
li?sc? li?sc?-a ?leaf?
dom dom-u ?house?
*balon-a
balon ?balloon?
*balon-u
guru guru ?guru?
Gorman and Yang?s acquisition-based analysis, embedded in a specific morphological
model that is not relevant to this thesis, is that neither suffix is sufficiently common in
the language to reach a point where the language user will treat them as productive. But
an equally important question is: what is the nature of the ban itself? It seems strange
to assume that the learner acquires explicit *balon-a and *balon-u constraints, and hence
Gorman and Yang offer a non-generation analysis: the two suffixes -a and -u are each
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specified to attach to a finite list of roots and neither is truly a default.
This analysis can be recast in PROP with the tools used for MCA in chapter 6. The
roots would be stored as (64), and the affix as in (65). Crucially, ballon and guru lack any
diacritic that (65) can pick up, and balon lacks an underlying path to %.
(64)
# >l i C tCA
# d o mU
# b a l o n
# g u r u %
(65)
[A] a
%
[U ] u
The idea is that when affixed to a form with an A or U feature the affix will be able
? ?
to find this feature and add a path to %, but in the case of ballon and guru it will
not find either feature. this means that in the genitive of balon there will be no path from
# to % whatsoever. This contrasts with the case of indeclinable nouns like guru in which
there is a path in the underlying form, so even though there are no [A] or [U ] features for
the affix to attach to, the form will still be pronounceable in much the same way as the
-en affix discussed in 5.3.9. The only new thing this analysis requires is the idea of roots
which do not underlyingly have a path from # to %. Given the assumptions so far, there
is no reason to posit any restrictions on the valid graphs allowed in the theory, and in this
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light disconnected graphs are allowed by default and it would take a special stipulation to
prevent them. I propose that there is no reason to ban them and they in fact serve to
explain paradigmatic gaps like in Polish: some roots lack a path from # to % and if the
affix fails to provide one the combination of the two will simply be unpronounceable.
9.6 Templatic Morphology
A major phenomenon that helped strengthen the position of Autosegmental Phonology?s
explanatory adequacy was its account of Templatic Morphology in Semitic. According to
the now standard account of McCarthy (1981), the formation of Arabic binyams in (66)
can be done by positing the CV-template of the binyan, the vowel melody of the aspect,
and the consonant structure of the root to be three separate morphemes inserted in parallel
225
and joined by autosegmental principles as in (66).
(66) Classical Arabic binyans from McCarthy (1981, p.385)
226
(67) Autosegmental analysis of Classical Arabic (Haile and Mtenje, 1988)
PROP is capable or recapitulating the gist of this analysis by simply positing three
parallel streams as in (68). Following the assumptions made so far this would be sufficient
to account for the pattern of contrasts of Classical Arabic.
(68) kutib, ?it was written?
u i
# C V C V C %
k t b
This is very straightforward, but it is worth mentioning because Raimy (2007) had
already proposed a way to handle templatic morphology in Multiprecedence without using
227
parallel streams. Raimy takes the vowels to be explicitly placed onto the root.
(69) Derivation of Binyan VII (Raimy, 2007)
Raimy?s approach departs from the classical analysis. It require the CVCV pattern of
binyams to emerge as an accidental side-effect of the explicit positioning of vowels rather
than to come as their own templates. This loses the generalization offered in the autoseg-
mental analysis. The PROP analysis on the other hand maintains the classical analysis
without any further assumptions.
9.7 Parallel features not pronounced throughout the form
An interesting type of variable-position affixes is also attested under the name of ?featural
affixation?. Consider the following Chaha data from Akinlabi (1996). The generalization is
that a third person singular masculine object is marked with labialization of the rightmost
labializable consonant, meaning a labial or a non-palatalized dorsal. In the absence of such
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a segment the form remains unchanged.
(70) Chaha object agreement
without object with 3sg.m. obj. gloss
da?na?g da?na?gw ?hit?
na?da?f na?da?fw ?sting?
na?ka?b na?ka?bw ?find?
na?ka?s na?kwa?s ?bite?
ka?fa?t ka?fwa?t ?open?
ba?ka?r ba?kwa?r ?lack?
qa?ta?r qwa?ta?r ?kill?
ma?sa?r mwa?sa?r ?seem?
ma?kya?r mwa?kya?r ?burn?
sa?da?d sa?da?d ?chase?
The first part of the account is to analyse the labialization as a parallel affix containing
a +labialized feature creating structures like (71). This immediately derives the forms in
which there is one or no labializable segment.
(71) na?da?fw
+labialized
# n a? d a? f %
The PROP account could stop here. The above is sufficient for all the existing contrasts
of Chaha, as in the cases of Mende or Siane in the previous chapter. The only question we
could ask is why is the labialization limited to the final labializable segment, rather than
being realized as labialization across all labializable segments of the form. For instance why
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is the form [na?ka?b] labialized as [na?ka?bw] and not *[na?kwa?bw]. Again I suspect that this
could be either language-specific phonetics or a late phonological rule. The latter could
simply consist of a rule adding a path from segments preceding labializable segments to the
[+labialized] feature.
(72) na?ka?bw
+labialized
# n a? k a? b %
However in general I would maintain that the details of the phonetic realization of a
form like (71) is not necessarily the concern of PROP. All that (71) specifies is that the
feature +labialized follows the beginning of the word and precedes the end of the word and
[na?ka?bw] satisfies this requirement. PROP underspecifies the exact details of linearization.
9.8 Featural parafix in Mokulu
The parallel affixation predicted by PROP has so far mostly been discussed in a few forms:
word tones, vowel harmony, single features, and CV templates. One pattern of parallel
affixation that did not fit in any of these categories is that of Mokulu as described in Roberts
(1994). When comparing the completive aspect to the citation form of verbs, Roberts
notes that ?the completive is uniformly characterized by an initial voiced consonant and a
high vowel? and attributes this to a pair of floating autosegmental features [+voice][+high].
