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Abstract:
The paper shows satisfiability in many propositional modal systems 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 logics (including \textit{K}, \textit{KD}, \textit{KT}
and \textit{KB}, their combinations as well as their multi-modal
versions), and related systems in artificial intelligence.
This alone is not 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.
