Inductive logic programming: From logic of discovery to machine learning

Inductive Logic Programming (ILP) is a study of machine learning systems that use clausal theories in first-order logic as a representation language. In this paper, we survey theoretical foundations of ILP from the viewpoints of Logic of Discovery and Machine Learning, and try to unify these two views with the support of the modern theory of Logic Programming. Firstly, we define several hypothesis construction methods in ILP and give their proof-theoretic foundations by treating then as a procedure which complete incomplete proofs. Next, we discuss the design of individual learning algorithms using these hypothesis construction methods. We review known results on learning logic programs in computational learning theory, and show that these algorithms are instances of a generic learning strategy with proof completion methods.