According to Roberts this is a fully regular pattern and the only major idiosyncrasy is that
230
initial /t/ is immune to this voicing.
(73) Mokulu from Roberts (1994, p.95)
Roberts?s analysis can be straightforwardly translated into PROP with an affix that
carries the two features.
(74)
+voi +hi
# k o p p e %
This type of small non-spreading featural affix of more than one feature seems rather
rare, cross-linguistically but PROP handles it straightforwardly. It is one more example of
the type of rare word-formation patterns that can be easily accounted for in PROP.
9.9 Peak Delay
In ch. 3 we saw how the phenomenon of tone donation could be handled in PROP with
forms such as (75) in which the tone is both independent from the segmental features of its
morpheme and simultaneously linearly ordered, two things that autosegmenta lrepresenta-
tions cannot do at once.
(75)
231
T %
# A B C
[#? ]
This analysis can be interestingly connected to the Peak Delay analysis of apparent
tone shift in some languages. For instance consider Kikuyu as described in Kaplan (2008,
citing Clements 1984). The interesting pattern is that although rOr and mo are underlying
toneless, the morpheme ma causes them to surface with a high tone. The traditional
autosegmental analysis is that ma comes with a H tone, which shifts to the following vowel.
(76)
to rOr aG a ?we look at?
to mo rOr aG a ?we look at him/her?
to ma rO?r aG a ?we look at at them?
ma? rO?r aG a ?they look at?
ma? mo? rOr aG a ?they look at him/her?
ma? ma? rO?r aG a ?they look at them?
Studying a similar phenomenon in Chichewa, Myers (1999) found an interesting phonetic
generalization: the f0 peak of the tone is predictably aligned not with the vowel it happens
on, but with the previous one. Kaplan (2008) proposes that there is in fact no tone shift
in the phonology of Kikuyu, rather the tone is still associated with the vowel of its original
morpheme, but phonetic implementation allows the exact realization of alignment to be
parametrizable such that a tone associated with a vowel can be set as aligning the center of
the vowel with the peak of the tone, or as aligning the center of the vowel with the onset of
the tone rise. In the latter case the peak may be on the next vowel despite being associated
with its original vowel in the phonology.
In PROP we can make sense of these phonetic findings without adding anything new.
If tone donation works as in ch. 3, the form of the ma morpheme would be like (77) and
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attach as in (78).
(77)
H [[V ]? ]
# m a
[#? ]
(78)
H
m a
# r O r %
Crucially in such a representation, the donated tone is in fact ?associated? with the vowel
that the tone immediately follows while it has no direct relation with the vowel it was put
in parallel with. the information the phonology contains is that H follows [a] and precedes
[r]; the fact that that puts it in parallel to [O] is not strictly part of the representation. It
seems perfectly reasonable then that in the phonetic implementation of such a structure
the timing of the H tone will be more correlated with the vowel it does in fact follow in
the representation than with the one it happens to be parallel with. As such in PROP we
can derive the phonetic insight of Myers (1999) and Kaplan (2008) without having to add
any parameter in the phonology. The phonetic implementation only has the precedence
commands it gets when it comes to schedule the motor commands of speech, so if the
donated tone is only specified in relation to the previous vowel then it will be scheduled in
relation to that vowel.
Hence in PROP the crucial contrast is not in whether alignment with the peak is ranked
above alignment with the onset, but simply boils down to (79) vs. (80). In (79) the tone is
scheduled after the previous vowel and it will therefore be aligned with it. In (80) on the
other hand, the vowel and the tone both follow and precede the same segments, so they are
233
both scheduled in time after the same segment, and hence they will tend to align.
(79)
T
V C V C
(80)
T
V C V C
9.10 Self-placing affixes & Prosodic Optimization
In chapter 4, we saw examples of affix position determined in the phonology, either through
the use of empty segments forcing parallel segments to align with them, or with explicit
diacritics in the representation. And above we saw parallel affixes with some optionality as
to where they could surface, to be determined either by phonology or phonetic convention.
In all of those cases there was something explicit enforcing the compatibility of the two
parallel streams: often one stream was ?deficient? in some way and need some sort of ?host? on
which to surface, like the consonants lacking a +consonant feature in Afar or the individual
features in Chaha or in all of the vowel harmony examples we have seen. And if the parafix
consisted of full autonomous phonemes then their location needed to be ?guided? somewhat,
either through a sticky end specifying their attachment point or as in the Siouan examples
of unpredictable infixation through diacritics on the form.
But there is a logical option that is worth mentioning in addition to those, namely
affixes consisting of full autonomous phonemes whose position is unspecified in the repre-
sentation, allowing them to surface wherever they fit best, perhaps with some free variation,
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imbricating themselves into a stem.
(81) abstract example of imbrication
x y z
# a b c d e f %
 [abc-xyz-de]
This idea of infixes being inserted wherever they prosodically fit best is the standard
analysis of infixation in OT. Recall the Taglog infixes from ch.2, repeated in (82). The
OT analysis of this pattern is that constraints against codas and onset-less vowels are
disfavouring *um-tawag and favouring t-um-awag over it. According the the OT analysis
the affix is infixed in order to prosodically optimize the surface form.
(82) Tagalog um-infixation (Kager (1999), citing French (1988))
alis um-alis ?leave?
tawag t-um-awag ?rewarded?
