A Logic for Default Reasoning About Probabilities

TL;DR

This paper introduces a logic that unifies statistical probabilities and subjective beliefs within a single framework, using cross entropy minimization to ensure rational inference about probabilities.

Contribution

It presents a novel logical system that models both statistical and subjective probabilities in one space, with semantics justified by desirable properties and cross entropy minimization.

Findings

The logic effectively models the influence of statistical info on beliefs.

Semantics are well-founded and exhibit reasonable properties.

Cross entropy minimization is central to the logic's reasoning process.

Abstract

A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given are well suited to model the influence of statistical information on the formation of subjective beliefs. Cross entropy minimization is a key element in these semantics, the use of which is justified by showing that the resulting logic exhibits some very reasonable properties.