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Abstract

Resolution for the first order logic can be considered as a practical tool for obtaining a decision procedures for some theories (cf. \cite{arm}). For modal logics, however, there is no uniform formulation of the resolution principle, yet the normal modal logics are the most probable candidates to be decidable theories. The translational methods for modal logic, treated for instance in \cite{ohl}, yet possess some uniformness property, but does not let one to extract proofs from the refutations. On the other hand, direct methods (cf. \cite{far}, \cite{abadi}) are local which gives not much practical use of them. This paper presents some arguments on generalization of the classical propositional resolution method to the language of modal logic. We give a resolution calculus for modal logic $\K$ that inherits some features of classical resolution and propose some suggestions of how can it be used for other modal logics.