Learning of Logic Programs with Non-determinate, Non-discriminating Literals

Abstract

Recently there has been an increasing interest in learning systems which induce first-order logic programs from examples. However, due to the intractability of the hypothesis space, such systems which use exhaustive search, e.g., MIS, are unable to learn reasonably complex programs. Previous solutions have been proposed to overcome this difficulty : while some systems restrict their hypothesis space, others use heuristics or additional knowledge such as analogical structures or abstraction. However, existing systems still have limitations. GOLEM gives up completeness by restricting the hypothesis space to only determinate clauses. A determinate clause is a clause composed of only determinate literals. A literal is determinate if each new variable in it has only one binding. Even the commonly used generate-and-test programs generate candidate solutions for their test routine, and thus are non-determinate. FOIL avoids exhaustive search by using Gain heuristic to select a literal that greedily discriminates positive examples from negative examples. Although it is able to learn some classes of problems efficiently, the heuristic fails to capture other aspects of usefulness of a literal, i.e., it overlooks a useful literal which produces no discrimination. For instance, a literalpartition (Head, Tail, List 1, List 2) in the quick-sort program does not discriminate between positive and negative examples. We propose a new heuristic-based approach to the learning of Horn-clause logic program with list structure. Our system, CHAM, learns a class of complex programs not learned by previous systems, i.e., non-determinate programs out of the learning space of GOLEM, and programs with non-discriminating literals which pose difficulties for FOIL. Experiments on learning Prolog programs with list structure have shown that while being able to learn a large class of programs, CHAM preserves efficiency in various test problems.