PSPACE Reasoning for Graded Modal Logics

@article{Tobies2001PSPACERF,
  title={PSPACE Reasoning for Graded Modal Logics},
  author={Stephan Tobies},
  journal={J. Log. Comput.},
  year={2001},
  volume={11},
  pages={85-106}
}
We present a PS PACE algorithm that decides satisfiability of the graded modal lo gic 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 complexi ty of the problem. Thus, we exactly fix the complexity of the problem and refute a E XPTIME-hardness conjecture. We extend the results to… CONTINUE READING
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