Model generation theorem proving with finite interval constraints

Abstract

Model generation theorem proving (MGTP) is a class of deduction procedures for first-order logic that were successfully used to solve hard combinatorial problems. For some applications the representation of models in MGTP and its extension CMGTP is too redundant. Here we suggest to extend members of model candidates in such a way that a predicate p can have not only terms as arguments, but at certain places also subsets of totally ordered finite domains. The ensuing language and deduction system relies on constraints based on finite intervals in totally ordered sets and is called IV-MGTP. It is related to constraint programming and many-valued logic, but differs significantly from either. We show soundness and completeness of IV-MGTP. First results with our implementation show considerable potential of the method.