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Logic in Linguistics : Cambridge Textbooks in Linguistics - Jens Allwood

Logic in Linguistics

Cambridge Textbooks in Linguistics

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

Paperback

Published: 14th November 1977
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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.

'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

Prefacep. viii
Symbols and notational conventionsp. ix
Logic for linguistsp. 1
Set theoryp. 3
Sets and elementsp. 3
Relations between setsp. 5
Operations on setsp. 6
Relations and functionsp. 9
Inference and logical analysis of sentencesp. 15
Inferencep. 15
Logical formp. 18
Sentences and propositionsp. 20
Possible worlds and the truth-set of a propositionp. 22
Analytic and synthetic sentencesp. 23
Simple and compound sentencesp. 24
The depth of the logical analysisp. 25
Propositional logicp. 26
Connectivesp. 26
The meaning of the logical connectivesp. 30
Negationp. 30
Conjunctionp. 32
Disjunctionp. 34
Implicationp. 37
Equivalencep. 40
How to indicate constituent structurep. 42
The syntax and semantics of propositional calculusp. 44
Syntaxp. 45
Semanticsp. 47
Tautologies and contradictionsp. 50
Truth tablesp. 50
Predicate logicp. 58
Extending the logical analysisp. 58
Quantifiersp. 61
Summary of the syntax of predicate logicp. 71
The semantics of predicate logicp. 72
True in all interpretationsp. 77
Summary of the semantics of predicate logicp. 83
A formal version of the semanticsp. 84
Formal properties of relationsp. 88
Reflexivityp. 88
Symmetryp. 89
Transitivityp. 89
Conversep. 90
Structure of the domain and co-domain of relationsp. 90
Deductionp. 96
The deductive systemp. 96
Deduction rules in everyday conversationp. 104
Modal logicp. 108
Modal operatorsp. 108
Strict implicationp. 110
Other modalitiesp. 111
Problems connected with scope and identity in modal logicp. 114
'De dicto'--'de re' ambiguitiesp. 114
Specificityp. 116
Opacityp. 117
Cross-world identificationp. 119
Counterfactual sentencesp. 120
Tense logic and reference pointsp. 121
Intensional logic and categorial grammarp. 125
Intensions and extensionsp. 125
Intensionp. 127
The Fregean principlep. 130
The Fregean principle and categorial grammarp. 132
Categories, intensions and typesp. 136
Further extensionsp. 148
Second-order predicate logic and predicate operatorsp. 148
Presuppositions and definite descriptionsp. 149
Pragmatic analysis of presuppositionsp. 153
The abstraction- or lambda-operatorp. 155
Logic for linguists?p. 158
Generalp. 158
The concept of meaningp. 158
The role of formal languages in analysing natural languagep. 164
The limitations of classical logicp. 168
Referencesp. 172
Answers to exercisesp. 175
Indexp. 181
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521291743
ISBN-10: 0521291747
Series: Cambridge Textbooks in Linguistics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 196
Published: 14th November 1977
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.53 x 14.91  x 1.14
Weight (kg): 0.28