Inductive Learning of Logic Programs From Positive Facts Using Minimal Multiple Generalization

Abstract

We consider the polynomial time inferability of primitive Prologs from positive facts. The class of primitive Prologs is a proper subclass of that of linear Prologs which is known to be inferable from only positive facts. In this paper, we discuss the polynomial time inferability of the subclass using minimal multiple generalizations. The minimal multiple generalization is a natural extension of the least generalization given by Plotkin in 1970. The minimal multiple generalization generalizes given first order words by several words, while the least generalization does by a single word. The property of the minimal multiple generalization makes it possible to perform fine generalization and to construct the heads of several clauses in a target program at the same time. We give an outline of a consistent polynomial time inference algorithm which identifies the class of primitive Prologs in the limit. The algorithm infers the heads of clauses in a target program as a minimal multiple generalization of a set of given positive facts. Furthermore, we give a similar result on the inferability of a subclass of context-free transformations which includes several well-known Prolog programs.