Certainty-factor-like structures in Bayesian belief networks

The certainty-factor model was one of the most popular models for the representation and manipulation of uncertain knowledge in the early rule-based expert systems of the 1980s. After the model was criticised by researchers in artificial intelligence and statistics as being ad-hoc in nature, researchers and developers have stopped looking at the model. Nowadays, it is often stated that the model is merely interesting from a historical point of view. Its place has been taken over by more expressive formalisms for the representation and manipulation of uncertain knowledge, in particular, by the formalism of Bayesian belief networks. In this paper, it is shown that this view underestimates the importance of the principles underlying the certainty-factor model. In particular, it is shown that certainty-factor-like structures occur frequently in practical Bayesian network models as causal independence assumptions. In fact, the noisy-OR and noisy-AND models, two probabilistic models frequently employed, appear to be reinventions of combination functions previously introduced as part of the certainty-factor model. This insight may lead to a reappraisal of the certainty-factor model.