Meaning, Logic And Ludics

By: Alain Lecomte

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Hardcover | 23 March 2011

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388 Pages

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22.86 x 15.24 x 2.24

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This book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda-mu and Lambek-Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's 'proof as meaning' approach, which was first based on Martin-Loef's Type Theory.Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax-semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students, and academics alike, in the field of computational linguistics.

Industry Reviews

This book presents a large part of the ongoing research on linguistics and proof theory, as developed by the author and also by some other researchers. The very interesting content, previously unavailable in book form, is made intuitive and pleasant to read. -- Mathematical Reviews "Mathematical Reviews"

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Preface	p. vii
Introduction	p. 1
The Logical Space of Meaning	p. 1
The Aim of This Book	p. 4
Starting from Traditional Formal Semantics	p. 4
Semantics and the History of Logic (1): Intuitionism	p. 5
Curry-Howard	p. 5
Lambek and the substructural hypothesis	p. 5
Semantics and the History of Logic (2): Classicism	p. 6
Semantics and the History of Logic (3): Linear Logic	p. 7
Presentation of the Book	p. 10
Truth-Conditional Meaning
Compositional Approaches and Binding	p. 15
Representing Logical Meaning: The Binding Issue	p. 15
The syntactic notion of binding	p. 15
The semantic notion of binding	p. 18
The model-theoretic notion of binding	p. 18
Syntactic Derivations and Semantic Composition	p. 20
Montague Grammar Revisited	p. 20
From rules to sequents	p. 20
On relatives and quantification	p. 24
Examples	p. 25
On binding	p. 29
A Theory of Simple Types	p. 30
Heim and Kratzer's Theory	p. 33
Interpreting derivation trees	p. 33
Predicate modification	p. 38
Variables and binding	p. 39
Towards a proof-theoretic account of binding	p. 50
Derivationalism	p. 53
Introduction	p. 53
Categorial Grammars	p. 54
The (Pure) Lambek Calculus	p. 60
The mathematics of sentence structure	p. 60
A categorical system	p. 61
Minimalist Grammars	p. 61
Minimalist principles	p. 61
Features	p. 65
Minimalist grammars	p. 66
Merge	p. 66
Move	p. 67
Minimalist grammars and categorial grammars	p. 73
Binding as ôCooper storageö	p. 74
The interpretation of derivational trees	p. 75
The semantic interpretation of Merge	p. 76
The semantic interpretation of Move	p. 78
Concluding Remarks	p. 80
Logic
Deductive Systems	p. 85
Fitch's Natural Deduction System	p. 85
Conjunction	p. 87
Implication	p. 88
Disjunction	p. 89
Negation	p. 90
Natural Deduction in Intuitionistic Logic	p. 91
Tree format	p. 91
Normalization	p. 92
Sequent format	p. 93
Intuitionistic Sequent Calculus	p. 94
Structural rule	p. 94
Identity rules	p. 95
Logical rules	p. 95
An example of a proof in intuitionistic logic	p. 96
The cut rule	p. 97
Lists and sets	p. 98
Structural rules	p. 98
Classical Sequent Calculus	p. 99
Structural rules	p. 99
Identity rules	p. 100
Logical rules	p. 100
Some Properties of the Sequent Calculus	p. 102
Subformula property	p. 102
Cut-elimination	p. 103
Linear Logic	p. 103
Identity rules	p. 103
Logical rules	p. 104
Exponentials	p. 105
Constants	p. 107
The one-sided calculus	p. 108
Intuitive interpretation	p. 109
Back to the Lambek Calculus	p. 115
The Lambek calculus as non-commutative linear logic	p. 115
Linguistic Applications of the Additives	p. 118
Proof Nets	p. 119
A geometrization of logic	p. 119
