Using Resolution for Testing Modal Satisfiability and Building Models

Hustadt, U. and Schmidt, R. A. (2000)

In Gent, I. P. and van Maaren, H. and Walsh, T. (eds), SAT 2000: Highlights of Satisfiability Research in the Year 2000. Frontiers in Artificial Intelligence and Applications 63, IOS Press, Amsterdam. Also to appear in a special issue of Journal of Automated Reasoning. BiBTeX, PostScript.

This paper presents a translation-based resolution decision procedure for the multi-modal logic $\textit{K}_{(m)}(\cap,\cup,\smile)$ defined over families of relations closed under intersection, union and converse. The relations may satisfy certain additional frame properties. Different from previous resolution decision procedures which are based on ordering refinements our procedure is based on a selection refinement, the derivations of which correspond to derivations of tableaux or sequent proof systems. This procedure has the advantage that it can be used both as a satisfiability checker and a model builder. We show that tableaux and sequent-style proof systems can be polynomially simulated with our procedure. Furthermore, the finite model property follows for a number of extended modal logics.

Renate A. Schmidt
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