In contrast the PROP analysis of this pattern in ch.2 had sticky-ends directly placing
the affix before the first vowel, which derives the same pattern in more explicit terms. But
if PROP were to borrow Prosodic Optimization as a phonetic scheduling principle, we could
replace the explicit sticky-end analysis with a parafix like (83) and leave the ordering entirely
up to the phonetic motor planning. If we posit the equivalent of constraints against codas
or onset-less syllables in the phonetic, or even just a bias in favor of CVCV alternations,
this could enforce the imbrication.
u m
# t a w a g %
In his dissertation on infixation, Yu (2003) spends a major part of the second chapter
arguing against Prosodic Optimization in the placement of infixes. Yu finds that all infixes
can be specified for their point of attachment and that none of them require an optimization
analysis. In fact he finds many infixes whose position does not optimize anything, or even
creates marked structures. This is, in my opinion, a good argument against the type of
235
situation in (82). He also notes a lack of infixes whose placement actually varies signifi-
cantly based on the structure of its host. The Tagalog infix above is very consistent in being
placed before the first vowel of the noun. Yu concludes that a theory with explicit place-
ment of infixes better accounts for the facts and that Prosodic Optimization is empirically
inadequate.
There is however one language pattern that seems to be counter to Yu?s generalization
that Prosodic Optimization is never needed in the analysis, and unfortunately Yu does not
discuss it in his dissertation although he mentions other infixes from the the same lan-
guage. In Alabama (Muskogean), there is an interesting word-formation pattern that I
will only sketch here. This example is doubly worth mentioning because on top of being a
Prosodic Optimisation pattern, an analysis already exists that crucially depends on under-
lying unordered segments. Here is how (Montler and Hardy, 1991, p.2) introduce the facts
of Alabama negation:
(83)
The negative appears variously as a suffix, infix, or prefix with the shapes -ki, -
ikko, -ki -, -kii-, or ik-. We shall show that each of these is derivable given (1) the
phonological shape of the stem to which it is attached, (2) the underlying form /k/,
/ i/ which is unspecified for linear order, and (3) a general constraint on the shape
of Alabama verbs to the effect that they must conform to a heavy-light word-final
syllable frame.
This is too amenable to a PROP analysis to ignore here. And underlying form unspec-
ified for linear order is what PROP is most uniquely capable of. I will refer the reader to
236
Montler and Hardy (1991) for a list of examples, I will only copy the generalizations:
(84) Alabama /k/,/i/ affix placement (copied from Montler and Hardy 1991, p.7)
(85) Negative Placement (copied from Montler and Hardy 1991, p.9)
(a) If the onset of the final syllable is /k/, then place before it.
(b) If the stem already conforms to the Alabama verb insert /k/, /i/ into the
rime of the penultimate syllable. (c) Elsewhere, place /k/, /i/ so as to conform
to Verb Frame.
Contrary to Yu?s claim, there does not seem to be an easy way to specify the position of
this affix as a definite attachment point. there is no anchor point that we can single out as
what the infix consistently precedes or follow. The position and order of the segments will
be such that it optimizes the syllable structure of the word. In PROP the analysis would
be to posit a parafix that puts both a /k/ and an /i/ in parallel to the whole form, and
then the phonology of the language determines the position after that.
(86) Alabama negative affix
i
# %
k
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Just like in the discussion of surfcae optimization for allomorphy in 5.4.6, I mention this
idea more as a logical possiblity than as a serious proposal and I will not push this idea
any further. I am not at all convinced that this is the best analysis, even of Alabama. I
find it mostly worth mentioning for its already using unspecified linear order. It might not
be absolutely necessary for this account to work to appeal to the equivalent of Prosodic
Optimization. There could be a series of rules that explicitly add the arrows between the
/k/, /i/, and the stem necessary to derive the pattern. Some arbitrariness is already needed
to handle the stems with final onset /k/.
9.11 Above the ?word?: graphs all the way up
The discussion so far has been restricted to the word and some clitics. However I take for
granted the following two claims that have been made previously in the literature:
? Syntax-all-the-way-down: There is not special word-building morphology and the
mechanisms responsible for building syntactic structures also serve to assemble mor-
phemes together (Lieber 1992; Halle and Marantz 1993, among many others).
? There is no such things as words: the notion of word does not have a special theoretical
status. (Marantz, 1997)
Given the assumption that the word level is not special, it would be strange if the graph-
based word formation I posited in this thesis was arbitrarily restricted to the traditional
word. So it would be useful to discuss the application of PROP above the ?word? level.
There are independence arguments to think that the phenomena we have discussed
in terms of PROP are not restricted to the word level. Consider first reduplication. Lidz
(2001) shows that echo-reduplication in Kannada can target chunks much larger than single
words. The semantics of ?X and X-like things? conveyed by full reduplication, replacing the
first CV of the second copy with gi(i)-. Lidz provides examples of reduplication copying
anything from single roots (87) and functional items (88), to entire VPs (89) and PPs (90).
(87) ooda-giida beeDa
run-run proh ?Don?t run or do related activities?
238
(88) meelee-giilee
above-red
?Above and the like?
(89) nannu baagil-annu much-id-e giigilannu muchide anta heeLa-beeDa
I-nom door-acc close-pst-1S red that say-proh
?Dona?t say that I closed the door or did related activities.?
(90) pustav-annu meejin-a meele giijina meele nooD-id-e
book-acc table-gen on red see-pst-1s
?I saw the book on the table and in related places.?
These examples suggest that however reduplication is done, its mechanics must be available
at any point in the morphosyntactic structure-building system. It cannot be restricted to
a word-formation module or otherwise exclusive to wordhood. Specifically if reduplication
is done in the lines of Raimy (2000) with loops in the representation, then a graph-based
representations must be in use all the way up in syntax.
The PROP affix required for this reduplication is something along the lines of (91),
adding a path from the end of what it attaches to to the segment following the first vowel.
But crucially it must be able to be affixed to the phonological output of very large syntactic
chunks such as an entire VP.
(91) Kannada ?X and related things?
[ ? %] g i [#? C ? V ? ]
Idsardi and Raimy (2013) distinguish linearization in the syntax from serialization of a
multiprecedence graph in phonology. The proposal of this section amounts to positing that
all linearization is serialization.
The existence of non-concatenative phenomena requiring ?morphological?-type machin-
ery high in the syntax argue against the family of hypotheses that I will broadly group
as Node-Ordering theories of linearization. The two main theories of order in syntax are
239
Head-Directionality Parameters (HDP) and the Linear Correspondence Axiom (LCA). The
former puts order as a binary parameter putting the head before or after its complement.
