ORDER-SORTED RIGID E-UNIFICATION

Abstract

Rigid E-Unification is a special type of unification which arises naturally when extending Andrew's method of matings to logic with equality. We study the rigid E-Unification problem in the presence of subsorts. We present an order sorted method for the computation of order sorted rigid-E-unifiers. The method is based on an unsorted one which we refine and extend to handle sort information. Our approach is to incorporate the sort information within the method so as to leverage it. We show via examples how the order sorted method is able to detect failures due to sort conflicts at an early stage in the construction of potential rigid E Unifiers. The algorithm presented here is NP-complete, as is the unsorted one. This is significant, specially due to the complications presented by the sort information.