Evidential confirmation as transformed probability

TL;DR: This work unifies two of the leading approaches to confirmation theory, by showing that a revised MYCIN Certainty Factor method is equivalent to a special case of Dempster-Shafer theory and substantially resolves the "taxe-them-or-leave-them" problem of priors.

Abstract: 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 transformed (Bayesian) probability, but also in terms of each other; which: • 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; • 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 the 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 aggregating "parallel" updates or changes in probability; and • in particular marries evidential confirmation to the strengths of Bayesian, arbitrary-conditional, probability: especially, if-then rules and forward and backward chaining.