Propagating Belief Functions with Local Computations

In this article, we describe a way to propagate belief functions in certain kinds of trees using only local com-putations. This scheme generalizes the computational scheme proposed by Shafer and Logan for diagnostic trees of the type studied by Gordon and Shortliffe2,3 and the slightly more general scheme proposed by Shafer4 for hierar-chical evidence. It also generalizes the computational scheme proposed by Pearl5 for Bayesian causal trees. Pearls causal trees and Gordon and Shortliffes diagnostic trees are both ways of breaking down the evidence that bears on a large problem into smaller items of evidence that bear on smaDler parts of the problem so that these smaller problems can be dealt with one at a time. This localization of effort is often essential to make the process of probability judgment feasible, both for the person who is making probability judg-