The latter even more strictly posits that the order between syntactic objects is determined
by asymmetric c-command, yielding a universal head-initial word-order. Both of these
purely concatenative theories will fail to explain any non-concatenative phenomenon in lin-
earization. Reduplication was just given as an example but there are others we will see
below.
Independent problems with the LCA have been pointed out multiple times in the liter-
ature. Uriagereka (2005, p.47) discussed the fact that the specific order produced by the
LCA is arbitrary, as c-command could map onto precedence in either direction. Wojdak
(2005, p.72-73) argues that this is a concpetual challenge for the idea. Wojdak also brings
up empirical problems in that the LCA ruins analyses relying on differences in base order.
She mentions the proposal that Dutch and Basque crucially differ in the base OV-VO or-
der from Vicente (2004,2005). She also mentions the problem of analyses with rightward
movement in Beerman, Leblanc, and van Riemsdiek (1997). Abels and Neeleman (2012)
discuss the fact that some of the empirical predictions that have served as a confirmation
of the LCA such as the derivation of Greenberg?s Universal 20 by Cinque (2005) can be
derived in other natural ways, and that the claim that the LCA can derive phrase structure
is false. Further criticism has come from specialists of languages traditionally analyzed as
head-final or specifier-final claiming failure of explanatory or sometimes even descriptive
adequacy of LCA-compliant analyses of these languages, e.g. Cho on the problems it poses
for Korean, Kural (1997) for Turkish, Rohrbacher (1994) for German and Yiddish, Bayer
(1999) for Bengali, and Wojdak (2005, ch.3) for Nuu-Chah-Nulth among many others.
Non-concatenative phenomena are a further empirical problem that argues not only
against the LCA, but also against HDPs. We have seen reduplication in linearization. A
second phenomenon that argues for the mechanics of non-concatenative morphology apply-
ing all the way up syntactic structures is the case of endoclitics: the rare phonomenon of
morphemes with clitic-like syntax in that they have syntactic scope over an entire phrase
that they phonologically lean on, except that they surface infixed within a peripheral mor-
pheme of their complement rather than as a proclitic or enclitic. This phenomenon is most
240
convincingly described in Pashto (Kopris and Davis 2005; Kopris 2009; Bo?gel 2010; Din
2013, among others) and Udi (Harris 2000, 2002). Examples of the person marker endo-
clitics in Udi are in (92). The two part of the discontinuous morphemes broken by the
endoclitic are glossed with subscripts 1 and 2.
(92) Udi endoclitics (from Harris 2000)
a. pasc?aG-un Gar-en go?lo? be-ne-G-sa met?a-laxo
?
king-gen boy-erg much look1-3sg-look2-pres this.gen-on
?The prince looks at this for a long time?
b. kaGuz-ax a-z-q?-e
letter-dat receive1-1sg-receive2-aorII
?I received the letter.?
Endoclitics pose a problem to proponents to Node-Ordering Theories. Whatever ac-
counts for linear order in Udi must have access to segments and be more powerful than
something whose only options are ?before? and ?after?. In PROP however if order is only
determined in the phonology via lexical items and their sticky-ends, endoclitics are unsur-
prising.
Yet another type of problem is the case of simultaneous linearization of syntactic items.
The clearest case for this is from signed languages. Ever since Liddell (1980) it has been
known that in American Sign Language non-manual markers typically occur over extended
portions of the sentence. Liddel found that the topic marker was realized simultaneously
to the entire topic. Many other examples have since been described. For example Jessica
Harmon demonstrates the simultaneous articulation of non-manual adverbs, here a mouth
movement resembling [po], simultaneous to the VP it modifies as in (93) (Harmon, 2016),
and non-manual negation simultaneous to what it has scope over (Harmon, 2017). Asada
(2017) echoes Harmon?s finding about adverbs and VPs in Hong Kong Sign Language and
further found examples of parallel conjunctions conveying simultaneity of the events.
(93)
241
It has been known since Liddell (1977) and Baker and Padden (1978) that the scope of
these non-manuals is the c-command domain of the functional item spelled-out as a non-
manual, i.e. everything under its sister node. This simultaneity has led Harmon and Asada
to argue in favor of a multidominance structure following Hornstein (2009) to account for
the linearization, but no independent syntactic evidence is given for this structure; it is only
required for them because of the limitations of Node-Ordering Theories.
In contrast PROP can maintain the classical c-command analysis and create parallel
structures in the phonology. The adverb simply has syntactic scope over the VP, but its
UR does not specify an ordering between its non-manual element and the phonological
content of the VP. For PROP it is completely unsurprising that a morpheme can be put in
parallel to another in sign languages since parafixation is needed for spoken languages too.
Pressing on this point, it is worth noting that multiple researchers have highlighted the
simultaneity as an essential and fundamental difference between sign languages and spoken
languages, taken as purely linear in organization. Frishberg (1975) puts it most succinctly
with the claim that ?the essential character of language based on a sound signal is its se-
quential nature? and ?[t]he corresponding essential character of a language based on a visual
signal is simultaneity.? Aronoff et al. (2005) expand on this view with the thesis they call
the ?paradox of sign language phonology?. I hope that the discussion so far has sufficiently
shown that multiple phenomena of spoken languages benefit from simultaneous analyses.
Linearity vs. simultaneity in morphology are both allowed and nothing we should consider
the ?essential character? of one modality or another. Simultaneous morphology is allowed
in sign languages because it is allowed in Language, and many phenomena instantiate this
possibility in spoken languages too. Conversely unambiguous sequential morphology is also
attested in signed languages, e.g. the agentivier suffix of ASL (Sandler and Lillo-Martin,
2006, p.64-66).
