Natural Language Semantics, 1e

by Gillon

ISBN: 9780262350761 | Copyright 2019

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An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline.


This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted.


The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on.The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.

A first-rate introduction to the recursive definition of languages and their compositional interpretation based on logic and model theory: clear, rigorous, careful, and thorough, with useful, partially solved exercises every step of the way. Highly recommended whether for classroom use or self-instruction.

Edward Keenan Professor, Department of Linguistics, UCLA


Natural Language Semantics does two things: it teaches absolutely everything a student needs to know about logic for every semantic topic in linguistics, while providing an introduction to various semantic theories and the formal development at work within them.

Francis Jeffry Pelletier Emeritus Canada Research Chair in Cognitive Science, Philosophy, and Linguistics, Simon Fraser University; Emeritus Professor of Philosophy and Computing Science, University of Alberta


This lucid, solid, and comprehensive book offers a rare opportunity of learning logic and natural language theory as an almost unified topic. Gillon is unique in the breadth of his knowledge, and he matches this with the pedagogical skills to guide the reader from ancient India to contemporary type theory.

Peter Pagin Professor, Department of Philosophy, Stockholm University

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Contents (pg. vii)
Preface (pg. ix)
Table of Greek Letters (pg. xv)
1. Language, Linguistics, Semantics: An Introduction. (pg. 1)
1. The Study of Language before the Twentieth Century (pg. 1)
2. The Birth of Linguistics (pg. 2)
2.1 Linguistics and Psychology (pg. 3)
2.2 Linguistics and Logic (pg. 17)
3. Conclusion (pg. 33)
3.1 Topics Covered and Their Interconnections (pg. 33)
3.2 Some Remarks on Empirical Inquiry (pg. 35)
2. Basic Set Theory (pg. 51)
1. Introduction (pg. 51)
2. Sets and Their Members (pg. 51)
2.1 Some Important Sets (pg. 53)
2.2 The Size of a Set (pg. 54)
2.3 Relations between Sets (pg. 55)
3. Operations on Sets (pg. 63)
4. Sequences (pg. 66)
4.1 Ordered Pairs (pg. 67)
4.2 Cartesian Product (pg. 68)
5. Families of Sets (pg. 70)
5.1 The Power Set Operation (pg. 70)
5.2 Operations on Families of Sets (pg. 72)
6. Relations (pg. 75)
6.1 Binary Relations on a Set (pg. 76)
6.2 Binary Relations from a Set to a Set (pg. 86)
6.3 Function (pg. 90)
3. Basic English Grammar (pg. 105)
1. Introduction (pg. 105)
2. Traditional Grammar of English (pg. 106)
2.1 Parts of Speech (pg. 106)
2.2 Clauses (pg. 118)
2.3 The Limitations of Traditional English Grammar (pg. 120)
3. Syntax of English (pg. 122)
3.1 Immediate Constituency Analysis (pg. 123)
3.2 Constituency Grammar (pg. 130)
3.3 Corroborating Evidence (pg. 138)
3.4 Problems (pg. 145)
4. Conclusion (pg. 165)
4. Language and Context (pg. 175)
1. Context (pg. 175)
2. Setting and Exophora (pg. 177)
2.1 Person (pg. 180)
2.2 Temporal Order (pg. 182)
2.3 Spatial Location (pg. 184)
2.4 Further Subtleties (pg. 185)
3. Cotext: Endophora and Ellipsis (pg. 188)
3.1 Endophora (pg. 189)
3.2 Ellipsis (pg. 196)
4. Context and Ambiguity (pg. 201)
5. Conclusion (pg. 205)
5. Language and Belief: Implicatures and Presuppositions (pg. 209)
1. Language, Communication, and Belief (pg. 209)
2. Implicatures (pg. 210)
2.1 Grice's Maxims (pg. 212)
2.2 Properties of Implicatures (pg. 217)
2.3 Implicatures and Ambiguity (pg. 219)
3. Presupposition (pg. 222)
3.1 Triggers of Presupposition (pg. 224)
3.2 The Common Ground (pg. 226)
3.3 Presupposition, Entailment, and Implicature (pg. 228)
4. What Is Intended and What Is Understood (pg. 231)
5. Conclusion (pg. 234)
6. Classical Propositional Logic: Notation and Semantics (pg. 237)
1. Arguments (pg. 237)
2. Classical Propositional Logic (pg. 241)
2.1 Notation (pg. 244)
2.2 Semantics (pg. 254)
7. Classical Propositional Logic: Deduction (pg. 275)
1. Deduction (pg. 275)
2. Formula Natural Deduction (pg. 277)
