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- W2007671683 abstract "Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, ∧, ◊, and □. Previously, the only known result was that the complexity of the satisfiability problem for K drops from PSPACE‐complete to coNP‐complete. In this paper we show that not all modal logics behave like K. In particular, we show that the complexity of the satisfiability problem with respect to frames in which each world has at least one successor drops from PSPACE‐complete to P, but that in contrast the satisfiability problem with respect to the class of frames in which each world has at most two successors remains PSPACE‐complete. As a corollary of the latter result, we also solve the open problem from the complexity classification of description logics. In the last section, we classify the complexity of the satisfiability problem for K for all other restrictions on the set of operators." @default.
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- W2007671683 date "2001-08-01" @default.
- W2007671683 modified "2023-10-18" @default.
- W2007671683 title "The Complexity of Poor Man's Logic" @default.
- W2007671683 doi "https://doi.org/10.1093/logcom/11.4.609" @default.
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