If one or the other modality strongly biases languages to converge more toward a si-
multaneous or sequential character, this will have to be more indirect than an ?essential
242
character?.
Vowel Harmony and Tone also contain phenomena that challenges the notion of word-
hood. Even though Vowel harmony has been argued to be a universally word-bound phe-
nomenon (usually employing some notion of Phonological Word), Downing (2018, citing
Mutaka, 1995) shows that Kinande ATR harmony is phrasal and can spread to an entire
DP, from the adjective to the noun, but not within VPs from a noun to a verb, making
an analysis based purely on prosodic phrasing impossible. This is a problem for theories
where word-hood is important, but in PROP this is simply a case where the noun is put
in parallel to the ?ATR feature of the adjective. Similarly for tone, Marlo et al. (2015,
p.8) discuss the fact that in Kuria tone assignment is a phrasal process. For verbs with the
/4/-melody, the melodic H is assigned to the fourth mora of the stem. If the stem is shorter
than 4 moras then the tone surfaces on the following noun. I PROP both cases are simply
the extension of what we have seen so far with a root being put with another root in a way
that makes it parallel to a feature.
We can think of the ?syntax all the way down? proposal in the following way: we al-
ready need a structure-building operation to bring syntactic items together in syntax and
the simplest theory is that the same operation is bringing morphemes together in words.
Analogously and complementarily, PROP offers a data structure and mechanics for the con-
struction of phonological structures in words, and the simplest theory is that these account
for phonological material above words too. Syntax all the way down and graphs all the way
up.
Node-ordering hypotheses were predicated on the assumption that phonology can only
deal with linearized inputs. With the advent of Minimalism in particular the goal was to
make linearization in syntax forced by bare-output conditions at PF in the sense of Chomsky
(1995). E.g. Uriagereka (2005) sees the LCA as the minimally complex way to reuse a
relation that exists in syntax and convert it into another to satisfy the PF requirement that
its input be linearized.
But in PROP, this condition on PF is unnecessary. Phonology deals perfectly well with
inputs lacking any ordering between them. PROP is self-linearizing. Vocabulary items
carry the sticky ends that will place them onto a stem, and serialization will take care of
243
finalizing the final order. As such with PROP there is no need to say anything whatsoever
in syntax about linear order. There is no order in syntax proper and there is no order
imposed at PF either. Syntax is unordered hierarchical structure throughout.
There is one caveat however, namely all cases we have seen so far had the asymmetric
form of one affix with one or more sticky-end attaching onto a static stem build from a root
with a # and %. This can work without issue for all cases in which a head merges with a
complement, and it can even work with roots merged with a complement if we allow roots
to contain sticky-ends since nothing we said so far dissallows those, but it is not yet able
to handle more symmetric cases involving Merge applying to two phrases, each with a root
and affixes around them like (94). These cases are not easily analyzable as having one side
containing sticky-ends.
There are probably multiple ways to solve this issue and I will propose one grounded
in an assumption that is increasingly common in the world of Morphology, namely that
the input to vocabulary insersion is a Dependency Graph, as opposed to a Constituency
Graph, following in particular Svenonius (2016) who uses Mirror Theory following Brody
(1997, 2000); Svenonius and Bye (2011); Svenonius (2012); Adger (2012).
In this framework, heads do not project over their complements as in (94), rather they
take their complement as a dependent as in (95).
(94)
XP
X Y
(95)
X
Y
Crucially, structures that traditional X-bar theory treat as specifier-head-complement
like (96) have two dependents as in (97).
244
(96)
XP
YP X?
X ZP
(97)
X
Y Z
Assuming that this is the structure on which spell-out applies we can resolve the prob-
lem we faces with Merging two phrases: in Mirror Theory two phrases can only meet as
dependents of a head. Two phrases therefore never meet on their own, they always meet
with a head. As long as this head contains the phonological material with sticky ends
capable of attaching its dependents together, PROP will go without any issue.
Consider the spell-out rules in (98) applying to the dependency tree in (97). Bottom-up
spell-out would first target Y and Z to transfer as (98-a) and (98-b) to the phonology,
simply putting them together unordered as in (99). Then X would be targeted for spell-out
to tranfer (98-c) onto (98), yielding (100) and the order [abcxyz]
(98)
a. X ?? /[c]? [x]/
b. Y ?? /#? a? b? c? %/
c. Z ?? /#? x? y ? z ? %/
(99)
a b c
# %
x y z
245
(100)
a b c
# %
x y z
This spell-out order ensures that a head is always spelled onto any complex phrases
merging together, and this head can be responsible for imposing an order between them.
Or as in the case of ASL above for not imposing one and leaving them parallel. In the
example above X is phonologically null and only imposes an order between the segments of
Y and the segments of Z, but naturally it can also include overt segments to add between
them, as well as a prefixed or a suffixed part, up to the complexity of the UR of X.
The structure in (100) immediately derives a number of useful facts. For instance con-
sider the case of vowel harmony in compounds. In Finnish for instance, in the case of
compounds with different backness specifications, the second member will control the back-
ness of its suffixes. Va?limaa-Blum (1999) gives the example of tarhaka?a?rme+tta? ?of the
garden snake?, in which the suffix is front in accordance with kaa?rme, with complete disre-
gard for the backness of tarha. This follows automatically from the assumptions adopted
so far. In the form in (101) the +bk and -bk both scope over the end of the word and seem
like they would equally spread to suffixes, but the addition of an order between the two
roots as in (102) resolves the ambiguity as the scope of -bk is now fully nested within that
of +bk, and thus by the Nesting Principle discussed in chapter 3 that one will win in that
246
scope, and hence that one will be realized over any subsequent suffix.
(101)
+bk
t A r h A
# %
k A A r m e
-bk
(102)
+bk
t A r h A
# %
k A A r m e
-bk
The example of the head in (100) above is unnatural in that it relies on knowing that
the last segment of Y is c and the first of Z is x, but in a realistic derivation any segment
can overtly end any phrase. A hack to solve this is to posit that all phrases of a certain
type begin or end with a silent affix that introduces a feature onto the phonological chunk
for the head to target.
