Sorted resolution-based calculi

Abstract

In this part we consider several resolution-based calculi with order-sorted signatures. We investigate resolution, paramodulation and factoring, G. Plotkin's resolution with built-in equational theories, J. Morris' E-resolution and M. Stickels theory resolution. We show that the completeness results that hold in the unsorted case or in the case of simple signatures [Wa83] hold also in the presence of term delarations. The results concerning the fact that the functionally reflexive axioms are not needed for clause sets with equations are in general not liftable, as shown in an example.

In this part we assume that there are no ill-sorted terms and literals. Furthermore, we sometimes omit the adjective ‘well-sorted’, but always mean that every thing is well-sorted, in particular substitutions are well-sorted.