Conditioning Accept-Desirability models in the context of AGM-like belief change
Kathelijne Coussement, Gert de Cooman, Keano De Vos
TL;DR
The paper develops an abstract conditioning framework for Accept-Desirability models (AD-models) in a general linear option space, unifying classical and quantum probabilistic inference. It introduces a conditioning rule based on induced indifference from event occurrences and ties conditioning to belief expansion and revision within a generalized AGM-belief-change structure. The work shows that, in precise subcontexts, the conditioning-based revision aligns with Bayes' Rule and Lüders' Rule and satisfies the AGM postulates in propositional and full previsional regimes, while revealing violations (dilation-related) in the general setting. Specialized subcases for propositional AD-models and full conditional previsions demonstrate where standard postulates hold and how updates can be interpreted as full-meet revisions or restricted expansions. Overall, the framework provides a unified lens for belief change across classical and quantum domains and clarifies when AGM postulates remain tenable under abstract conditioning.
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.