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Description :
Summary
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.
Brendan S. Gillon is Professor of Linguistics and an Associate of the Department of Philosophy at McGill University.
Content :
Preface ix
Table of Greek Letters xv
1 Language, Linguistics, Semantics: An Introduction 1
2 Basic Set Theory 51
3 Basic English Grammar 105
4 Language and Context 175
5 Language and Belief: Implicatures and Presuppositions 209
6 Classical Prepositional Logic: Notation and Semantics 237
7 Classical Prepositional Logic: Deduction 275
8 English Connectors 321
9 Classical Predicate Logic 375
10 Grammatical Predicates and Minimal Clauses in English 397
11 Classical Quantificational Logic 457
12 Enrichments of Classical Quantificational Logic 521
13 The Lambek Calculus and the Lambda Calculus 551
14 Noun Phrases in English 615
15 Conclusion 673
References 683
List of Symbols 693
Index 701
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