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The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E where A and B are Boolean terms and α is a relational term. Examining what we can say about dynamic models when we use formulas to describe them, we successively address the axiomatization/completeness issue and the decidability/complexity issue of our dynamic logics of the region-based theory of discrete spaces.
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DOI 10.3166/jancl.17.39-61
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References found in this work BETA

Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
Multi-Dimensional Modal Logic.Maarten Marx - 1997 - Kluwer Academic Publishers.

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Citations of this work BETA

A System of Relational Syllogistic Incorporating Full Boolean Reasoning.Nikolay Ivanov & Dimiter Vakarelov - 2012 - Journal of Logic, Language and Information 21 (4):433-459.
Sahlqvist Theorems for Precontact Logics.Philippe Balbiani & Stanislav Kikot - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic. CSLI Publications. pp. 55-70.

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