Consider the English double-object construction. Following Pylkka?nen (2002), they
have the structure in (103), with an applicative head joining the indirect and the direct
247
object. Converted into a Mirror-theoretic dependency structure it would look like (104).
(103) English low applicatives (Pylkka?nen, 2002, p.19)
VoiceP
I
Voice
bake ApplP
him
Appl cake
(104) Mirror-theory version of (103)
Voice
I bake
Appl
him cake
If the UR of Appl is to be responsible for ordering him and cake, something must be on
there to be picked on by the sticky-ends of the applicative. A plausible way would be for
the the dative case and accusative case are covert affixes, respectively a suffix and a prefix,
which covertly introduce features, respectively D and A, in the correct place on the form
as in (105) and (106).
(105)
# h I m %
D
248
(106)
A
# k e k %
With this in place the applicative could be specified as in (107) and create the correct
structure in (108)
(107)
[D] [A]
(108)
h I m
# A D %
k e k
This is far from an elegant analysis. These features do little more than recapitulate
syntactic information in the phonology. This is not an illuminating analysis, but simply a
demonstration of how PROP could take over the task of linearizing syntax with only the
phonological items? sticky-ends serving to order phonological material with regard to each
other.
9.12 Intonation as morphemes
If PROP is extended to phenomena far above the ?word? level, its power to add parallel
tonal structure can be applied to handle intonational melodies as morphemes. This was
proposed before, e.g. by Cheng et al. (2000) for French Yes/No raising intonation, and
more generally by Wakefield (2016) who proposed that intonation is fundamentally caused
249
by morphemes with scope over the whole sentence with meanings/functions comparable
to sentence-final particles that are clearly morphemic, building his argument on the fact
that many Cantonese sentence-final particles translate consistently into English intonational
contours. For instance he proposes that the two yes/no interogative particles of Cantonese
aa4 and me1 have a one-to-one relationship with subtly different yes/no question intonation
contours in English with a mid-rising and a high-rising final contour respectively.
(109) Translation of aa4-suffixed sentence (copied from Wakefield (2016))
(110) Translation of me1-suffixed sentence (copied from Wakefield (2016))
In PROP we can directly capture this analysis. It suffices to posit a single syntactic
head, common to Cantonese and English and very high in the syntax, which is spelled out
250
as enclitic in Cantonese and as a parafix in English.
9.13 Syllables and Stress
The notions of syllables and stress have been conspicuously absent from this dissertation.
The role of the syllable in PROP deserves a much more detailed exploration than can be
given here. Being all about precedence, PROP does not immediately mesh well with the
standard understanding of the syllable as a hierarchical unit. There are a number of logical
ways we could proceed. At one extreme we could join the ranks of syllable-skeptics and
seek to eliminate the syllable as an explanatory unit of the theory (e.g. Samuels 2009), at
another extreme we could abandon pure PROP and admit hierarchical syllables on top of
the graphs needed for other phenomena.
Alternatively we could integrate syllables by just admitting them as a symbol of the
theory without making any other claims about it. This was briefly suggested by Idsardi
(2019) who proposed PROP structures such as (111) for the syllable [ju]. Here ? is just one
symbol among all the others and whatever effects it has would come from its placement.
(111)
?
front round
# %
C V
high
There are some benefits to this idea. For instance it allows for direct encoding of certain
facts of syllable organization such as the notion of ambisyllabicity. For instance the differ-
251
ence between (112) and (113) is simply whether the middle consonant is only in the scope of
the second syllable or in the scope of both. The latter might be what ambisyllabicity really
is. Under this view, a syllabification algorithm would be about inserting ??s contextually,
e.g. in parallel to every V.
(112) No overlap between syllables
? ?
# C V C V C %
(113) Ambisyllabic Consonant
? ?
# C V C V C %
Stress could be handled in an analogous way with simple stress nodes added in parallel
to syllabic and segmental nodes, e.g. in (114).
(114) No overlap between syllables
stress
? ?
# C V C V C %
This proposal about stress has the advantage that it can potentially be used to translate
bracket-based metrical-grid analyses such as Idsardi (1992). In Idsardi?s system brackets
are added via rules that create domains from which a Head can be projected. E.g. the
analysis of Koya in (115) consists of five rules: 1) first add a bracket to the left of heavy
element (here syllables), 2) add a left bracket on the left of the leftmost element, 3) project
the leftmost element of each domain to the next tier, 4) add a left bracket on the left of the
leftmost element ofthis new tier, and 5) project the leftmost elelement of this new tier onto
yet another. This generates the Koya stress pattern of main initial stress and secondary
252
stress on every subsequent heavy syllable.
(115) Koya stress Idsardi (1992, p.15)
We can convert this style of analysis by reinterpretating the brackets as ?there is a
stress on this side?. Rather than rules adding a bracket that creates a constituent that will
eventually project, we can skip these middlemen and talk of rules adding stress directly in
parallel to heavy syllables and to the whole word. ?Projection? in this view would be about
the subsequent realization of this stress at one location within its span in language-specific
ways.
(116)
stress
stress
stress
# L L H L L L H L L %
Yet another possibility would be to dispense with special symbols for syllables and
employ only the notion of precedence like (117). A word like (117-a) would be syllabified
253
with the addition of arcs from onsets to onsets like (117-b), and then footed as in (117-c).
(117)
a. # a d v e r t i z m e n t %
b.
# a d v e r t i z m e n t %
c.
