Nonground Abductive Logic Programming with Probabilistic Integrity Constraints
This work addresses the need for more expressive probabilistic logical models in AI, though it appears incremental as it builds on existing ALP frameworks.
The paper tackles the problem of handling uncertain information and hypothetical reasoning by extending Abductive Logic Programming (ALP) to include probabilistic integrity constraints with variables, and presents a sound and complete proof procedure for this enriched language.
Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints `a la IFF, possibly annotated with a probability value. We first present the overall abductive language, and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.