Proof Plans for the Correction of False Conjectures

Abstract

Theorem proving is the systematic derivation of a mathcmaticM proof from a set of axioms by the use of rules of inference. We ~re interested in a related but far less explored problem: the analysis and correction of false conjectures, especiMly where that correction involves finding a collection of antecedents that, together with a set of axioms, transform non-theorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenoraenom Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct non-theorems.