This paper presents a simple logical framework for abduction, with probabilities associated with hypotheses. The language is an extension to pure Prolog, and it has straight-forward implementations using branch and bound search with either logic-programming technology or ATMS technology. The main focus of this paper is arguing for a form of representational adequacy of this very simple system for diagnostic reasoning. It is shown how it can represent model-based knowledge, with and without faults, and with and without non-intermittency assumptions. It is also shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. 1

This paper presents a simple framework for Hornclause 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. 1