A PSpace Algorithm for Graded Modal Logic

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Abstract

We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(K R)—a natural extension of propositional modal logic K R 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.