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 dropped from PSPACE-complete to coNP-complete (Schmidt-Schauss and Smolka [8] and Donini et al. [3]). 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 Donini et al.’s complexity classification of description logics [2]. In the last section, we classify the complexity of the satisfiability problem for K for all other restrictions on the set of operators.
Supported in part by grant NSF-INT-9815095. Work done in part while visiting the University of Amsterdam.
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© 2000 Springer-Verlag Berlin Heidelberg
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Hemaspaandra, E. (2000). The Complexity of Poor Man’s Logic. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_19
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DOI: https://doi.org/10.1007/3-540-46541-3_19
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