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

  • Authors
  • Dov M. Gabbay

Part of the Synthese Library book series (SYLI, volume 92)

Table of contents

  1. Front Matter
    Pages I-XI
  2. An Introduction to General Intensional Logics

    1. Front Matter
      Pages 1-1
    2. Dov M. Gabbay
      Pages 3-24
  3. An Introduction to One Dimensional Modal Logics

    1. Front Matter
      Pages 25-25
    2. Dov M. Gabbay
      Pages 27-35
    3. Dov M. Gabbay
      Pages 44-60
    4. Dov M. Gabbay
      Pages 61-70
    5. Dov M. Gabbay
      Pages 71-80
    6. Dov M. Gabbay
      Pages 81-93
  4. Technical Results for Propositional Calculi

    1. Front Matter
      Pages 107-107
    2. Dov M. Gabbay
      Pages 109-123
    3. Dov M. Gabbay
      Pages 124-135
  5. Introduction to Many Dimensional Modal Logics and Applications

    1. Front Matter
      Pages 137-137
    2. Dov M. Gabbay
      Pages 139-156
    3. Dov M. Gabbay
      Pages 157-164
    4. Dov M. Gabbay
      Pages 165-175
  6. Special Systems

    1. Front Matter
      Pages 177-177
    2. Dov M. Gabbay
      Pages 193-201
    3. Dov M. Gabbay
      Pages 202-212
  7. The Decision Problem

    1. Front Matter
      Pages 213-213
    2. Dov M. Gabbay
      Pages 215-229
    3. Dov M. Gabbay
      Pages 230-265
    4. Dov M. Gabbay
      Pages 266-272
  8. Special Topics

    1. Front Matter
      Pages 273-273
    2. Dov M. Gabbay
      Pages 275-281
    3. Dov M. Gabbay
      Pages 282-295
  9. Back Matter
    Pages 297-312

About this book


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.


15th century English English literature conditional interpret linguistics literature logic modal logic philosophy proposition quantifiers reduction semantic semantics

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1976
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-1455-7
  • Online ISBN 978-94-010-1453-3
  • Buy this book on publisher's site