Cooperation of abduction and induction in logic programming

We propose an integration of abduction and induction where the two inference processes cooperate in order to perform more powerful inferences. We assume the definitions of abduction and induction as given in Abductive Logic Programming and Inductive Logic Programming. Abduction helps induction by generating atomic hypotheses that can be used as new examples or for completing an incomplete background knowledge. Induction helps abduction by generalizing explanations. We present a learning algorithm that integrates abduction and induction. The algorithm solves a new learning problem where both the background and the target theory are abductive theories and abductive derivability is used as the example coverage relation. We then show how the algorithm can be applied to learning from incomplete knowledge and learning exceptions