Belief updating

Uncertainty is present in most tasks that require intelligent behaviour. Probability theory has by far the longest tradition in problems connected with uncertainty, but the Dempster-Shafer theory provides more general model. A central problem of this theory is conditioning. M. Spies´s paper (1994) presents a new approach to a solution of this problem, by establishing a link between conditional events and discrete random sets. Conditional events were introduced as sets of equivalent events under conditioning. These sets are targets of a multivalued mapping and conditional belief functions were introduced. We study properties of these functions in the cases that belief functions were obtained by Bayesian conditioning from an unconditional belief function