Complexity of Some Problems in Modal and Intuitionistic Calculi

Complexity of provability and satisfiability problems in many non-classical logics, for instance, in intuitionistic logic, various systems of modal logic, temporal and dynamic logics was studied in [3, 5, 9, 22, 23, 24]. Ladner [9] proved that the provability problem is \(\textsf{\textup{PSPACE}}\)-complete for modal logics K, T and S4 and \(\textsf{\textup{coNP}}\)-complete for S5. Statman [24] proved that the problem of determining if an arbitrary implicational formula is intuitionistically valid is \(\textsf{\textup{PSPACE}}\)-complete.

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