Probabilistic Horn abduction and Bayesian networks

This paper presents a simple framework for Horn-clause abduction, with probabilities associated with hypotheses. The framework incorporates some assumptions about the rule base and some independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a descrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequancy. It also shows how Bayesian networks can be extended beyond a propositional language, and shows a relationship between probability and argument based systems.