Nonground Abductive Logic Programming with Probabilistic Integrity Constraints

TL;DR

This paper extends abductive logic programming to incorporate probabilistic integrity constraints with variables, providing a formal semantics and a sound, complete proof procedure for uncertain reasoning.

Contribution

It introduces a probabilistic abduction framework with integrity constraints and variables, along with a sound and complete proof procedure based on Distribution Semantics.

Findings

Defined a probabilistic abductive language with integrity constraints

Proved the soundness and completeness of the extended proof procedure

Established a formal semantics for probabilistic abduction with variables

Abstract

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.