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Although informal models of evidential reasoning have been successfully applied in automated reasoning systems, it is generally difficult to define the range of their applicability. In addition, they have not provided a basis for consistent management of evidence bearing on hypotheses that are related hierarchically. The Dempster-Shafer (D-S) theory of evidence is appealing because it does suggest a coherent approach for dealing with such relationships. However, the theory's complexity and potential for computational inefficiency have tended to discourage its use in reasoning systems. In this paper we describe the central elements of the D-S theory, basing our exposition on simple examples drawn from the field of medicine. We then demonstrate the relevance of the D-S theory to a familiar expert-system domain, namely the bacterial-organism identification problem that lies at the heart of the mycin system. Finally …