Characterizing the NP-PSPACE gap in the satisfiability problem for modal logic
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 between K and S4 is PSPACE-hard, while for S5 it is NP-complete. We show that it is negative introspection, the axiom -K-p double right arrow K-K-p, 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.
s5 negative introspection euclidean property k5 pspace np knowledge representation