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.
Author(s): Jens Allwood, Lars-Gunnar Andersson, Osten Dahl
Series: Cambridge Textbooks in Linguistics
Edition: 1
Publisher: Cambridge University Press
Year: 1977
Language: English
Pages: 200
Cover
Title Page
Copyright Page
Table of Contents
Preface
Symbols and notational conventions
1 Logic for linguists
2 Set theory
2.1 Sets and elements
2.2. Relations between sets
2.3. Operations on sets
2.4. Relations and functions
3 Inference and logical analysis of sentences
3.1 Inference
3.2. Logical form
3.3. Sentences and propositions
3.4. Possible worlds and the truth-set of a proposition
3.5. Analytic and synthetic sentences
3.6. Simple and compound sentences
3.7. The depth of the logical analysis
4 Propositional logic
4.1. Connectives
4.2. The meaning of the logical connectives
4.2.1. Negation ~
4.2.2. Conjunction &
4.2.3. Disjunction v
4.2.4. Implication ?
4.2.5. Equivalence
4.3. How to indicate constituent structure
4.4. The syntax and semantics of propositional calculus
4.5 Syntax
4.6 Semantics
4.7 Tautologies and contradiction
4.8.Truth tables
EXERCISES
5 Predicate logic
5.1. Extending the logical analysis
5.2 Quantifiers
5.3 Summary of the syntax of predicate logic
5.4 The semantics of predicate logic
5.5 True in all interpretations
5.6 Summary of the semantics of predicate logic
5.7. A formal version of the semantics
5.8. Formal properties of relations
5.8.1. Reflexivity
5.8.2. Symmetry
5.8.3. Transitivity
5.8.4. Converse
5.8.5. Structure of the domain and co-domain of relations
EXERCISES
6 Deduction
6.1. The deductive system
6.2. Deduction rules in everyday conversation
EXERCISES
7 Modal logic
7.1. Modal operators
7.2. Strict implication
7.3. Other modalities
7.4. Problems connected with scope and identity in modal logic
7.4.1.De dicto- de re ambiguities
7.4.2. Specificity
7.4.3. Opacity
7.4.4. Cross-world identification
7.5. Counterfactual sentences
7.6. Tense logic and reference points
EXERCISES
8 Intensional logic and categorial grammar
8.1. Intensions and extensions
8.2. Intension
8.3. The Fregean principle
8.4. The Fregean principle and categorial grammar
8.5. Categories, intensions and types
EXERCISES
9 Further extensions
9.1. Second-order predicate logic and predicate operators
9.2. Presuppositions and definite descriptions
9.3. Pragmatic analysis of presuppositions
9.4. The abstraction- or lambda-operator
10 Logic for linguists?
10.1. General
10.2 The concept of meaning
10.3. The role of formal languages in analysing natural language
10.4. The limitations of classical logic
References
Answers to exercises
INDEX
