Evidential Confirmation as Transformed Probability

A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several researchers have gone so far as to invent new formalisms and methods. We show how to represent two major such alternative approaches to evidential confirmation not only in terms of transformed (Bayesian) probability, but also in terms of each other. This unifies two of the leading approaches to confirmation theory, by showing that a revised MYCIN Certainty Factor method [12] is equivalent to a special case of Dempster-Shafer theory. It yields a well-understood axiomatic basis, i.e. conditional independence, to interpret previous work on quantitative confirmation theory. It substantially resolves the "taxe-them-or-leave-them" problem of priors: MYCIN had to leave them out, while PROSPECTOR had to have them in. It recasts some of confirmation theory's advantages in terms of the psychological accessibility of probabilistic information in different (transformed) formats. Finally, it helps to unify the representation of uncertain reasoning (see also [11]).