Predicate invention and utilization

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Abstract
Inductive logic programming (ILP) involves the synthesis of logic programs from examples. In terms of scientific theory formation ILP systems define observational predicates in terms of a set of theoretical predicates. However, certain basic theorems indicate that with an inadequate theoretical vocabulary this is not always possible. Predicate invention is the augmentation of a given theoretical vocabulary to allow finite axiomatization of the observational predicates. New theoretical predicates need to be chosen from a well-defined universe of such predicates. In this paper a partial order of utilization is described over such a universe. This ordering is a special case of a logical translation. The notion of utilization allows the definition of an equivalence relationship over new predicates. In a manner analogous to Plotkin, clause refinement is defined relative to given background knowledge and a universe of new predicates. It is shown that relative least clause refinement is defined and unique whenever there exists a relative least general generalization of a set of clauses. Results of a preliminary implementation of this approach are given.

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