The complexity of model checking for intuitionistic logics and their modal companions

Authors:
Martin Mundhenk;Felix Weiß
Affiliations:
Universität Jena, Institut für Informatik, Jena, Germany;Universität Jena, Institut für Informatik, Jena, Germany
Venue:
RP'10 Proceedings of the 4th international conference on Reachability problems
Year:
2010

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Abstract

We study the model checking problem for logics whose semantics are defined using transitive Kripke models. We show that the model checking problem is P-complete for the intuitionistic logic KC. Interestingly, for its modal companion S4.2 we also obtain P-completeness even if we consider formulas with one variable only. This result is optimal since model checking for S4 without variables is NC1-complete. The strongest variable free modal logic with P-complete model checking problem is K4. On the other hand, for KC formulas with one variable only we obtain much lower complexity, namely LOGDCFL as an upper bound.