Conditioning Accept-Desirability models in the context of AGM-like belief change

TL;DR

This paper introduces a new conditioning rule for Accept-Desirability models within an abstract framework that unifies classical and quantum probabilities, extending belief revision to imprecise probabilities.

Contribution

It proposes a novel conditioning rule and analyzes its properties, including compatibility with AGM belief revision axioms in a generalized probabilistic setting.

Findings

The new conditioning rule introduces indifferences after observing events.

AGM axioms hold in classical propositional logic case.

The framework unifies classical, quantum, and imprecise probabilities.

Abstract

We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract setting allows us to unify classical and quantum probabilities, and extend them to an imprecise probabilities context. We introduce a new conditioning rule for our Accept-Desirability models, based on the idea that observing an event introduces new indifferences between options. We associate a belief revision operator with our conditioning rule, and investigate which of the AGM axioms for belief revision still hold in our more general framework. We investigate two interesting special cases where all of these axioms are shown to still hold: classical propositional logic and full conditional probabilities.