Summary of A New Normative Theory of Probabilistic Logic

TL;DR

This paper introduces a new axiomatization of probabilistic logic that avoids finite additivity, broadening the understanding of belief models beyond numerical probabilities and clarifying the structure of probability ranges.

Contribution

It presents a novel axiomatization of probabilistic logic that does not rely on finite additivity, expanding the types of models and probability ranges considered.

Findings

Models do not require numerical probabilities.

Provides conditions for the range set of probability functions.

Clarifies when the range set is isomorphic to real numbers.

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 10,1/ with the usual arithmetical operations?