Multi-Dimensional Modal Logic

By: Maarten Marx, Yde Venema

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Hardcover | 30 November 1996

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256 Pages

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25.4 x 17.15 x 2.54

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Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.)
This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.

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Preface
Multi-dimensional modal logic	p. 1
Two-dimensional modal logics	p. 11
Arrow logic	p. 43
Modal logics of intervals	p. 93
Modal logics of relations	p. 113
Multi-dimensional semantics for every modal language	p. 169
Open problems	p. 181
Modal Similarity Types	p. 185
A Modal Toolkit	p. 199
Bibliography	p. 223
List of symbols	p. 233
Index	p. 237
Table of Contents provided by Blackwell. All Rights Reserved.

Multi-Dimensional Modal Logic

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Hardcover

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