Decidability by Resolution for Propositional Modal Logics

Authors:
Renate A. Schmidt
Affiliations:
Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, U.K. e-mail: R.A.Schmidt@doc.mmu.ac.uk
Venue:
Journal of Automated Reasoning
Year:
1999

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Abstract

The paper shows that satisfiability in a range of popular propositional modal systems can be decided by ordinary resolution procedures. This follows from a general result that resolution combined with condensing, and possibly some additional form of normalization, is a decision procedure for the satisfiability problem in certain so-called path logics. Path logics arise from normal propositional modal logics by the optimized functional translation method. The decision result provides an alternative method of proving decidability for modal logics, as well as closely related systems of artificial intelligence. This alone is not interesting. A more far-reaching consequence of the result has practical value, namely, many standard first-order theorem provers that are based on resolution are suitable for facilitating modal reasoning.