Linear resolution for consequence finding

Abstract

In this paper, we re-evaluate the consequence finding problem within first-order logic. Firstly, consequence finding is generalized to the problem in which only interesting clauses having a certain property (called characteristic clauses) should be found. The use of characteristic clauses enables characterization of various reasoning problems of interest to AI, including abduction, nonmonotonic reasoning, prime implicates and truth maintenance systems. Secondly, an extension of the Model Elimination theorem proving procedure (SOL-resolution) is presented, providing an effective mechanism complete for finding the characteristic clauses. An important feature of SOL-resolution is that it constructs such a subset of consequences directly without testing each generated clause for the required property. We also discuss efficient but incomplete variations of SOL-resolution and their properties, which address finding the most specific and the least specific abductive explanations.