by Stephan Tobies
J. of Logic and Computation
ftp://www-lti.informatik.rwth-aachen.de/pub/papers/2000/Tobies-JLC-2000.ps.gz
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Abstract:
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. We extend the results to the logic Gr(K R
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