  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 10,1/ with the usual arithmetical operations?
