An Inference Rule for Hypothesis Generation

Abstract

There are many new application fields for automated deduction where we have to apply abductive reasoning. In these applications we have to generate consequences of a given theory having some appropriate properties. In particular we consider the case where we have to generate the clauses containing instances of a given literal L. The negation of the other literals in such clauses are hypothesis allowing to derive L. In this paper we present an inference rule, called L-inference, which was designed in order to derive those clauses, and a L-strategy. The L-inference rule is a sort of Input Hyperresolution. The main result of the paper is the proof of the soundness and completeness of the L-inference rule. The L-strategy associated to the L-inference rule, is a saturation by level with deletion of the tautologies and of the subsumed clauses. We show that the L-strategy is also complete. 1