提出新型条件化规则，统一经典与量子概率框架下的信念更新。
Conditioning Accept-Desirability models in the context of AGM-like belief change
- 基于观测事件引入新无差异性，设计新条件化规则
- 在经典逻辑与全条件概率下，全部AGM公理仍成立
- 适用于不确定奖励的广义线性空间，拓展至不精确概率
我们在一个抽象决策框架中讨论接受-偏好模型的条件化问题，其中不确定性收益位于一般线性空间中，事件是该空间上的特殊投影算子。这一抽象设定使我们能够统一经典与量子概率，并将其扩展至不精确概率情境。我们提出一种新的接受-偏好模型条件化规则，其核心思想是：观测事件会引入选项间的新的无差异关系。我们为该条件化规则定义了一个信念修正算子，并研究了在更一般的框架下哪些AGM信念修正公理仍然成立。我们考察了两个有趣特例：经典命题逻辑和全条件概率，证明在这些情形下所有AGM公理均保持有效。
原文摘要 · Abstract (English)
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.
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