Kripke's Worlds : an introduction to modal logics via Tableaux [electronic resource] / Olivier Gasquet, Andreas Herzig, Bilal Said, François Schwarzentruber.

Kripke's Worlds : an introduction to modal logics via Tableaux [electronic resource] / Olivier Gasquet, Andreas Herzig, Bilal Said, François Schwarzentruber.

9783764385040 electronic book
3764385049 electronic book
9783764385033

Basel : Birkhäuser, 2014.

English

1 online resource (xv, 198 pages) : illustrations.

10.1007/978-3-7643-8504-0 doi

QA9.46

511.3/14

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.

Includes bibliographical references and index.

Access limited to authorized users.

Description based on online resource; title from PDF title page (SpringerLink, viewed November 25, 2013).

Studies in universal logic.

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