Uniform Interpolation by Resolution in Modal Logic

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Abstract

The problem of computing a uniform interpolant of a given formula on a sublanguage is known in Artificial Intelligence as variable forgetting. In propositional logic, there are well known methods for performing variable forgetting. Variable forgetting is more involved in modal logics, because one must forget a variable not in one world, but in several worlds. It has been shown that modal logic K has the uniform interpolation property, and a method has recently been proposed for forgetting variables in a modal formula (of mu-calculus) given in disjunctive normal form. However, there are cases where information comes naturally in a more conjunctive form. In this paper, we propose a method, based on an extension of resolution to modal logics, to perform variable forgetting for formulae in conjunctive normal form, in the modal logic K .