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Title Kripke's Worlds : an introduction to modal logics via Tableaux / Olivier Gasquet, Andreas Herzig, Bilal Said, François Schwarzentruber
Published Basel : Birkhäuser, 2014
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Description 1 online resource (xv, 198 pages) : illustrations
Series Studies in Universal Logic
Studies in universal logic.
Contents Modelling things with graphs -- Talking about graphs -- The basics of the model construction method -- Logics with simple constraints on models -- Logics with transitive accessibility relations -- Model Checking -- Modal logics with transitive closure
Summary Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible worlds model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given a logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed November 25, 2013)
Subject Modality (Logic)
Mathematics.
Form Electronic book
Author Gasquet, Olivier, author
ISBN 3764385049 (electronic bk.)
9783764385040 (electronic bk.)