Conditioning and AGM-like belief change in the Desirability-Indifference framework

TL;DR

This paper extends the AGM belief change framework to include conditioning within the Desirability-Indifference framework, accommodating both classical and quantum probability theories through abstract notions of options and events.

Contribution

It introduces a generalized approach to belief change that unifies classical and quantum probability theories within the Desirability-Indifference framework.

Findings

Extended AGM framework to conditioning in Desirability-Indifference setting

Unified classical and quantum probability theories in belief change

Provides abstract notions of options and events for belief updates

Abstract

We show how the AGM framework for belief change (expansion, revision, contraction) can be extended to deal with conditioning in the so-called Desirability-Indifference framework, based on abstract notions of accepting and rejecting options, as well as on abstract notions of events. This level of abstraction allows us to deal simultaneously with classical and quantum probability theory.