Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics / Edition 1

by Dov M. Gabbay

Overview

This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer­ ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.

Product Details

ISBN-13:	9789027706560
Publisher:	Springer Netherlands
Publication date:	09/30/1976
Series:	Synthese Library , #92
Edition description:	1976
Pages:	312
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

0: An Introduction to General Intensional Logics.- 0 / Consequence Relations.- 1: An Introduction to One Dimensional Modal Logics.- 1 / Basic Notions.- 2 / General Theory of Unary Intensional Connectives.- 3 / Basic Necessity Systems.- 4 / Basic Tense Systems.- 5 / Possible Worlds with Varying Domains.- 6 / Equality and Proper Names.- 7 / Propositional Statability Operators.- 2: Technical Results for Propositional Calculi.- 8 / The Finite Model Property.- 9 / Selective Filtration.- 3: Introduction to Many Dimensionel Modal Logics and Applications.- 10 / Two Dimensional Propositional Tense Logics.- 11 / An Appendix.- 12 / Some Applications.- 4: Special Systems.- 13 / Relative Necessity Operators and the Subjunctive Conditional.- 14 / Propositional Quantifiers.- 15 / Basic Entailment Type Logics.- 5: The Decision Problem.- 16 / The Reduction Method.- 17 / Some Decidability Results.- 18 / The Decision Problem for Predicate Systems.- 6: Special Topics.- 19 / Completeness for Frames.- 20 / The Interpolation Theorem.- 7: Notes and Some References.- Scheme of the Book.- References.- Index of Names.