# a d v e r t i z m e n t %
Although these arcs may appear to be be vacuous for introducing redundant precedence
relations, the idea behind this representation would be to capitalize on the idea sketched in
?9.9 above that precedence arcs regulate the timing between segments. The arcs added in
(117) would have the effect of enforcing a kind of abstract rhythm between certain stretches
of phonological material. Although the notion of stress-timed vs. syllable-timed languages
from Pike (1945, p.34-36) has fallen out of favour since Dauer (1983), the presence of such
arcs could contribute to the speakers? perception of isochrony in their language, even if this
perception is not phonetically real. Under this view syllable effects and stress would then
be computed on the basis of these structures with rules sensitive to preceding or succeeding
more than one segment.
The question of how to handle prosodic structures in PROP is definitely an open question
that requires further research.
9.14 Bracketing Paradoxes
There are a number of so-called bracketing paradoxes that do not pose any problem anymore
in PROP. Consider the classic example of nuclear physicist. The claim is that the semantics
requires the analysis [[nuclear physic]+-ist] (a nuclear physicist is a specialist of nuclear
physics, not a physicist who is nuclear) while the phonology requires [nuclear + [physic+ist]]
because physicist is one word in which [k]&[s] allomorphy took place. But in PROP there is
254
no problem because allomorphy is a purely linear phenomena in the sense that it is entirely
decided by what an affix attaches to and requires no notion of phonological word. If (118) is
the representation of physicist then nuclear physicist can be as in (119) in which it doesn?t
matter whether or not nuclear is added before or after -ist ; -ist simply follows the whole
form and allomorphically selects the [s] by attaching to it, regardless of the internal syntactic
complexity of the nuclear physics compound which word-formation is not sensitive to.
(118) physicist
k
# f i z i %
s i s t
(119) nuclear physicist
n u k l e a r
k
# f i z i %
s i s t
9.15 Marginal Phenomena
This final section of this chapter will cover marginal phenomena which PROP may be
able to handle, but that I am not even convinced properly belong to a narrow theory of
word-formation. The discussion is meant to be suggestive of the power of analysis of PROP.
9.15.1 Blends
The first is blends formed from two other words like smog< smoke + fog, brunch<
breakfast+lunch or spork spoon + fork. One could imagine that this is done with the
255
use of parallel streams for the two source words as in (120).
(120)
s m o k %
#
f A g
Maybe the above could be sufficient for the system to implement some sort of post-
phonological ?convention? linearizing the above with the onset of one and the rest of the
other. A common scenario is blends overlapping at their meeting point when they have
some segments in common (Bat-El, 2006). Alternatively this could be made explicit with
a vocabulary item adding an arrow.
(121)
s m o k %
#
f A g
I am not convinced that a synchronic analysis of blends as word-formation is even
necessary. The creation of new words is too open-ended to be reduced to a single word-
formation module and smog may synchronically be simply its own vocabulary item in cur-
rent I-languages. But occasionally some blends appear to be almost productive, like blends
formed on the word entertainment, including advertainment, infotainment, edutainment,
wintertainment, politainment, and realitainment. At some point it might be simpler to
posit that a new root -tainment was abduced and that these forms are simple compounds,
but the above would be a possible account if one were to argue for blends being productively
created in a language through regular word-formation.
9.15.2 Ablaut Reduplication
A second interesting but borderline pattern is English ablaut-reduplication in forms like
tick-tock, flip-flop, chit-chat, ding-dong, etc. The reduplication part is straightforward to
analyze in multiprecedence a? la Raimy (2000), but the overall pattern of a front-high vowel
256
followed by a non-high back vowel is something multiprecedence has no way to enforce. In
Multiprecedence a replacement vowel would be handled as fixed segmentism, with a vowel
added that will surface in one of the copies. Note that the ?base? of those reduplicated forms,
by which I mean the copy identical to the presumed unreduplicated word from which the
reduplicated form is derived, is sometimes the first and sometimes the second, e.g. tick-
tock < tick, but chit-chat < chat. Multiprecedence lacks a way to consistently enforce the
high-and-front to non-high-and-back pattern to determine the order short of specifying a
serialization order for each such form, which does not capture the pattern.
(122)
A
# t i k %
(123)
i
# ? ? t %
In contrast, the greater flexibility of PROP allows for the pattern to be specified on top
of and separately from the reduplication. We can posit a forms like (124) and (125), where
the fixed pattern is in parallel to the entire form and the reduplication, rather than posit a
257
specific vowel, posit an underspecified overwriting vowel.
(124)
??? ?? ?? ????+hi
?? ? ??bk? ??
?hi?
+bk?
V
# t i k %
(125)
??? ?? ?? ????+hi? ?
? ?
? ???hi
??
bk +bk?
V
# ? ? t %
Crucially, the two looped forms are indeterminate. The forms tiktVk and tVktok are
equally good resolutions to the loop of (124), and similarly ?at?Vt and ?Vt?at for (125).
But in both cases only one order ?fits? with the overarching melody. The /i/ of ?tick? is
incompatible with {?hi,+bk} and hence the derivation prefers tik-tVk, which puts the
underspecified /V/ in parallel to {?hi,+bk}, making it surface as [A], whereas the /?/ of
?chat? is incompatible with {+hi,?bk}, hence the derivation prefers ?V-t?at, which puts
the underspecified /V/ in parallel to {+hi,?bk}, making it surface as [i]. My suggestion is
therefore an account in which indeterminate reduplicated forms can be settled on the basis
of other facts about the form. This analysis thus captures the generality of the high-front
to non-high-back pattern
Again, this analysis assumes that this ablaut reduplication is a synchronic and produc-
tive pattern of English, which I am not convinced of.
258
Chapter 10
Conclusion
The simple idea that we started from in this dissertation was what if we remove the stipu-
lation that one segment has to follow or precede exactly one other, i.e. what if phonology
did not operate on strings? This question was already posed by Raimy (2000) and the
theory of Multiprecedence, who proposed that reduplication benefits from a representation
capable of handling loops. The purpose of this dissertation was to expand on the logical
possibilities of Multiprecedence when its representational freedom is harnessed to handle
phenomena other than reduplication.
Let us review the phenomena which we have explored as potentially attributable to the
representation with PROP.
