A PSpace Algorithm for Graded Modal Logic

  • Stephan Tobies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)


We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)—a natural extension of propositional modal logic KR by counting expressions—which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute a ExpTime-hardness conjecture. This establishes a kind of “theoretical benchmark” that all algorithmic approaches can be measured with.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Stephan Tobies
    • 1
  1. 1.LuFg Theoretical Computer ScienceRWTH AachenGermany

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