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An Abductive-Inductive Algorithm for Probabilistic Inductive Logic Programming

The integration of abduction and induction has lead to a variety of non-monotonic ILP systems. XHAIL is one of these systems, in which abduction is used to compute hypotheses that subsume Kernel Sets. On the other hand, Peircebayes is a recently proposed logic-based probabilistic programming approach that combines abduction with parameter learning to learn distributions of most likely explanations. In this paper, we propose an approach for integrating probabilistic inference with ILP. The basic idea is to redefine the inductive task of XHAIL as a statistical abduction, and to use Peircebayes to learn probability distribution of hypotheses. An initial evaluation of the proposed algorithm is given using synthetic data.