We present the system LAP (Learning Abductive Programs) that is able to learn abductive logic programs from examples and from a background abductive theory. A new type of induction problem has been dened as an extension of the Inductive Logic Programming framework. In the new problem denition, both the background and the target the- ories are abductive logic programs and abductive derivability is used as the coverage relation. LAP is based on the basic top-down ILP algorithm that has been suit- ably extended. In particular, coverage of examples is tested by using the abductive proof procedure dened by Kakas and Mancarella [24]. As- sumptions can be made in order to cover positive examples and to avoid the coverage of negative one...