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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.
