A New Introduction to Modal Logic

by Cresswell,M.J.

• ISBN13: 9780415126007
• ISBN10: 0415126002
• Format: Paperback
• Copyright: 1996-09-12
• Publisher: Routledge

Summary

This long-awaited book replaces not one but both of Hughes and Cresswell's two previous classic studies of modal logic:An Introduction to Modal LogicandA Companion to Modal Logic. A New Introduction to Modal Logichas been completely rewritten by the authors to incorporate all the developments that have taken place since 1968 both in modal propositional logical and modal predicate logic, but without sacrificing the clarity of exposition and approachability that were essential features of the earlier works. The book takes readers through the most basic systems of modal prepositional logic right up to systems of modal predicate with identity. It deals with both technical developments such as completeness and incompleteness, and finite and infinite models, and discusses philosophical applications, especially, in the area of modal predicate logic.

Table of Contents

A New Introduction to Modal Logic	p. i
Preface	p. ix
Basic Modal Propositional Logic	p. 1
The Basic Notions	p. 3
The Systems K, T and D	p. 23
Notes	p. 49
The Systems S4, S5, B, Triv and Ver	p. 51
Notes	p. 70
Testing for Validity	p. 72
Conjunctive Normal Form	p. 94
Completeness	p. 111
Notes	p. 123
Normal Modal Systems	p. 125
Canonical Models	p. 127
Notes	p. 142
Finite Models	p. 145
Notes	p. 156
Incompleteness	p. 159
Notes	p. 170
Frames and Systems	p. 172
Notes	p. 190
Strict Implication	p. 193
Notes	p. 206
Glimpses Beyond	p. 210
Notes	p. 230
Modal Predicate Logic	p. 233
The Lower Predicate Calculus	p. 235
The Completeness of Modal Lpc	p. 256
Notes	p. 272
Expanding Domains	p. 274
Notes	p. 287
Modality and Existence	p. 289
Notes	p. 310
Identity and Descriptions	p. 312
Intensional Objects	p. 330
Further Issues	p. 349
Axioms, Rules and Systems	p. 359
Table I: Normal Modal Systems	p. 367
Table II: Non-Normal Modal Systems	p. 368
Solutions to Selected Exercises	p. 369
Bibliography	p. 384
Index	p. 398
Table of Contents provided by Publisher. All Rights Reserved.