2.1 Formulae in a Column (pg. 277)
2.2 Formulae in a Tree (pg. 297)
3. Sequent Natural Deduction (pg. 302)
3.1 Sequents in a Column (pg. 303)
3.2 Sequents in a Tree (pg. 309)
4. Gentzen Sequent Calculus (pg. 315)
4.1 Left and Right Introduction (pg. 316)
4.2 Left and Right Introduction (pg. 317)
4.3 Left and Right Introduction (pg. 317)
4.4 Left and Right Introduction (pg. 318)
5. Substructural Logics (pg. 320)
8. English Connectors (pg. 321)
1. Introduction (pg. 321)
2. English Connectors and Clauses (pg. 322)
2.1 Open Problems for English Connectors (pg. 327)
3. Truth and Independent, Declarative Clauses (pg. 329)
4. The English Coordinator and (pg. 330)
4.1 Apparent Problems for the English Coordinator and (pg. 332)
4.2 Open Problems for the English Coordinator and (pg. 339)
5. The English Coordinator or (pg. 344)
5.1 Apparent Problems for the English Coordinator or (pg. 345)
5.2 Open Problems for the English Coordinator or (pg. 350)
6. The English Subordinator if (pg. 353)
6.1 Apparent Problems for the English Subordinator if (pg. 357)
6.2 Open Problems for the English Subordinator if (pg. 360)
7. The English Adverb not (pg. 367)
7.1 The Syntax of not (pg. 368)
7.2 Open Problems for the English Adverb not (pg. 370)
8. Conclusion (pg. 371)
9. Classical Predicate Logic (pg. 375)
1. Introduction (pg. 375)
2. Notation (pg. 376)
2.1 Formulae of CPDL (pg. 379)
2.2 Formulae and Subformulae (pg. 380)
3. Semantics (pg. 383)
3.1 Semantic Properties and Relations (pg. 389)
4. Deduction (pg. 394)
10. Grammatical Predicates and Minimal Clauses in English (pg. 397)
1. Introduction (pg. 397)
2. Minimal English Clauses (pg. 398)
2.1 Verb Phrases: Verbs and Their Complements (pg. 399)
2.2 Adjective Phrases: Adjectives and Their Complements (pg. 413)
2.3 Prepositions (pg. 417)
2.4 Nouns (pg. 419)
3. A Structure for an English Lexicon (pg. 420)
3.1 Constituency Grammar with Enriched Categories (pg. 422)
3.2 Semantics (pg. 427)
3.3 Defining Constituency Valuation Rules (pg. 429)
3.4 Further Extensions (pg. 438)
3.5 Open Problems (pg. 451)
4. Conclusion (pg. 454)
11. Classical Quantificational Logic (pg. 457)
1. Notation (pg. 457)
2. Classical Valuations for CQL (pg. 465)
2.1 Syncategorematic Definitions of Valuations for CQL (pg. 466)
2.2 Categorematic Definition of Valuations for CQL (pg. 488)
2.3 Semantic Properties and Relations (pg. 497)
3. Deduction (pg. 506)
3.1 Elimination (pg. 506)
3.2 Introduction (pg. 507)
3.3 Introduction (pg. 509)
3.4 Elimination (pg. 510)
12. Enrichments of Classical Quantificational Logic (pg. 521)
1. Introduction (pg. 521)
2. Classical Quantificational Logic with Identity (pg. 522)
3. Monadic Quantificational Logic (pg. 526)
3.1 One-Place Monadic Quantificational Logic (pg. 527)
3.2 Two-Place Monadic Quantificational Logic (pg. 535)
4. Conclusion (pg. 547)
13. The Lambek Calculus and the Lambda Calculus (pg. 551)
1. Introduction (pg. 551)
2. The Lambek Calculus (pg. 552)
2.1 Formula Deduction (pg. 553)
2.2 Sequent Deduction (pg. 557)
2.3 Gentzen Sequent Deduction (pg. 566)
2.4 Cut Elimination (pg. 570)
3. The Lambda Calculus (pg. 578)
3.1 Notation of the Lambda Calculus (pg. 579)
3.2 Semantics: Functional Structures (pg. 592)
3.3 Deduction (pg. 595)
4. The Lambek Typed Lambda Calculus (pg. 603)
14. Noun Phrases in English (pg. 615)
1. Introduction (pg. 615)
2. Simple Noun Phrases in English (pg. 615)
2.1 English Nouns (pg. 616)
2.2 Adjectives (pg. 624)
2.3 Determiners (pg. 628)
3. Putting Things Together (pg. 629)
3.1 Simple Clauses with Quantified Noun Phrases (pg. 630)
3.2 Adjectives Again (pg. 636)
3.3 Prepositional Phrases (pg. 639)
3.4 Restrictive Relative Clauses (pg. 641)
3.5 Quantified Noun Phrases Again (pg. 646)
3.6 Nonclausal Coordination (pg. 660)
4. Conclusion (pg. 670)
15. Conclusion (pg. 673)
1. Introduction (pg. 673)
2. Retrospective (pg. 673)
3. What Has Not Been Covered (pg. 677)
4. Related Approaches (pg. 680)
References (pg. 683)
List of Symbols (pg. 693)
Index (pg. 701)

Brendan S. Gillon

Brendan S. Gillon is Professor of Linguistics and an Associate of the Department of Philosophy at McGill University.


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