Learning logic programs with negation as failure

Normal logic programs are usually shorter and easier to write and understand than definite logic programs. As a consequence, it is worth investigating their learnability, if Inductive Logic Program- ming is to be proposed as an alternative tool for software development and Software Engineering at large. In this paper we present an exten- sion of the ILP system TRACY, called TRACY-not, able to learn normal logic programs. The method is proved to be sound, in the sense that it outputs a program which is complete and consistent w.r.t.the ex- amples, and complete, in the sense that it does find a solution when it exists. Compared to learning systems based on extensionality,TRACY and TRACY not are less dependent on the kind and number of training examples, which is due to the intensional evaluation of the hypothe- ses and, for TRACY-not, to the possibility to have restricted hypothesis spaces through the use of negation.