Induction of logic programs by example-guided unfolding

Abstract

Resolution has been used as a specialisation operator in several approaches to top-down induction of logic programs. This operator allows the overly general hypothesis to be used as a declarative bias that restricts not only what predicate symbols can be used in produced hypotheses, but also how the predicates can be invoked. The two main strategies for top-down induction of logic programs, Covering and Divide-and-Conquer, are formalised using resolution as a specialisation operator, resulting in two strategies for performing example-guided unfolding. These strategies are compared both theoretically and experimentally. It is shown that the computational cost grows quadratically in the size of the example set for Covering, while it grows linearly for Divide-and-Conquer. This is also demonstrated by experiments, in which the amount of work performed by Covering is up to 30 times the amount of work performed by Divide-and-Conquer. The theoretical analysis shows that the hypothesis space is larger for Covering, and thus more compact hypotheses may be found by this technique than by Divide-and-Conquer. However, it is shown that for each non-recursive hypothesis that can be produced by Covering, there is an equivalent hypothesis (w.r.t. the background predicates) that can be produced by Divide-and-Conquer. A major draw-back of Divide-and-Conquer, in contrast to Covering, is that it is not applicable to learning recursive definitions.