Reasoning with belief functions: An analysis of compatibility

Abstract

This paper examines the applicability of belief funstions methodology in three reasoning tasks: (1) representation of incomplete knowledge, (2) belief updating, and (3) evidence pooling. We find that belief functions have difficulties representing incomplete knowledge, primarily knowledge expressed in conditional sentences. In this context, we also show that the prevailing practices of encoding if-then rules as belief function expressions are inadequate, as they lead to counterintuitive conclusions under chaining, contraposition, and reasoning by cases. Next, we examine the role of belief functions in updating states of belief and find that, if partial knowledge is encoded and updated by belief function methods, the updating process violates basic patterns of plausibility and the resulting beliefs cannot serve as a basis for rational decisions. Finally, assessing their role in evidence pooling, we find that belief functions offer a rich language for describing the evidence gathered, highly compatible with the way people summarize observations. However, the methods available for integrating evidence into a coherent state of belief capable of supporting plausible decisions cannot make use of this richness and are challenged by simpler methods based on likelihood functions.