Generalized Modal Satisfiability

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dc.creatorHemaspaandra, Edith
dc.creatorSchnoor, Henning
dc.creatorSchnoor, Ilka
dc.date2008-04-17
dc.date.accessioned2026-07-07T12:18:22Z
dc.date.available2026-07-07T12:18:22Z
dc.descriptionIt is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal case, and study the dual problem of validity as well.
dc.description32 pages, 3 figures. Some of the results appeared in STACS 2006
dc.identifierhttps://arxiv.org/abs/0804.2729
dc.identifierhttp://arxiv.org/abs/0804.2729
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212385
dc.subjectComputational Complexity
dc.subjectLogic in Computer Science
dc.titleGeneralized Modal Satisfiability
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