A general framework for comparing numerical uncertainty theories

Deciding which of the existing uncertainty theories is the appropriate one to use in the formalization of a given problem is still a difficult task. It is possible to compare these theories either using pragmatic considerations (e.g. efficiency) or experimentally applying them on a set of problems; however, up to now there is no general frame in which we can compare the uncertainty theories with respect to their meanings. Our work aims to develop a general formalism for representing and reasoning with uncertain knowledge, which provides such a framework and is not restricted in using one specific uncertainty theory as a basis. This formalism is based on the work of Carnap's logical foundation of probability. But, instead of propositions, we regard distinctions as elementary notions. Up until now, the following theories can be expressed within the framework: Bayes theory, fuzzy set theory, Dempster/Shafer theory (belief functions) and upper/lower probability theory.