This paper presents a simple framework for Horn-clause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete 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 adequacy. It also shows how Bayesian networks can be extended beyond a propositional language. This paper also shows how a language with only (unconditionally) independent hypotheses can represent any probabilistic knowledge, and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language.
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