Maximal unifiable subsets and minimal nonunifiable subsets

Abstract

We address the problem of collecting information about failures and successes while unifying a set of equations. This is relevant to the study of efficient backtracking, for which Cox used the concept of maximal unifiable subsets while Bruynooghe and Pereira used a notion which is closely related to that of minimal non-unifiable subsets. As we show, both these concepts play a fundamental role in the process of exploring the search space for breadth first resolution in logic programs. In a special case they lead to similar search strategies but in general have complementary and even incompatible aspects. We then show that an algorithm due to Yasuura is particularly well suited as a basis for a method to construct the maximal unifiable subsets and minimal non-unifiable subsetsin conjunction with the unification process. In addition to its simplicity this method provides an answer for two problems raised by Cox concerning the preservation of successful partial computations and unification without occur check.