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DOI: 10.4230/LIPIcs.FSTTCS.2011.264
URN: urn:nbn:de:0030-drops-33495
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3349/
Kieronski, Emanuel ; Michaliszyn, Jakub ; Otop, Jan

Modal Logics Definable by Universal Three-Variable Formulas

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Abstract

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.

BibTeX - Entry

@InProceedings{kieronski_et_al:LIPIcs:2011:3349,
  author =	{Emanuel Kieronski and Jakub Michaliszyn and Jan Otop},
  title =	{{Modal Logics Definable by Universal Three-Variable Formulas}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{264--275},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Supratik Chakraborty and Amit Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3349},
  URN =		{urn:nbn:de:0030-drops-33495},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2011.264},
  annote =	{Keywords: modal logic, decidability}
}

Keywords: modal logic, decidability
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)
Issue date: 2011
Date of publication: 01.12.2011

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