{"type":"ScholarlyArticle","title":"Characterizing the NP-PSPACE Gap in the Satisfiability Problem for Modal Logic","authors":[{"name":"Joseph Y. Halpern","slug":"joseph-y-halpern","given":"Joseph Y.","family":"Halpern","affiliation":""},{"name":"Leandro Chaves Rêgo","slug":"leandro-chaves-rego","given":"Leandro Chaves","family":"Rêgo","affiliation":""}],"abstract":"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 axiom 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.","doi":null,"url":"https://ijcai.org/proceedings/2007/371","pdf":"https://ijcai.org/proceedings/2007/0371.pdf","markdown":"https://ijcai.org/proceedings/2007/371.md","bibtex":"https://ijcai.org/proceedings/2007/bibtex/371","volume":{"slug":"2007","title":"Proceedings of the Twentieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2007","url":"https://ijcai.org/proceedings/2007/","year":2007,"location":"Hyderabad, India","dates":"","editors":"Ramon López de Mántaras","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":371,"pages":{"first":2306,"last":2310},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}