A Logic for Reasoning about Upper Probabilities

TL;DR

This paper introduces a propositional logic framework for reasoning about uncertainty using sets of probability measures, providing a complete axiomatization and analyzing computational complexity.

Contribution

It presents a novel logic for upper probabilities with a sound, complete axiomatization and establishes NP-completeness of the satisfiability problem.

Findings

Logic effectively models uncertainty with probability intervals

Axiomatization is sound and complete

Satisfiability is NP-complete, matching propositional logic complexity

Abstract

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.