Integrating induction and abduction in logic programming

We propose an approach for the integration of abduction and induction in Logic Programming. We define an Abductive Learning Problem as an extended Inductive Logic Programming problem where both the background and target theories are abductive theories and where abductive derivability is used as the coverage relation instead of deductive derivability. The two main benefits of this integration are the possibility of learning in presence of incomplete knowledge and the increased expressive power of the background and target theories. We present the system LAP (Learning Abductive Programs) that is able to solve this extended learning problem and we describe, by means of examples, four different learning tasks that can be performed by the system: learning from incomplete knowledge, learning rules with exceptions, learning from integrity constraints and learning recursive predicates.