This paper studies equivalence issues in inductive logic programming. A background theory
B 1 is inductively equivalent to another background theory B 2 if B 1 and B 2 induce the
same hypotheses for any given set of examples. Inductive equivalence is useful to compare
inductive capabilities among agents having different background theories. Moreover, it
provides conditions for optimizing background theories through appropriate program
transformations. In this paper, we consider three different classes of background theories …