Building Decision Procedures for Modal Logics from Propositional Decision Procedures: The Case Study of Modal K(m)

Abstract

The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we consider satisfiability in modal K ( m ), that is modal K with m modalities, and develop an algorithm, called K SAT , on top of an implementation of the Davis–Putnam–Longemann–Loveland procedure. K SAT is thoroughly tested and compared with various procedures and in particular with the state-of-the-art tableau-based system K RIS . The experimental results show that K SAT outperforms K RIS and the other systems of orders of magnitude, highlight an intrinsic weakness of tableau-based decision procedures, and provide partial evidence of a phase transition phenomenon for K ( m ).