Summary of A New Normative Theory of Probabilistic Logic
This work addresses foundational issues in probabilistic logic for researchers in logic and probability theory, but it appears incremental as it builds on existing axiomatic frameworks.
The paper tackles the problem of developing a normative theory of probabilistic logic by presenting a new axiomatization that avoids finite additivity while retaining useful inference rules, and it provides sharper answers to questions about the range sets of probability functions, including conditions for isomorphism to real numbers in [0,1].
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?