Cut-elimination in proof nets	p. 124
Proof Nets for the Lambek Calculus	p. 125
Concluding Remarks	p. 126
Curry-Howard Correspondence	p. 127
Introduction	p. 127
A Correspondence Between Types and Formula	p. 128
An Example of a Combinator	p. 132
Concluding Remarks	p. 134
Proof Theory Applied to Linguistics
Using the Lambek Calculus and Its Variants	p. 137
Introduction	p. 137
Using the Lambek Calculus	p. 137
Summary of the rules	p. 137
Natural deduction presentation	p. 138
Examples	p. 139
Compositional semantics	p. 143
Limitations of the Lambek calculus	p. 145
Flexible Types	p. 148
Flexible Montague grammar	p. 148
Variable-free semantics	p. 149
Non-associative Lambek Calculus	p. 151
Semantics of the Lambek Calculus	p. 153
Monoidal semantics	p. 153
Relational semantics	p. 154
An Extension of the Lambek Calculus: The Lambek-Grishin Calculus	p. 157
Adding new connectives	p. 157
Rules	p. 158
The Grishin postulates	p. 159
Grammatical Reasoning	p. 163
Motivations	p. 163
Modal Preliminary	p. 164
Necessity and possibility	p. 164
Axiomatization	p. 164
Residuation and Modalities	p. 166
Linguistic Applications	p. 169
Back to Quantification	p. 171
Kripke Semantics	p. 173
Concluding Remarks and Observations	p. 174
A Type-Theoretical Version of Minimalist Grammars	p. 177
Inserting Chains	p. 177
Head Movement	p. 189
Adjoining and Scrambling	p. 190
Semantics Without Cooper Storage	p. 193
Cooper storage and hypothetical reasoning	p. 193
One or two derivations?	p. 195
Concluding Remarks: Some Tracks to Explore	p. 201
Grammars in Deductive Forms	p. 203
Introduction	p. 203
Convergent Grammars	p. 203
CVG types and rules: Semantics	p. 203
CVG types and rules: Syntax	p. 205
An example	p. 206
Labelled Linear Grammars	p. 206
Binding in LLG	p. 215
Pronouns as pronounced variables	p. 215
On reflexives	p. 220
On Phases	p. 220
Comparing CVG and LLG	p. 221
Concluding Remarks	p. 222
Continuations and Contexts	p. 223
The Use of Continuations in Semantics	p. 223
Continuations and quantification	p. 223
Continuizing a grammar	p. 224
Call-by-value and call-by-name	p. 228
Symmetric Calculi	p. 232
Towards the ¿¿-calculus	p. 232
Applications of the ¿¿-calculus to the problem of scope construal	p. 237
¿¿¿-calculus	p. 239
Call-by-name vs call-by-value	p. 243
Back to implication	p. 245
Subtraction	p. 246
Back to links between logic and duality	p. 247
From the ¿¿-calculus to the ¿¿¿-calculus	p. 256
A small linguistic example	p. 256
Concluding Remarks and Further Works	p. 259
Proofs as Meanings	p. 263
From Intuitionistic Logic to Constructive Type Theory	p. 263
Proof processes and proof objects	p. 263
Judgements	p. 266
Dependent types	p. 271
Contexts	p. 274
Formalizing Montague Grammar in Constructive Type Theory	p. 278
Predicate calculus	p. 279
Translation into predicate calculus	p. 280
Introducing dependent types	p. 281
Dynamical Interpretation and Anaphoric Expressions	p. 282
If … then sentences	p. 282
A presuppositional account	p. 285
From Sentences to Dialogue	p. 287
Ludics
Interaction and Dialogue	p. 291
Dialogue and Games	p. 291
Introduction	p. 291
Game semantics	p. 292
Internal games	p. 300
Comparison between the two frameworks	p. 304
Ludics	p. 306
Focusing proofs	p. 306
Paraproofs	p. 310
An easy application to natural language	p. 314
Designs	p. 317
Behaviours	p. 328
Some particular behaviours	p. 328
What logic for ludics?	p. 330
Sums and products	p. 332
Discursive relations	p. 337
The Future in Conclusion	p. 347
Bibliography	p. 353
General Index	p. 363
Author Index	p. 367
Table of Contents provided by Ingram. All Rights Reserved.

Meaning, Logic And Ludics

At a Glance

Hardcover

Industry Reviews

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