Modal Logic
Series: Oxford Logic Guides; 35;
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Product details:
- Publisher Clarendon Press
- Date of Publication 27 March 1997
- ISBN 9780198537793
- Binding Hardback
- No. of pages620 pages
- Size 242x164x39 mm
- Weight 1066 g
- Language English
- Illustrations line figures, tables 0
Categories
Short description:
This is a mathematically-oriented advanced textbook in modal logic, a discipline conceived in philosophy and having found applications in mathematics, artificial intelligence, linguistics, and computer science. It presents in a systematic and comprehensive way a wide range of classical and novel methods and results and can be used by a specialist as a reference book.
MoreLong description:
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, `it is 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 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. 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 is treated 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.
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.
Table of Contents:
Introduction
Classical logic
Intuitionistic logic
Modal logics
From logics to classes of logics
Canonical models and filtration
Incompleteness
Algebraic semantics
Relational semantics
Canonical formulas
Kripke completeness
The finite approximability
Tabularity
Post completeness
Interpolation
The disjunction property and Halldén completeness
The decidability of logics
Admissibility and drivability of inference rules
The decidability of logics' properties
Complexity problems
Reference
Index
