Finite-valued Lukasiewicz modal logic is PSPACE-complete

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Finite-valued Lukasiewicz modal logic is PSPACE-complete

Computational Complexity
Fuzzy Description Logics
Lukasiewicz Logic
modal many-valued logic

Publication Type:

Conference Paper

Authors:

Fèlix Bou; Marco Cerami; Francesc Esteva

Source:

Twenty-second International Joint Conference on Artificial Intelligence (IJCAI 2011), Barcelona, p.774 - 779 (2011)

ISBN:

978-1-57735-516-8

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.