A PSpace Algorithm for Graded Modal Logic
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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