{"type":"ScholarlyArticle","title":"Finite-Valued Lukasiewicz Modal Logic Is PSPACE-Complete","authors":[{"name":"Félix Bou","slug":"felix-bou","given":"Félix","family":"Bou","affiliation":""},{"name":"Marco Cerami","slug":"marco-cerami","given":"Marco","family":"Cerami","affiliation":""},{"name":"Francesc Esteva","slug":"francesc-esteva","given":"Francesc","family":"Esteva","affiliation":""}],"abstract":"It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i.e. in all these cases it is PSPACE-complete.","doi":"10.5591/978-1-57735-516-8/IJCAI11-136","url":"https://ijcai.org/proceedings/2011/136","pdf":"https://ijcai.org/proceedings/2011/0136.pdf","markdown":"https://ijcai.org/proceedings/2011/136.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/136","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":136,"pages":{"first":774,"last":778},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}