Logic in Linguistics

by Edited by Jens Allwood , Lars-Gunnar Andersson , Osten Dahl

• ISBN13: 9780521291743
• ISBN10: 0521291747
• Format: Paperback
• Copyright: 1977-10-28
• Publisher: Cambridge University Press

Summary

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 now 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 recent 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 cooperation between logicians and linguistics in studying the structure of language, and it is the overall aim of the book to promote this cooperation.

Table of Contents

Preface	viii
Symbols and notational conventions	ix
Logic for linguists	1	(2)
Set theory	3	(12)
Sets and elements	3	(2)
Relations between sets	5	(1)
Operations on sets	6	(3)
Relations and functions	9	(6)
Inference and logical analysis of sentences	15	(11)
Inference	15	(3)
Logical form	18	(2)
Sentences and propositions	20	(2)
Possible worlds and the truth-set of a proposition	22	(1)
Analytic and synthetic sentences	23	(1)
Simple and compound sentences	24	(1)
The depth of the logical analysis	25	(1)
Propositional logic	26	(32)
Connectives	26	(4)
The meaning of the logical connectives	30	(12)
Negation	30	(2)
Conjunction	32	(2)
Disjunction	34	(3)
Implication	37	(3)
Equivalence	40	(2)
How to indicate constituent structure	42	(2)
The syntax and semantics of propositional calculus	44	(1)
Syntax	45	(2)
Semantics	47	(3)
Tautologies and contradictions	50	(1)
Truth tables	50	(8)
Predicate logic	58	(38)
Extending the logical analysis	58	(3)
Quantifiers	61	(10)
Summary of the syntax of predicate logic	71	(1)
The semantics of predicate logic	72	(5)
True in all interpretations	77	(6)
Summary of the semantics of predicate logic	83	(1)
A formal version of the semantics	84	(4)
Formal properties of relations	88	(8)
Reflexivity	88	(1)
Symmetry	89	(1)
Transitivity	89	(1)
Converse	90	(1)
Structure of the domain and co-domain of relations	90	(6)
Deduction	96	(12)
The deductive system	96	(8)
Deduction rules in everyday conversation	104	(4)
Modal logic	108	(17)
Modal operators	108	(2)
Strict implication	110	(1)
Other modalities	111	(3)
Problems connected with scope and identity in modal logic	114	(6)
`De dicto'-`de re' ambiguities	114	(2)
Specificity	116	(1)
Opacity	117	(2)
Cross-world identification	119	(1)
Counterfactual sentences	120	(1)
Tense logic and reference points	121	(4)
Intensional logic and categorial grammar	125	(23)
Intensions and extensions	125	(2)
Intension	127	(3)
The Fregean principle	130	(2)
The Fregean principle and categorial grammar	132	(4)
Categories, intensions and types	136	(12)
Further extensions	148	(10)
Second-order predicate logic and predicate operators	148	(1)
Presuppositions and definite descriptions	149	(4)
Pragmatic analysis of presuppositions	153	(2)
The abstraction- or lambda-operator	155	(3)
Logic for linguists	158	(14)
General	158	(1)
The concept of meaning	158	(6)
The role of formal languages in analysing natural language	164	(4)
The limitations of classical logic	168	(4)
References	172	(3)
Answers to exercises	175	(6)
Index	181