A Useful Algebraic Property of Robinson's Unification Algorithm

Abstract

This memo presupposes some acquaintance with "A Machine Oriented Logic Based on the Resolution Principle", J.A. Robinson, JACM Jan65. The reader unfamiliar with this paper should be able to get a general idea of the theorem if he knows that OA is a post operator indicating a minimal set of substitutions (most general substitution) necessary to transform all elements of the set of formulae, A, into the same element (to "unify" A), so that when OA exists AOA is a set with one element (a "unit"). Example: A={f(x),y f(g(u)), f(g(z))} UA= {g(u)/x, f(g(u))/y, u/z} AOA= {f(g(u))} Another most general unifier of A is {g(z)/x, f(g(z))/y, z/u}.