Finite-valued Lukasiewicz modal logic Is PSPACE-complete

Authors:
Félix Bou;Marco Cerami;Francesc Esteva
Affiliations:
University of Barcelona, Barcelona, Spain;IIIA, CSIC, Bellaterra, Spain;IIIA, CSIC, Bellaterra, Spain
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Year:
2011

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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.