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Inductive Logic Programming (ILP) is a machine learning technique that relies on logic programs as a representation language. Most of the effort in the field of ILP has concentrated on a restricted class of problems, providing solutions that do not fully support negation. On the other hand, integration of negation and nonmonotonic reasoning in logic programming is common and important for a number of problems. This thesis presents an approach to nonmonotonic ILP that is based on a transformation of the original problem to a problem that can be solved by employing abductive reasoning. In particular we present a general framework for the transformation that can be used as reference for concrete implementations. We instantiate the transformation to derive two alternative implementations that are rooted in the two dominant computational logic paradigms: Prolog and Answer Set Programming (ASP). In the first case, we derive an implementation, called TAL, that is based on the abductive proof procedure SLDNFA and uses a customisable best-first search on the space of abductive solutions. In the second case the transformation is further refined in order to exploit the computational properties of available ASP solvers. In the proposed system called ASPAL, a theory is constructed from a set of mode declarations and used to extend the search of the underlying solver, so enabling the derivation of inductive hypotheses. We provide completeness and soundness results for the framework and the ILP systems presented and show how, as a consequence of this, it is possible to induce complex multi-predicate hypotheses involving negation, recursion and the definition of elements of the domain that are not directly observed. We validate the framework on established ILP benchmark problems, on some nonmonotonic ILP problems proposed in the literature. Furthermore we demonstrate the approach on a novel application of nonmonotonic ILP to the revision of normative frameworks. |
