Completion and Equational Theorem Proving using Taxonomic Constraints
Jörg Denzinger · 1995
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. 1 Introduction The problem we are interested in is equational theorem proving (although taxonomic constraints can also be used by other theorem proving approaches that are based on the generation of facts): Given a set E of equations and a goal s = t, we want to prove s =E t. Methods based on the Knuth-Bendix completion (see [KB70]) have t...