Induction as Consequence Finding

This paper presents a general procedure for inverse entailment which constructs inductive hypotheses in inductive logic programming. Based on inverse entailment, not only unit clauses but also characteristic clauses are deduced from a background theory together with the negation of positive examples. Such clauses can be computed by a resolution method for consequence finding. Unlike previous work on inverse entailment, our proposed method called CF-induction is sound and complete for finding hypotheses from full clausal theories, and can be used for inducing not only definite clauses but also non-Horn clauses and integrity constraints. We also show that CF-induction can be used to compute abductive explanations, and then compare induction and abduction from the viewpoint of inverse entailment and consequence finding.