Representing Bayesian Networks within Probabilistic Horn Abduction

TL;DR

This paper introduces a framework that unifies Bayesian networks and Horn clause abduction, enabling probabilistic reasoning with logical structures and potential extensions beyond propositional logic.

Contribution

It establishes a relationship between Bayesian networks and Horn clause abduction, providing a new foundation for probabilistic logical reasoning and approximate inference.

Findings

Can represent any probabilistic knowledge in Bayesian networks

Provides a basis for approximate posterior probability computation

Suggests extensions of Bayesian networks beyond propositional logic

Abstract

This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language.