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293 Pages·2010·24.67 MB·English

A Theory of Individual-Level Predicates
Based on Blind Mandatory Implicatures.
Constraint Promotion for Optimality Theory
by
ARHIvNES
Giorgio Magri
M.A. Philosophy, Universita degli Studi di Milano, Italy, 2001
M.A. Mathematics, Universith degli Studi di Milano, Italy, 2002
Submitted to the Department of Linguistics and Philosophy
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
•1 8~ ISTRUTE
OFTECHNOLOGY
at the
Massachusetts Institute of Technology DEC0 1 2009
September 2009 LIE
BRARIES
@2009 Giorgio Magri. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute
publicly paper and electronic copies of this thesis document in whole or in part in
any medium now known or hereafter created.
Author .......... ......... .... .................. .....................
Department of Linguistics and Philosophy
Certified by .............. ........ .... , .. ..... .... ..... ...... " l.o..gl .
.AAldbarmig ht
Associate Professor of Linguistics
Thesis supervisor
..... ;/........................anny .o. x
Certified by ....... ............
Danny Fox
Professor of Linguistics
Thesis supervisor
Accepted by ...................... . ... ... ... .... ... .. .. ... ... .. .....
Irene Heim
Professor of Linguistics
Chair, Department of Linguistics and Philosophy

A Theory of Individual-Level Predicates
Based on Blind Mandatory Implicatures.
Constraint Promotion for Optimality Theory
by Giorgio Magri
Submitted to the Department of Linguistics and Philosophy on August 28, 2009,
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Part I of this dissertation proposes an implicature-based theory of individual-level
predicates. The idea is that we cannot say '#John is sometimes tall' because the sen-
tence triggers the scalar implicature that the alternative 'John is always tall' is false
and this implicature mismatches with the piece of common knowledge that tallness
is a permanent property. Chapter1 presents the idea informally. This idea faces two
challenges. First, this scalar implicature must be mandatory and furthermore blind
to common knowledge. Second, it is not clear how this idea extends to other prop-
erties of individual-level predicates. Chapter2 makes sense of the surprising nature
of these special mismatching implicatures within the recent grammatical framework
for scalar implicatures of Chierchia (2004) and Fox (2007a). Chapter 3 shows how
this implicature-based account can be extended to other properties of individual-
level predicates, such as restrictions on their bare plural subjects, on German word
order and extraction, and on Q-adverbs.
Part H of this dissertation develops a theory of update rules for the OT on-line algo-
rithm that perform constraint promotion too, besides demotion. Chapter4 explains
why we need constraint promotion, by arguing that demotion-only update rules are
unable to model Hayes' (2004) early stage of the acquisition of phonology. Chap-
ter 5 shows how to get constraint promotion, by means of two different techniques.
One technique shares the combinatoric flavor of Tesar and Smolensky's analysis of
demotion-only update rules. The other technique consists of adapting to OT results
from the theory of on-line algorithms for linear classification. The latter technique
has various consequences interesting on their own, explored in Chapter 8. Chapters
6 and 7 start the investigation of the properties of update rules that perform promo-
tion too, concentrating on the characterization of the final vector and on the number
of updates.
Thesis supervisors: Adam Albright, Danny Fox
Title: Associate Professor of Linguistics Professor of Linguistics
4
Academic acknowledgements
I do not like to say my things in public. Even less to write them down. So I will keep my written
public academic acknowledgements short, and thank people in person. I wish to thank Adam Al-
bright, Gennaro Chierchia, Danny Fox, and Irene Heim. I also wish to thank Marta Abrusan, Asaf
Bachrach, Emmanuel Chemla, Cleo Condoravdi, Kai von Fintel, Mark Johnson, Angelika Kratzer,
Sabine Iatridou, Livio Pizzocchero, Philippe Schlenker, Benjamin Spector, and Donca Steriade.

