LIPIcs.STACS.2008.1356.pdf
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On the Complexity of Elementary Modal Logics
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25th International Symposium on Theoretical Aspects of Computer Science
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication date: 2008-02-06
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Edith Hemaspaandra and Henning Schnoor. On the Complexity of Elementary Modal Logics. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 349-360, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.STACS.2008.1356
https://doi.org/10.4230/LIPIcs.STACS.2008.1356
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.
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