Hybrid Probabilistic Logics: Theoretical Aspects, Algorithms and Experiments

Abstract

Steffen Michels Hybrid Probabilistic Logics: Theoretical Aspects, Algorithms and Experiments Probabilistic logics aim at combining the properties of logic, that is they provide a structured way of expressing knowledge and a mechanical way of reasoning about such knowledge, with the ability of probability theory to deal with uncertainty. Such probabilistic logics can serve as a basis to automate uncertainty reasoning, based on a structured and interpretable representation of knowledge. There is a wide spectrum of probabilistic logic languages, which differ in the fundamental balance between how expressive a language is and how hard it is to reason about knowledge expressed in the language. On the one hand, a language should be expressive enough to allow one to express all knowledge required to model a problem at hand. On the other hand, it should still be possible to draw useful conclusions in reasonable time. In this thesis we propose probabilistic logics with a unique balance between expressiveness and hardness of reasoning, which perfectly matches the requirements for many problem domains. On the expressivity side, we want to support hybrid models, i.e. combining discrete and continuous factors. On the reasoning side, we want to preserve soundness of reasoning, which means that conclusions drawn from knowledge agree with that knowledge. This may seem a basic requirement, but all common inference methods for hybrid models are either restricted to only a small class of such models, or provide only unsound reasoning, based on approximations that come without any guarantees. This thesis covers a wide range of results. We provide a theoretical basis for probabilistic logics with the properties outlined above, but we also propose efficient inference algorithms, which we evaluate theoretically and experimentally. We also design practical languages, suitable for knowledge representation, and show applicability using a challenging real-world problem.