An Efficient Subsumption Algorithm for Inductive Logic Programming

In this paper we investigate the efficiency of – subsumption (` ), the basic provability relation in ILP. As D ` C is NP–complete even if we restrict ourselves to linked Horn clauses and fix C to contain only a small constant number of literals, we investigate in several restrictions of D. We first adapt the notion of determinate clauses used in ILP and show that –subsumption is decidable in polynomial time if D is determinate with respect to C. Secondly, we adapt the notion of k–local Horn clauses and show that – subsumption is efficiently computable for some reasonably small k. We then show how these results can be combined, to give an efficient reasoning procedure for determinate k–local Horn clauses, an ILP–problem recently suggested to be polynomial predictable by Cohen (1993) by a simple counting argument. We finally outline how the –reduction algorithm, an essential part of every lgg ILP–learning algorithm, can be improved by these ideas.