Summary of A New Normative Theory of Probabilistic Logic

Abstract By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity axiom, yet which retains many useful inference rules. Many of the examples of this theory—its models—do not use numerical probabilities. Put another way, this article gives sharper answers to the two questions — 1. What kinds of sets can used as the range of a probability function? 2. Under what conditions is the range set of a probability function isomorphic to the set of real numbers in the interval [0,1] with the usual arithmetical operations?