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

1. Front Matter

   Pages I-XI

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2. An Introduction to General Intensional Logics

   1. Front Matter

      Pages 1-1

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   2. Consequence Relations

      • Dov M. Gabbay

      Pages 3-24

3. An Introduction to One Dimensional Modal Logics

   1. Front Matter

      Pages 25-25

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   2. Basic Notions

      • Dov M. Gabbay

      Pages 27-35

   3. General Theory of Unary Intensional Connectives

      • Dov M. Gabbay

      Pages 36-43

   4. Basic Necessity Systems

      • Dov M. Gabbay

      Pages 44-60

   5. Basic Tense Systems

      • Dov M. Gabbay

      Pages 61-70

   6. Possible Worlds with Varying Domains

      • Dov M. Gabbay

      Pages 71-80

   7. Equality and Proper Names

      • Dov M. Gabbay

      Pages 81-93

   8. An Appendix on Propositional Statability Operators

      • Dov M. Gabbay

      Pages 94-105

4. Technical Results for Propositional Calculi

   1. Front Matter

      Pages 107-107

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   2. The Finite Model Property

      • Dov M. Gabbay

      Pages 109-123

   3. Selective Filtration

      • Dov M. Gabbay

      Pages 124-135

5. Introduction to Many Dimensional Modal Logics and Applications

   1. Front Matter

      Pages 137-137

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   2. Two Dimensional Propositional Tense Logics

      • Dov M. Gabbay

      Pages 139-156

   3. An Appendix

      • Dov M. Gabbay

      Pages 157-164

   4. Some Applications

      • Dov M. Gabbay

      Pages 165-175

6. Special Systems

   1. Front Matter

      Pages 177-177

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   2. Relative Necessity Operators and the Subjunctive Conditional

      • Dov M. Gabbay

      Pages 179-192

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

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