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Abstract

The paper shows satisfiability in many propositional modal systems, including \textit{K}, \textit{KD}, \textit{KT} and \textit{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 \emph{path logics}. Path logics arise from propositional and normal uni- and multi-modal logics by the \emph{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.