Logic in Linguistics

By: Jens Allwood, Osten Dahl, Lars-Gunnar Andersson, J. Bresnan (Contribution by), B. Comrie (Contribution by)

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Paperback | 14 November 1977

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196 Pages

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22.86 x 15.24 x 1.14

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An elementary introduction to formal logic, particularly intended for linguists and others interested in languages. Concepts and theories developed within formal logic for the study of artificial languages have for some time been fruitfully applied to the study of natural languages and some knowledge of them is necessary for students of linguists (especially semantics). With this need in mind the authors offer a clear, succinct and basic introduction to set theory, inference, propositional and predicate logic, deduction, modal and intensional logic, and various concomitant extensions of these. There is a discussion too of the relation between linguistics and logical analysis and between logic and natural language. The authors see increasing scope for co-operation between logicians and linguistics in studying the structure of language, and it is the overall aim of the book to promote this co-operation.

Industry Reviews

'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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Preface	p. viii
Symbols and notational conventions	p. ix
Logic for linguists	p. 1
Set theory	p. 3
Sets and elements	p. 3
Relations between sets	p. 5
Operations on sets	p. 6
Relations and functions	p. 9
Inference and logical analysis of sentences	p. 15
Inference	p. 15
Logical form	p. 18
Sentences and propositions	p. 20
Possible worlds and the truth-set of a proposition	p. 22
Analytic and synthetic sentences	p. 23
Simple and compound sentences	p. 24
The depth of the logical analysis	p. 25
Propositional logic	p. 26
Connectives	p. 26
The meaning of the logical connectives	p. 30
Negation	p. 30
Conjunction	p. 32
Disjunction	p. 34
Implication	p. 37
Equivalence	p. 40
How to indicate constituent structure	p. 42
The syntax and semantics of propositional calculus	p. 44
Syntax	p. 45
Semantics	p. 47
Tautologies and contradictions	p. 50
Truth tables	p. 50
Predicate logic	p. 58
Extending the logical analysis	p. 58
Quantifiers	p. 61
Summary of the syntax of predicate logic	p. 71
The semantics of predicate logic	p. 72
True in all interpretations	p. 77
Summary of the semantics of predicate logic	p. 83
A formal version of the semantics	p. 84
Formal properties of relations	p. 88
Reflexivity	p. 88
Symmetry	p. 89
Transitivity	p. 89
Converse	p. 90
Structure of the domain and co-domain of relations	p. 90
Deduction	p. 96
The deductive system	p. 96
Deduction rules in everyday conversation	p. 104
Modal logic	p. 108
Modal operators	p. 108
Strict implication	p. 110
Other modalities	p. 111
Problems connected with scope and identity in modal logic	p. 114
'De dicto'--'de re' ambiguities	p. 114
Specificity	p. 116
Opacity	p. 117
Cross-world identification	p. 119
Counterfactual sentences	p. 120
Tense logic and reference points	p. 121
Intensional logic and categorial grammar	p. 125
Intensions and extensions	p. 125
Intension	p. 127
The Fregean principle	p. 130
The Fregean principle and categorial grammar	p. 132
Categories, intensions and types	p. 136
Further extensions	p. 148
Second-order predicate logic and predicate operators	p. 148
Presuppositions and definite descriptions	p. 149
Pragmatic analysis of presuppositions	p. 153
The abstraction- or lambda-operator	p. 155
Logic for linguists?	p. 158
General	p. 158
The concept of meaning	p. 158
The role of formal languages in analysing natural language	p. 164
The limitations of classical logic	p. 168
References	p. 172
Answers to exercises	p. 175
Index	p. 181
Table of Contents provided by Syndetics. All Rights Reserved.

Logic in Linguistics

At a Glance

Paperback

Industry Reviews

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How to return your order

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