Building decision procedures for modal logics from propositional decision procedures: the case study of modal K

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 describe an algorithm, based on an implementation of the Davis-Putnam-Longemann-Loveland procedure, which tests satisfiability in modal K. The algorithm is compared with a tableau based decision procedure. The experimental results show that our algorithm outperforms this system. The testing is performed following a newly developed methodology which, among other things, allows us to classify problems according to an easy to hard pattern.