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. Some of these have become widely used and theoretically explored [ 17, 15). We show how to represent two major approaches to evidential confirmation not only in terms of transform£Jd (Bayesian) probability, but also in terms of each other; which: • unifies two of the leading approaches to confirmation theory, by showing that a revfsed MYCIN Certainty Factor method [12] is equivalent to a special case of Dempster-Shaler theory; • gives us a well-understood axiomatic basis, i.e. conditional independence, to interpret previous work on quantitative confirmation theory; in particular, • provides a new axiomatic analysis and interpretation of Dempster's Rule for an important special case; • which gives a firmer epistemological basis for acquiring, and for using in decisions, Dempster-Shafer belief functions aggregated via Dempster's Rule; • substantially resolves the "take-them-or-leave-them" problem of priors: MYCIN had to leave them out, while PROSPECTOR had to have them in; • recasts some of confirmation theory's advantages in terms of the psychological accessibility of probabilistic information in different (transformed) formats; • helps to unify ttw representation of plausible/ inexact/ uncertain reasoning (see also [11]); • clarifies the place of evidential confirmation in a general scheme for probabilistic reasoning: as concerned with nggrcgating "pnrallcl" updates or c�angcs in probability; and • in particular marries evidential confirmation to the strengths of Bayesian, arbitrary-conditional, probability: especially, if-then rules and forward and bac�;ward chaining.