The Complexity of Model Checking for Intuitionistic Logics and Their Modal Companions

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.

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