On satisfiability problem in modal logic S5

Yakoub Salhi

Abstract: This article aims at studying different aspect of the satisfiability problem in the modal logic S5. We first introduce a new resolution method that is syntactically pure in the sense that does not use explicitly semantic information. Then, we propose simplification rules that can be applied during preprocessing and solving. Some of these rules can be seen as adaptations of existing simplification rules for CNF formulas in classical propositional logic. Finally, we argue in favor of modeling in S5 to solve NP-complete problems. Indeed, we provide encodings that allow us to solve three different well-known NP-complete problems: graph coloring, Hamiltonian path, and closest string. Our models in S5 show in particular that the possible-worlds semantics allows solving NP-complete problems with fewer propositional variables than in classical propositional logic.