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A Resolution Calculus for Modal Logics
, 1988
"... A syntax transformation is presented that eliminates the modal logic operators from modal logic formulae by shifting the modal context information to the term level. The formulae in the transformed syntax can be brought into conjunctive normal form such that a clause based resolution calculus withou ..."
Abstract

Cited by 89 (7 self)
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A syntax transformation is presented that eliminates the modal logic operators from modal logic formulae by shifting the modal context information to the term level. The formulae in the transformed syntax can be brought into conjunctive normal form such that a clause based resolution calculus without any additional inference rule, but with special modal unification algorithms, can be defined. The method works for firstorder modal logics with the two operators # and à and with constantdomain Kripke semantics where the accessibility relation is serial and may have any combination of the following properties: reflexivity, symmetry, transitivity. In particular the quantified versions of the modal systems T, S4, S5, B, D, D4 and DB can be treated. Extensions to nonserial and varyingdomain systems are possible, but not presented here.