Probabilistic Horn abduction and Bayesian networks

David Poole

In Artificial Intelligence, Volume 64, Numbers 1, pages 81-129, 1993.


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.

You can get the pdf.

Related Papers

D. Poole, ``Logic Programming, Abduction and Probability: a top-down anytime algorithm for estimating prior and posterior probabilities'', New Generation Computing, 11(3-4), 377-400, 1993.

The code described there is available, along with the example programs described in the AI Journal paper.

Probabilistic Horn abduction has been developed further in the independent choice logic. See:

D. Poole, The Independent Choice Logic for modelling multiple agents under uncertainty.

D. Poole, Abducing Through Negation As Failure: Stable models in the Independent Choice Logic.

To put this work in perspective, you should see a description of my probabilistic research and ongoing research.

Last updated 6 Sept 98 - David Poole