Completion and Equational Theorem Proving using Taxonomic Constraints

Abstract

We present an approach to prove several theorems in slightly different axiom systems simultaneously. We represent the different problems as a taxonomy, i.e. a tree in which each node inherits all knowledge of its predecessors, and solve the problems using inference steps on rules and equations with simple constraints, i.e. words identifying nodes in the taxonomy. We demonstrate that a substantial gain can be achieved by using taxonomic constraints, not only by avoiding the repetition of inference steps in the different problems but also by achieving run times that are much shorter than the accumulated run times when proving each problem separately.