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URN: urn:nbn:de:0030-drops-13561
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On the Complexity of Elementary Modal Logics

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Abstract

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide class of relevant logics: Many important subclasses of modal logics can be obtained by restricting the allowed models with first-order Horn formulas. We show that the satisfiability problem for each of these logics is either NP-complete or PSPACE-hard, and exhibit a simple classification criterion. Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard logics.

BibTeX - Entry

@InProceedings{hemaspaandra_et_al:LIPIcs:2008:1356,
  author =	{Edith Hemaspaandra and Henning Schnoor},
  title =	{{On the Complexity of Elementary Modal Logics}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{349--360},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1356},
  URN =		{urn:nbn:de:0030-drops-13561},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1356},
  annote =	{Keywords: }
}

Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2008
Date of publication: 2008


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