Characterizing the NP-PSPACE Gap in the Satisfiability Problem for Modal Logic
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چکیده
There has been a great deal of work on characterizing the complexity of the satisfiability and validity problem for modal logics. In particular, Ladner showed that the satisfiability problem for all logics betweenK andS4 is PSPACE-hard, while forS5 it is NP-complete. We show that it is negative introspection, the axiom ¬Kp ⇒ K¬Kp, that causes the gap: if we add this axiom to any modal logic between K and S4, then the satisfiability problem becomes NP-complete. Indeed, the satisfiability problem is NP-complete for any modal logic that includes the negative introspection axiom.
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تاریخ انتشار 2007