A Fixpoint Approach to Second-Order Quantifier Elimination with Applications to Correspondence Theory

Abstract

This paper is about automated techniques for (modal logic) correspondence theory. The theory we deal with concerns the problem of finding fixpoint characterizations of modal axiom schemata. Given a modal schema and a semantics based method of translating modal formulae into classical ones, we try to derive automatically a fixpoint formula characterizing precisely the class of frames validating this schema. The technique we consider can, in many cases, be easily applied without any computer support. Although we mainly concentrate on Kripke semantics, our fixpoint approach is much more general, as it is based on the elimination of second-order quantifiers from formulae. Thus it can be applied in second-order theorem proving as well. We show some application examples for the method which may serve as new, automated proofs of the respective correspondences.