  We present an algorithm, called Predict, for updating beliefs in causal
networks quantified with order-of-magnitude probabilities. The algorithm takes
advantage of both the structure and the quantification of the network and
presents a polynomial asymptotic complexity. Predict exhibits a conservative
behavior in that it is always sound but not always complete. We provide
sufficient conditions for completeness and present algorithms for testing these
conditions and for computing a complete set of plausible values. We propose
Predict as an efficient method to estimate probabilistic values and illustrate
its use in conjunction with two known algorithms for probabilistic inference.
Finally, we describe an application of Predict to plan evaluation, present
experimental results, and discuss issues regarding its use with conditional
logics of belief, and in the characterization of irrelevance.
