  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.
