Logic in Linguistics

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An elementary introduction to formal logic, particularly intended for linguists. Discusses the relation between linguistic and logical analysis and between logic and natural language.
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Overview

An elementary introduction to formal logic, particularly intended for linguists. Discusses the relation between linguistic and logical analysis and between logic and natural language.
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Editorial Reviews

From the Publisher
'For the most part, this book is a pleasant introduction to the main topics of modern elementary logic up as far as the semantics of natural languages. It also touches on some areas which belong more to the semantics of natural languages than to logic proper, such as the semantics of categorial grammars or the analysis of presuppositions. The first aim is to tell the reader what techniques are available rather than to train him in any of them. In this aim the book succeeds well: it is clear, readable, accurate and up to date. There are sensible exercises to most chapters, and adequate references for the reader who wants to go deeper … the book can certainly be recommended as a text.' Journal of Linguistics
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Product Details

  • ISBN-13: 9780521214964
  • Publisher: Cambridge University Press
  • Publication date: 9/15/1977
  • Series: Textbooks in Linguistics
  • Pages: 200
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.67 (d)

Table of Contents

Preface viii
Symbols and notational conventions ix
1 Logic for linguists 1
2 Set theory 3
2.1 Sets and elements 3
2.2 Relations between sets 5
2.3 Operations on sets 6
2.4 Relations and functions 9
3 Inference and logical analysis of sentences 15
3.1 Inference 15
3.2 Logical form 18
3.3 Sentences and propositions 20
3.4 Possible worlds and the truth-set of a proposition 22
3.5 Analytic and synthetic sentences 23
3.6 Simple and compound sentences 24
3.7 The depth of the logical analysis 25
4 Propositional logic 26
4.1 Connectives 26
4.2 The meaning of the logical connectives 30
4.2.1 Negation 30
4.2.2 Conjunction 32
4.2.3 Disjunction 34
4.2.4 Implication 37
4.2.5 Equivalence 40
4.3 How to indicate constituent structure 42
4.4 The syntax and semantics of propositional calculus 44
4.5 Syntax 45
4.6 Semantics 47
4.7 Tautologies and contradictions 50
4.8 Truth tables 50
5 Predicate logic 58
5.1 Extending the logical analysis 58
5.2 Quantifiers 61
5.3 Summary of the syntax of predicate logic 71
5.4 The semantics of predicate logic 72
5.5 True in all interpretations 77
5.6 Summary of the semantics of predicate logic 83
5.7 A formal version of the semantics 84
5.8 Formal properties of relations 88
5.8.1 Reflexivity 88
5.8.2 Symmetry 89
5.8.3 Transitivity 89
5.8.4 Converse 90
5.8.5 Structure of the domain and co-domain of relations 90
6 Deduction 96
6.1 The deductive system 96
6.2 Deduction rules in everyday conversation 104
7 Modal logic 108
7.1 Modal operators 108
7.2 Strict implication 110
7.3 Other modalities 111
7.4 Problems connected with scope and identity in modal logic 114
7.4.1 'De dicto'--'de re' ambiguities 114
7.4.2 Specificity 116
7.4.3 Opacity 117
7.4.4. Cross-world identification 119
7.5 Counterfactual sentences 120
7.6 Tense logic and reference points 121
8 Intensional logic and categorial grammar 125
8.1 Intensions and extensions 125
8.2 Intension 127
8.3 The Fregean principle 130
8.4 The Fregean principle and categorial grammar 132
8.5 Categories, intensions and types 136
9 Further extensions 148
9.1 Second-order predicate logic and predicate operators 148
9.2 Presuppositions and definite descriptions 149
9.3 Pragmatic analysis of presuppositions 153
9.4 The abstraction- or lambda-operator 155
10 Logic for linguists? 158
10.1 General 158
10.2 The concept of meaning 158
10.3 The role of formal languages in analysing natural language 164
10.4 The limitations of classical logic 168
References 172
Answers to exercises 175
Index 181
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