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Journal of Logic and Computation 2005 15(4):559-574; doi:10.1093/logcom/exi039
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Vol. 15 No. 4, © The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Modal Logics of Regions and Minkowski Spacetime

Ilya Shapirovsky and Valentin Shehtman

Institute for Information Transmission Problems, Russian Academy of Sciences, B. Karetny 19, 101447, Moscow, Russia. Email: ilshapir{at}netscape.net, shehtman{at}netscape.net

The paper studies modal logics of Kripke frames, in which possible worlds are regions in space with natural accessibility relations. These logics are also interpreted as relativistic temporal logics. Together with an overview, we prove some new results on completeness, decidability, complexity, and finite axiomatizability.

Keywords: Relativistic temporal logics, interval temporal logics, region, causal accessibility, chronological accessibility, ‘after’ relation, finite axiomatizability, Jankov–Fine formulas, finite model property, PSPACE, intuitionistic logic, information types

Received 28 May 2005.


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