Kernels on prolog proof trees: Statistical learning in the ILP setting

We develop kernels for measuring the similarity between relational instances using background knowledge expressed in first-order logic. The method allows us to bridge the gap between traditional inductive logic programming representations and statistical approaches to supervised learning. Logic programs will be used to generate proofs of given visitor programs which exploit the available background knowledge, while kernel machines will be employed to learn from such proofs. We report positive empirical results on Bongard-like and M-of-N problems that are difficult or impossible to solve with traditional ILP techniques, as well as on a real data set.