Resolution is a Decision Procedure for Many Propositional Modal Logics

Schmidt, R. A. (1998)

In Kracht, M., de Rijke, M., Wansing, H. and Zakharyaschev, M. (eds), Advances in Modal Logic, Volume 1. Lecture Notes 87, CSLI Publications, Stanford, 189-208. BiBTeX, with access restrictions: PostScript.

The paper shows satisfiability in many propositional modal systems, including K, KD, KT and KB, their combinations as well as their multi-modal versions, can be decided by ordinary resolution procedures. This follows from a general result that resolution and condensing is a decision procedure for the satisfiability problem of formulae in so-called path logics. Path logics arise from propositional and normal uni- and multi-modal logics by the optimised functional translation method. The decision result provides an alternative decision proof for the relevant modal systems, and related systems in artificial intelligence. However, this alone is not very interesting. A more far-reaching consequence of the result has practical value, namely, any standard first-order theorem prover that is based on resolution can serve as a reasonable and efficient inference tool for modal reasoning.

See also Decidability by Resolution for Propositional Modal Logics, In Journal of Automated Reasoning.
Renate A. Schmidt
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