Contents
Part I: A Theory of Individual Level Predicates Based on Blind and Manda-
tory Scalar Implicatures
1 Introduction 15
1.1 The Problem: restrictions on i-predicates . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 The idea: blind and mandatory mismatching implicatures . . . . . . . . . . . . . . . 16
1.3 The solution: i-predicates and scalar implicatures . . . . . . . . . . . . . . . . . . . 24
1.4 Im plications . .. .. .. .. .. .. . .... ... .. ... . . . . . . . . . . . . . 28
2 Oddness by mismatching scalar implicatures 29
2.1 The basic case .................... . . . . . . . . . . . . . . . . . . 30
2.1.1 First step: covert 'only'........... . . . . . . . . . . . . . . . . . . 3 1
2.1.2 Second step: blindness ........... . . . . . . . . . . . . . . . . . . 32
2.1.3 Third step: mandatoriness ......... . . . . . . . . . . . . . . . . . . 35
2.2 Extension to cases with multiple alternatives . . . . . . . . . . . . . . . . . . . . . . 4 1
2.3 Extension to downward entailing environments . . . . . . . . . . . . . . . . . . . . 50
2.4 Extension to Presuppositions ............ . ...... ................... 60
2.5 Miscellaneous issues ................ . . . . . . . . . . . . . . . . . . 68
2.5.1 An alternative approach based on Manner aId its inadequacy . . . . . . . . . 68
2.5.2 Predecessors ................ . . . . . . . . . . . . . . . . . . 70
2.5.3 Miscellaneous problematic cases . . . . . . . . . . . . . . . . . . . . . . . . 73
3 Application to individual level predicates 75
3.1 Existential Q-adverbs ................ . . . . . . . . . . . . . . . . . . 77
3.1.1 Existing accounts .............. . . . . . . . . . . . . . . . . . . 77
3.1.2 An account based on blind and mandatory mismatching implicatures . . . . . 82
3.2 Temporal modification ................................. 86
3.2.1 Existing accounts ................................ 86
3.2.2 An account based on blind and mandatory mismatching implicatures . . . . . 88
3.3 Bare plural subjects ................................... 93
3.3.1 Existing accounts .......................... ...... 94
3.3.2 An account based on blind and mandatory mismatching implicatures . . . . . 105
3.4 Word order and extraction in German . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.4.1 Existing accounts ................................ 111
3.4.2 An account based on blind and mandatory mismatching implicatures . . . . . 112
3.5 BPSs embedded under a universal operator . . . . . . . . . . . . . . . . . . . . . . 116
3.5.1 Existing accounts ................................ 117
3.5.2 An account based on blind and mandatory mismatching implicatures . . . . . 120
3.6 More facts on the distribution of existential BPSs . . . . . . . . . . . . . . . . . . . 123
3.6.1 First set of facts: existential BPSs that are non-kind denoting . . . . . . . . . 123
3.6.2 Second set of facts: BPSs associated with 'only' . . . . . . . . . . . . . . . 127
3.6.3 Third set of facts: generalized locatives? . . . . . . . . . . . . . . . . . . . . 128
3.6.4 Fourth set of facts: statives ........................... 129
3.7 Overt universal Q-adverbs ............................... 132
8 CONTENTS
Part II: Constraint promotion and the OT on-line model for the acquisition
of phonology 137
4 Why we need constraint promotion 139
4.1 OT preliminaries .............................. ...... 140
4.1.1 OT basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... 140
4.1.2 OT with comparative rows ..................... ...... 142
4.1.3 OT with ranking vectors ...................... ...... 145
4.2 The OT on-line algorithm: a computational perspective . . . . . . . . . . . . .. . . 148
4.2.1 Outline of the algorithm ...................... ...... 148
4.2.2 Generalities on demotion-only update rules . . . . . . . . . . . . . . .. . . 153
4.2.3 First example of demotion-only update rule: minimal and gradual ...... 154
4.2.3.1 Bound on the worst-case number of updates . . . . . . . . . . .. . . 155
4.2.3.2 Characterization of the final vector . . . . . . . . . . . . . ...... 157
4.2.3.3 Extension to an arbitrary initial vector . . . . . . . . . . . . .. .. . 158
4.2.4 Second example of demotion-only update rule: minimal and non-gradual . . 160
4.2.5 Third example of demotion-only update rule: non-minimal and gradual . . . 162
4.2.6 Promotion-demotion update rules . . . . . . 164
. .... °...........
