The application of goal-oriented heuristics for proving equational theorems via the unfailing Knuth-Bendix completion procedure. : A case study: lattice ordered groups

Abstract

In this report we present a case study of employing goal-oriented heuristics when proving equational theorems with the (unfailing) Knuth-Bendix completion procedure. The theorems are taken from the domain of lattice ordered groups. It will be demonstrated that goal-oriented (heuristic) criteria for selecting the next critical pair can in many cases significantly reduce the search effort and hence increase performance of the proving system considerably. The heuristic, goal-oriented criteria are on the one hand based on so-called “measures” measuring occurrences and nesting of function symbols, and on the other hand based on matching subterms. We also deal with the property of goal-oriented heuristics to be particularly helpful in certain stages of a proof. This fact can be addressed by using them in a framework for distributed (equational) theorem proving, namely the “teamwork-method”.