A Generalization of the Least General Generalization HirokiArimura,

In this chapter, we present a polynomial time algorithm, called a k-minimal multiple generalization (k-mmg) algorithm, where k 1, and its application to inductive learning problems. The algorithm is a natural extension of the least general generalization algorithm developed by Plotkin and Reynolds. Given a nite set of ground rst-order terms, the k-mmg algorithm generalizes the examples by at most k rst-order terms, while Plotkin's algorithm does by a single rst-order term. We apply the k-mmg algorithm to several learning problems in inductive logic programming, and knowledge discovery in databases.