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.

Inhalt

0: An Introduction to General Intensional Logics.- 0 / Consequence Relations.- 0. Basic Notions.- 1. Basic Completeness Theorem.- 2. Dependence of One Semantics on Another.- 1: An Introduction to One Dimensional Modal Logics.- 1 / Basic Notions.- 3. The Syntax.- 4. The Interpretation.- 5. The Completeness Theorem.- 2 / General Theory of Unary Intensional Connectives.- 6. Neighbourhood Systems.- 7. Kripke Systems.- 3 / Basic Necessity Systems.- 8. The Main Predicate Calculi.- 9. The Barcan Formula.- 10. Special Topics.- 4 / Basic Tense Systems.- 11. Basic Tense Systems.- 12. Exercises.- 5 / Possible Worlds with Varying Domains.- 13. Neighbourhood Structures with Varying Domains.- 14. Kripke Structures with Varying Domains.- 15. Exercises.- 6 / Equality and Proper Names.- 16. Pure Theory of Equality.- 17. Equality in Kripke Structures.- 18. Proper Names.- 7 / Propositional Statability Operators.- 19. Tensed Statability Operators.- 20. Modal Statability Operators.- 2: Technical Results for Propositional Calculi.- 8 / The Finite Model Property.- 21. Ordinary Filtration.- 22. Extensions of S4.3.- 23. Lack of the Finite Model Property.- 24. An Extension of S4 Without the Finite Model Property.- 9 / Selective Filtration.- 25. Selective Filtration in Non-reflexive World Structures.- 26. Reflexive Systems.- 27. Exercises.- 3: Introduction to Many Dimensionel Modal Logics and Applications.- 10 / Two Dimensional Propositional Tense Logics.- 28. The Systems G4 and G24.- 29. The Systems GJ4 and G2J4.- 30. The System Kt24.- 31. The System Kt2J4.- 32. The System G2.- 11 / An Appendix.- 33. A Theory of Proper Names and Conceptual Change.- 12 / Some Applications.- 34. Tense Logics and the Tenses of English.- 4: Special Systems.- 13 / Relative Necessity Operators and the Subjunctive Conditional.- 35. n-ry Entailment and Necessity Operators.- 36. A General Theory of the Conditional in Terms of a Ternary Operator.- 14 / Propositional Quantifiers.- 37. Systems Without the Comprehension Axiom.- 38. The Comprehension Axiom.- 15 / Basic Entailment Type Logics.- 39. Weak Entailment Systems.- 5: The Decision Problem.- 16 / The Reduction Method.- 40. The Reduction Method for Modal Systems.- 41. Some Completeness Theorems.- 17 / Some Decidability Results.- 42. Simple Results.- 43. More Decidability Results.- 44. Transfer Property.- 45. Exercises.- 46. On Decidable, Finitely Axiomatizable, Modal and Tense Logics Without the Finite Model Property.- 18 / The Decision Problem for Predicate Systems.- 47. Undecidability Results.- 48. Decidability Results.- 6: Special Topics.- 19 / Completeness for Frames.- 49. Completeness for Kripke Frames.- 50. Completeness for Neighborhood Frames.- 20 / The Interpolation Theorem.- 51. The Interpolation Theorem.- 7: Notes and Some References.- Scheme of the Book.- References.- Index of Names.