Polynomial Time Inference of Unions of Tree Pattern Languages

IEICE Transactions on Information and Systems E75-D, 426-434, 1992; Proc. 2nd International Workshop on Nonmonotonic and Inductive Logic 1991, Lecture Notes in Artificial Intelligence 659), 118-131, 1993.In this paper we consider the polynomial time inferability from positive data for unions of two tree pattern languages. A tree pattern is a structured pattern known as a term in logic programming and term rewriting systems, and a tree pattern language is the set of all ground instances of a tree pattern. We present a polynomial time algorithm to find a minimal union of two tree pattern languages containing given examples. Our algorithm can be considered as a natural extension of Plotkin\u27s least generalization algorithm, which finds a minimal single tree pattern language. By using this algorithm we can realize a polynomial time inference machine for unions of two tree pattern languages from positive data