A logic for reasoning about upper probabilities

TL;DR

This paper introduces a propositional logic for reasoning about uncertainty represented by sets of probability measures, providing a sound, complete axiomatization and analyzing its computational complexity.

Contribution

It presents a novel logic for upper probabilities, with a complete axiomatization and NP-complete satisfiability, advancing formal reasoning about probabilistic uncertainty.

Findings

Logic is sound and complete for reasoning about upper probabilities

Satisfiability problem is NP-complete, matching propositional logic complexity

Enables formal reasoning about uncertainty modeled by sets of probability measures

Abstract

We present a propositional logic %which can be used 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.