Decidability by Resolution for Propositional Modal Logics

Schmidt, R. A. (1999)

Journal of Automated Reasoning 22(4), 379-396. BiBTeX, DOI Link.

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 normalisation, is a decision procedure for the satisfiability problem in certain so-called path logics. Path logics arise from normal propositional modal logics by the optimised 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, any fair implementation of a first-order theorem prover which is based on resolution is suitable for facilitating modal reasoning.

See also Resolution is a decision procedure for many propositional modal logics, in Wansing et al (1998).
Renate A. Schmidt
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Last modified: 01 Jul 08
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