Modal Logic [Hardcover]

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume.

Introduction
1. Classical logic
2. Intuitionistic logic
3. Modal logics
4. From logics to classes of logics
5. Canonical models and filtration
6. Incompleteness
7. Algebraic semantics
8. Relational semantics
9. Canonical formulas
10. Kripke completeness
11. The finite approximability
12. Tabularity
13. Post completeness
14. Interpolation
15. The disjunction property and Halld?n completeness
16. The decidability of logics
17. Admissibility and drivability of inference rules
18. The decidability of logics' properties
19. Complexity problems
Reference
Index

This book is intended to serve both the neophyte and the already initiated in understanding the methods, tools (algebras and relational structures), and results of propositional modal logic. At the heart of the matter lies the unimodal modal logicKand its class of quasinormal extensions. Another family of logics which appears in a prominent secondary role is the class of superintuitionistic logics, the logics which are extensions of Heyting's intuitionistic logicInt.From several points of view superintuitionistic logics arlÓ$