Refinements of Resolution

Abstract

In Chapter 2 we have proved the correctness and completeness of the resolution principle. It might seem that these are already the key results of resolution theory. Although the (general) resolution principle is clearly superior to the PR-deduction principle and to methods based on Herbrand’s theorem, there are several reasons for further refining the deduction principle. First of all the high number of resolvents derivable from a set of clauses is a serious obstacle to practical applications. Thus it is significant that Robinson presented a paper on hyperresolution [Rob65a], a refinement to be described later, in the same year as his landmark paper on resolution [Rob65] was published. So one motivation for restricting the R-deduction principle is efficiency.