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Elementary Modal Logics over Transitive Structures

Authors Jakub Michaliszyn, Jan Otop



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Jakub Michaliszyn
Jan Otop

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Jakub Michaliszyn and Jan Otop. Elementary Modal Logics over Transitive Structures. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 563-577, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.CSL.2013.563

Abstract

We show that modal logic over universally first-order definable classes of transitive frames is decidable. More precisely, let K be an arbitrary class of transitive Kripke frames definable by a universal first-order sentence. We show that the global and finite global satisfiability problems of modal logic over K are decidable in NP, regardless of choice of K. We also show that the local satisfiability and the finite local satisfiability problems of modal logic over K are decidable in NExpTime.
Keywords
  • Modal logic
  • Transitive frames
  • Elementary modal logics
  • Decidability

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