4.2.6.1 A detailed explanation of Pater's counterrleexaxmapmle p.l.e......................165
4.2.6.2 On the analysis of promotion-demotion 169
4.3 The OT on-line algorithm: a modeling perspective . . . .....urpudleast.e.. ........ 172
4.3.1 Initialization .................. 172
4.3.2 Choice of the underlying form . . . . . . . . . 172
4.3.3 A toy example ................. 173
................
4.3.4 How to choose update rules .......... 175
................
5 How to get constraint promotion 179
5.1 A principled promotion-demotion update rule . . . . . . . . . . . . . . . . . . . . . 180
5.2 First proof of finite time convergence .......................... 185
5.2.1 First step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185
5.2.2 Second step ................................... 186
5.2.3 Third step . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . .187
5.2.4 Fourth step ................................... 191
5.3 Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191
5.3.1 First variant . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191
5.3.2 Second variant ................................. 192
5.3.3 Third variant .................................. 193
5.4 Second proof of finite time convergence . . . . . . . . . . . . . . . . . . . . . . . . 194
5.4.1 First step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195
5.4.2 Second step ................................... 195
5.4.3 Third step . ... .. .. .... .... .... . .. . ... .. .. ... . .197
5.5 M ore variants ...................................... 198
5.5.1 First variant .. .. ... .. .. .. .. .... ... ... . . .. . .. .. .199
5.5.2 Second variant ................................. 200
5.5.3 Third variant .................................. 203
Appendix: some classical results on linear on-line algorithms . . . . . . . . . . . . . . . .204
6 How to study constraint promotion: the final ranking vector 209
6.1 An invariant ... .. ... .. .. ... .. .. .... ... .. .. . . .. ... . .210
6.2 Preliminaries on OT phonotactics ............................ 215
6.3 Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220
6.3.1 First test case ... .. . ... . .... .... ... . . .. . . .. .. .. .221
6.3.2 Second test case: pseudo-korean . . . . . . . . . . . . . . . . . . . . . . . . 225
6.3.2.1 Stage I . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .228
6.3.2.2 Stage II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229
CONTENTS 9
6.3.2.3 Stage III . .. .. . .. .. .... .. ... . ... . . .. .. .. . .232
6.3.2.4 Stage IV ................................ 233
6.3.3 Third test case: the whole Azba typology . . . . . . . . . . . . . . . . . . . 233
7 How to study constraint promotion: number of updates 245
7.1 Constraint promotion might require many updates . . . . . . . . . . . . . . . . . . .246
7.1.1 A simple lower-bound on the best-case number of updates . . . . . . . . . . 247
7.1.2 A case with an exponential best-case number of updates . . . . . . . . . . . 249
7.1.3 A small remark on Pater's comparative tableaux . . . . . . . . . . . . . . . . 249
7.2 Formulations of the problem of the acquisition of phonology . . . . . . . . . . . . . 252
7.2.1 The Ranking problem ............................. 252
7.2.2 The Subset problem .............................. 254
7.2.3 Prince and Tesar's (2004) formulation of the Subset problem . . . . . . . . . 255
7.3 How to decide whether a problem is easy or not . . . . . . . . . . . . . . . . . . . .255
7.3.1 First step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256
7.3.2 Second step ................................... 257
7.3.3 Third step . ... .. .. . .. .... ... . .... .. . .. .. . ... .. 257
7.3.4 Fourth step ................................... 258
7.4 The problem of the acquisition of phonology is "hard" . . . . . . . . . . . . . . . .258
7.4.1 Complexity of the Ranking problem . . . . . . . . . . . . . . . . . . . . . . 259
7.4.2 Complexity of Prince and Tesar's Subset problem . . . . . . . . . . . . . . .261
7.4.3 Complexity of the Subset problem . . . . . . . . . . . . . . . . . . . . . . .267
8 Consequences for the relationship between standard and linear OT 271
8.1 The relationship between OT-compatibility and L-compatibility . . . . . . . . . . . .272
8.2 Computational consequences .............................. 276
8.3 M ore consequences ................................... 279
List of symbols used in part II 281
References 293
10 CONTENTS