Modal Logics Definable by Universal Three-Variable Formulas

Authors Emanuel Kieronski, Jakub Michaliszyn, Jan Otop

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Emanuel Kieronski
Jakub Michaliszyn
Jan Otop

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Emanuel Kieronski, Jakub Michaliszyn, and Jan Otop. Modal Logics Definable by Universal Three-Variable Formulas. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 264-275, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


We consider the satisfiability problem for modal logic over classes of structures definable by universal first-order formulas with three variables. We exhibit a simple formula for which the problem is undecidable. This improves an earlier result in which nine variables were used. We also show that for classes defined by three-variable, universal Horn formulas the problem is decidable. This subsumes decidability results for many natural modal logics, including T, B, K4, S4, S5.
  • modal logic
  • decidability


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