Probabilistic Logic Programming with Well-Founded Negation

Knowledge representation and inference in AI have been traditionally divided between logic-based and statistical approaches. During the past decade, the rapidly developing area of Statistical Relational Learning aims to combine the two frameworks for representation and inference. In many cases, these works include probabilistic reasoning within Logic Programming frameworks. These attempts are restricted in the sense that they use only two-valued negation-as-failure semantics. However, well-founded semantics is a widely accepted three-valued-logic negation semantics scheme, which is implemented in certain Logic Programming frameworks. In this paper we introduce probabilistic inference under the well-founded semantics scheme in a single Probabilistic Logic Programming framework, where the uncertainty can be described using both statistical information (probabilities) and a third logic value.