. We present an hybrid extensional-intensional Inductive Logic Programming algorithm. We then show how this algorithm solves the problem of global inconsistency of intensional systems when learning multiple predicates, without incurring in the problems of incompleteness and inconsistency of extensional systems. The algorithm is obtained by modifying an intensional system  for learning abductive logic programs. Extensionality is thus obtained by exploiting abduction: the training set is considered as a set of abduced literals that is taken as input by the abductive proof procedure used for the coverage of examples. 1 Introduction Logic programs are rarely constituted by a single predicate. However, most Inductive Logic Programming (ILP) systems have been designed for learning single predicates. If we synthesize multiple predicates programs by applying single predicate learners, we find two problems . The first is that adding a clause to a partial hypothesis can make pre..