Complexity of Some Problems in Modal and Intuitionistic Calculi

  • Larisa Maksimova
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2803)

Abstract

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.

We consider the complexity of some properties for non-classical logics which are known to be decidable. The complexity of tabularity, pre-tabularity, and interpolation problems in extensions of the intuitionistic logic and of the modal logic S4 is studied, as well as the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Larisa Maksimova
    • 1
  • Andrei Voronkov
    • 2
  1. 1.Institute of MathematicsNovosibirsk
  2. 2.University of Manchester 

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