A New Interpretation of the Resolution Principle

Abstract

We show in this paper that the application of the resolution principle to a set of clauses can be regarded as the construction of a term rewriting system confluent on valid formulas. This result allows the extension of standard properties and methods of equational theories (such as Birkhoff’s theorem and Knuth and Bendix completion algorithm) to quantifier-free first order predicate calculus.These results are extended to first order predicate calculus in an equational theory, as studied by Plotkin [], Slagle [] and Lankford [].This paper is a continuation of the work of Hsiang [], who has already shown that rewrite methods can be used in first order predicate calculus. The main difference is that Hsiang applies rewrite methods only as a refutational proof technique, trying to generate the equation TRUE=FALSE. We generalize these methods to satisfiable theories; in particular, we show that the concept of confluent rewriting system, which is the main tool for studying equational theories, can be extended to any quantifier-free first order theory. Furthermore, we show that rewrite methods can be used even if formulas are kept in clausal form.