Meta-Interpretive Learning (MIL) is a recent Inductive Logic Programming technique aimed at supporting learning of recursive definitions. A powerful and novel aspect of MIL is that when learning a predicate definition it automatically introduces sub-definitions, allowing decomposition into a hierarchy of reuseable parts. MIL is based on an adapted version of a Prolog meta-interpreter. Normally such a meta-interpreter derives a proof by repeatedly fetching first-order Prolog clauses whose heads unify with a given goal. By contrast, a meta-interpretive learner additionally fetches higher-order meta-rules whose heads unify with the goal, and saves the resulting meta-substitutions to form a program. This talk will overview theoretical and implementational advances in this new area including the ability to learn Turing computabale functions within a constrained subset of logic programs, the use of probabilistic representations within Bayesian meta-interpretive and techniques for minimising the number of meta-rules employed. The talk will also summarise applications of MIL including the learning of regular and context-free grammars, learning from visual representions with repeated patterns, learning string transformations for spreadsheet applications, learning and optimising recursive robot strategies and learning tactics for proving correctness of programs. The talk will conclude by pointing to the many challenges which remain to be addressed within this new area.

It has been twenty years since the distribution semantics was proposed for probabilistic logic programming (PLP). Since then a plethora of PLP languages with the distribution semantics were developed including PRISM,ICL,LPADs,ProbLog,P-log,CP-logic and PITA to name a few. In this talk I first review Fenstat's representation theorem which mathematically relates probability to first-order logic. One of its consequences is that if one wishes to consistently assign probabilities to first-order formulas, the assignment should be based on "the possible worlds with a probability distribution." There is more than one way of defining such worlds however. The distribution semantics is one way of doing it. The semantics starts with a simple computable distribution and transforms it to a complex one with the help of the least model semantics in logic programming. I then overview a brief history of PRISM, the first implementation of the distribution semantics with the ability of parameter learning for probabilistic modeling. It is a probabilistic Prolog enhanced with a rich array of built-in predicates for probability computation, parameter learning, Bayesian inference and so on. The true power of PLP languages such as PRISM comes out when they deal with recursively defined infinite models. Consider Markov chains that contain infinitely many transitions or probabilistic context free grammars (PCFGs) that contain infinitely many sentence derivations. These models sometimes require to compute an infinite sum of probabilities. The latest development of PRISM enables us to compute this infinite sum of probabilities using cyclic propositional formulas and also makes the EM algorithm available implemented on top of this computation mechanism. I show an example of such infinite computation in cyclic relational modeling applied to plan recognition from partial observations.

Probabilistic logic programs combine the power of a programming language with a possible world semantics; they are typically based on Sato's distribution semantics [8] and they have been studied for over twenty years now. In this talk, I shall report on recent progress in applying this paradigm to challenging applications. The first application domain will be that of robotics, where we have developed extensions of the basic distribution semantics to cope with dynamics as well continuous distributions [2]. The resulting representations are now being used to learn multi-relational object affordances, which specify the conditions under which actions can be applied on particular objects [3,4]. The second application is in a biological domain, where a decision theoretic extension of the distribution semantics [1] is the underlying inference engine of the PheNetic system [5,6], which extracts from an interactome, the sub-network that best explains genes prioritized through a molecular profiling experiment. Finally, I shall report on our results in applying ProbFOIL [7] to the problem of machine reading in CMU's Never Ending Language Learning system. ProbFOIL is an extension of the traditional rule-learning system FOIL for use with the distribution semantics.

[1] G. Van den Broeck, I. Thon, M. van Otterlo, L. De Raedt. DTProbLog: A decision-theoretic probabilistic Prolog. Proceedings of the AAAI Conference on Artificial Intelligence. AAAI 2010.
[2] B. Gutmann, I. Thon, A. Kimmig, M. Bruynooghe, and L. De Raedt. The magic of logical inference in probabilistic programming. Theory and Practice of Logic Programming, 2011(11), pages 663-680.
[3] Nitti, D., De Laet, T., De Raedt, L. (2013). A particle filter for hybrid relational domains. in Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS 2013 (pp. 2764-2771).
[4] Moldovan, B., Moreno, P., van Otterlo, M., Santos-Victor, J., De Raedt, L. (2012). Learning relational affordance models for robots in multi-object manipulation tasks. In Proc. IEEE International Conference on Robotics and Automation, ICRA 2012. 2012 (pp. 4373 -4378).
[5] De Maeyer D, Weytjens B, Renkens J, De Raedt L, Marchal K. PheNetic: network-based interpretation of molecular profiling data. Nucleic Acids Res. 2015.
[6] De Maeyer D, Renkens J, Cloots L, De Raedt L, Marchal K. PheNetic: network-based interpretation of unstructured gene lists in E. coli. Mol Biosyst. 2013 Jul;9(7):1594-603.
[7] De Raedt, L. Dries, A., Thon, I., Van den Broeck, G., Verbeke, M. Inducing Probabilistic Relational Rules from Probabilistic Examples, In Proc. International Joint Conference on AI, IJCAI 2015, in press.
[8] Sato, T., A Statistical Learning Method for Logic Programs with Distribution Semantics, In Proc. 12th International Conference on Logic Programming, ICLP 1995, pp. 715--729.