Introducing abduction into (Extensional) inductive logic programming systems

We propose an approach for the integration of abduction and induction in Logic Programming. In particular, we show how it is possible to learn an abductive logic program starting from an abductive background knowledge and a set of examples. By integrating Inductive Logic Programming with Abductive Logic Programming we can learn in presence of incomplete knowledge. Incomplete knowledge is handled by designating some pieces of information as abducibles, that is, possible hypotheses which can be assumed, provided that they are consistent with the current knowledge base. We then specialize the framework for FOIL, an ILP system adopting extensional coverage. In particular, we propose an extension of the FOIL algorithm that is able to learn from incomplete data.