In Chapter 3 we started from a simple and reasonable assumption: if two segments are
parallel, i.e. have no specification as to whether one precedes the other, then they may
be pronounced simultaneously up to phonetic compatibility. We saw that vowel harmony
and word-tone phenomena could be handled by parallel streams in the representation. If
a feature bundle can be set in parallel to another, and we posit that they can surface
simultaneously, then we have all the complexity needed to create the phenomena in question.
In chapter 4 we discussed the possible role of parallel structures in handling the place-
ment of affixes. If affixes can put in parallel to the stem they attach to, and restrictions of
phonetic compatibility constrain the coordination of parallel segments, then we can utilize
this to handle interesting phenomena of affixes with variable positions. But most affixes
need to explicitly say where they are to be inserted so I also made use of the sticky-end
technology to handle all types of affixation in a unified way.
Building on the two previous chapters, chapters 5 and 6 start from the observation that
given multiprecedence technology, there is enough freedom in phonological representation
to handle some amount of suppletion within a single underlying form. Again, rather than
259
an extra module dedicated only to this purpose, in PROP PCA arises entirely out of the
freedom of the basic representation and the mechanics of the sticky-end. As a bonus, doing
suppletion in the phonology has the advantage of creating a fully modular syntax prior to
phonology that does not need to see phonological context prior to lexical insertion, and it
resolves some puzzles in which phonology and allomorphy are intertwined.
Chapter 7 takes every innovation from the previous chapters and discusses their rela-
tionship with reduplication by discussing some examples with parallel structures. I hope
to show in this chapter that PROP is truly a continuation of Multiprecedence capable of
incorporating and expanding upon its insights with regard to reduplication as caused by
loops in the representation.
Chapter 8 was a promissory excursion into acquisition and cognitive science. There we
discussed how the handling of contradictory parallel features may boil down to general motor
planning and perception of auditory events. We discussed how the parallel representation
helps and redefines the learning problem of vowel harmony,
And finally chapter 9 was a grab bag of further issues that need to be addressed about
PROP as a theory, and tentative proposals that possibly benefit from the addition of un-
specified precedence in the theory.
Raimy?s 2000 Multiprecedence made reduplication an integral phenomenon of word-
formation arising from the raw combinatorics of the representation. This was a departure
from all other existing theories in which there was a ?core phonology? (Raimy, 2000, p.281)
of linear concatenative phenomena, with something extra and, curcially, different tacked
onto it to handle the non-core stuff. In Multiprecedence we see that reduplication is normal
and fundamentally arises from the same ingredients as everything else. In Multiprecedence
it would take extra stipulations to not have reduplication.
I hope that PROP can achieve the same for the other phenomena we have covered here.
In just the same way that reduplication is often viewed as something extra tacked onto a
concatenative phonology, the phenomena of vowel harmony and word-tone are often handled
with extra structures, processes and constructs specifically designed to handle them. Even
autosegmental phonology, for all non-linear that it is, is mostly treated as a string with
extra stuff around it. PROP takes the non-concatenative word-level phenomena as core.
260
They follow from the representation in a deeply inextricable way, and we see that it would
take extra stipulation to not have word-level phenomena of simultaneous morphology.
With PROP, a new picture of morphophonology can emerge in which reduplication,
harmony, word-tone, and allomorphy do not feel like extraneous processes seemingly tacked
onto a system that could exist without them. In PROP, the representation is simple and
unrestricted, and all these ?exotic? non-linear, non-concatenative, and irregular phenomena
exist not because they have entire pieces of machinery and modules of grammar dedicated
to them, but because those things are simply what is possible when the representation is
unrestricted and left to run free.
Removing the stipulation that phonology operates on strings explodes the range of
possible configurations, and yet it turns out that all the main new geometric possibilities
that this allows are attested in the world?s languages. Lops were covered by Raimy (2000)
as a way to handle reduplication. This dissertation mostly focuses on the phenomena that
could be handled with segments that are unordered which I have referred to as being in
parallel. From this I have proposed to derive multiple phenomena: when consisting of a few
features in parallel to many segments I have proposed that this accounts for vowel harmony
and word-tone. When branching within a single morpheme with separate sticky-end ends
that can attach in different contexts I have proposed that this accounts for allomorphy. when
affixation puts some affixes partially in parallel I have proposed that this may account for
assimilation. When underlyingly parallel segments can be ordered in different ways based
on context I have proposed that this accounts for metathesis. At least when looking at the
simple new representational possibilities of PROP, it appears to me that this combinatoric
richness matches the actual richness of morphophonological phenomena.
However there obviously are an infinitude of complex geometric structures that one
could build from the powerful system described here and it is logically impossible for all of
the geometric possibilities of directed graphs to be attested. But even short of infinitude
it is clear that only a small number of geometric patterns have been discussed here and we
may legitimately ask why, if PROP is correct, do we only see this small set of structures?
It could be that as presented in this thesis is overly powerful, or it could be that external
restrictions exist on attested phonological patterns. It is possible that Phonology is as
261
powerful as unrestricted PROP and the limitations in attested patterns is due to the limiting
effects of acquisition and diachrony on what is likely to be attested in a real language. It is
also possible that Phonology is intrinsically more powerful than phonetics/motor planning
can handle, if for example some complicated graphs are perfectly computable within the
phonology but too intricate to be interpretable downstream. This will, unfortunately, have
to be the topic of further research.
Downing (2001), in her review of Raimy (2000), worried that the addition of loops and
of a serialization algorithm capable of dealing with them only to account for reduplication
was too heavy a cost for phonological theory. My response here is that there is much more
that multiprecedence can be used for if we fully embrace its representational power.
There is a lot of work ahead for PROP. Everything here is very speculative. I hope
to have been able to sketch the start of a program seeking to unify the myriad phenom-
ena we covered here as straightforward manifestations of the combinatorics of the simple
representation of PROP.
262
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