Modal Logic

Hardcover | April 27, 1997

byAlexander Chagrov, Michael Zakharyaschev

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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 - `like it is necessary' in philosophy, `it is believed' in cognitive science, `itis provable' in mathematics and `it is true after executing a program' in computer science. It is an advanced text which starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantical and algebraic apparatus andcovering 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. For the first time 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. Unlike other books, modal logic istreated here as a uniform theory rather than a collection of a few particular systems. It is the only book presenting the theory of superintuitionistic logics.

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From the Publisher

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 - `like it is necessary' in philosophy, `it is believed' in cognitive science, `itis provable' in mathematics and `it is true ...

Alexander Chagrov is Professor of Mathematics at Tver State University. Michael Zakharyaschev is Professor of Mathematics at Moscow State University in Russia.
Format:HardcoverDimensions:620 pages, 9.21 × 6.14 × 1.54 inPublished:April 27, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198537794

ISBN - 13:9780198537793

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Table of Contents

Introduction1. Classical logic2. Intuitionistic logic3. Modal logics4. From logics to classes of logics5. Canonical models and filtration6. Incompleteness7. Algebraic semantics8. Relational semantics9. Canonical formulas10. Kripke completeness11. The finite approximability12. Tabularity13. Post completeness14. Interpolation15. The disjunction property and Hallden completeness16. The decidability of logics17. Admissibility and drivability of inference rules18. The decidability of logics' properties19. Complexity problemsReferenceIndex

Editorial Reviews

"This book presents a rich resource for modern mathematical modal logic, useful both as an advanced textbook and as a source for up-to-date results." --Zentralblatt fuer Mathematik 871/97