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By David Nunan, Roger Berry, Vivien Berry

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G. g. where Thus, and the normal is a state of aprobabilistic covers relation takes as arguments an example a hypothesis H and possibly the background theory B. It then returns a probability value between 0 and 1. So, the likelihood of the example The task of probabilistic inductive logic programming is then to find the hypothesis that maximizes the likelihood of the data where E denotes the set of examples. d. assumption this results in the maximization of The key contribution of this paper is that we present three probabilistic inductive logic programming settings that extend the traditional ones sketched above.

A Statistical Learning Method for Logic Programs with Distribution Semantics. In L. Sterling, editor, Proceedings of the Twelfth International Conference on Logic Programming (ICLP-1995), pages 715 – 729, Tokyo, Japan, 1995. MIT Press. 36 L. De Raedt and K. Kersting [43] E. Shapiro. Algorithmic Program Debugging. MIT Press, 1983. [44] A. Srinivasan. The Aleph Manual. uk/oucl/~research/areas/machlearn/Aleph/. [45] A. Srinivasan, S. Muggleton, R. King, and M. Sternberg. Theories for mutagenicity: A study of first-order and feature based induction.

In case that only propositional clauses are considered, SCOOBY coincides with greedy hill-climbing approaches for learning Bayesian networks [16]. 5 Learning from Probabilistic Proofs Given a training set E containing ground proofs as examples, one possible approach combines ideas from the early inductive logic programming system GOLEM [34] that employs Plotkin’s [39] least general generalization (LGG) with bottom-up generalization of grammars and hidden Markov models [46]. The resulting algorithm employs the likelihood of the proofs as the scoring function.

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