In this paper we investigate the learnability of relations in Inductive Logic Programming, by using equality theories as background knowledge. We assume that a hypothesis and an observation are respectively a definite program and a set of ground literals. The targets of our learning algorithm are relations. By using equality theories as background knowledge we introduce tree structure into definite programs. The structure enable us to narrow the search space of hypothesis. We give pairs of a hypothesis language and a knowledge language in order to discuss the learnability of relations from the view point of inductive inference and PAC learning.