Hybrid Probabilistic Logic Programming

An important issue in artificial intelligence and many other fields is modeling the domain of interest. Given a model it is possible to perform inference to answer questions of interest, or make decisions to maximize a given utility. An active research topic concerns declarative languages for modeling and learning a wide range of applications. In particular, probabilistic logic programming combines first-order-logic with probability theory to model uncertainty. However, the majority of such languages do not support continuous random variables, or their support for continuous variables is limited. In this thesis we address this issue extending probabilistic logic programming techniques to deal with hybrid relational domains, involving both discrete and continuous random variables. We first propose a new inference algorithm for the language of Distributional Clauses, that supports zero-probability evidence, including algebraic constraints for which most frameworks fail. Secondly, we extend the algorithm for filtering in temporal domains. Finally, we propose a planner to solve Markov Decision Processes described with Distributional Clauses. The proposed algorithms are tested in several synthetic and real-world problems showing that they are competitive with respect to the state of the art. In particular, we showed how the framework can be used to exploit relational and continuous information jointly to improve state estimation in robotics and vision applications.status: publishe