Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow for an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical probabilities we show that a class TμMP of theories can be selected in which probabilities are introduced as classical averages of Kolmogorovian probabilities over sets of (microscopic) contexts, which endows them with an epistemic interpretation. The conditions characterizing TμMP are compatible with classical mechanics (CM), statistical mechanics (SM), and QM, hence we assume that these theories belong to TμMP. In the case of CM and SM, this assumption is irrelevant, as all of the notions introduced in them as members of TμMP reduce to standard notions. In the case of QM, it leads to interpret quantum probability as a derived notion in a Kolmogorovian framework, explains why it is non-Kolmogorovian, and provides it with an epistemic interpretation. These results were anticipated in a previous paper, but they are obtained here in a general framework without referring to individual objects, which shows that they hold, even if only a minimal (statistical) interpretation of QM is adopted in order to avoid the problems following from the standard quantum theory of measurement.

中文翻译：

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语境理论中的 Kolmogorovian 与非 Kolmogorovian 概率

大多数学者坚持认为量子力学 (QM) 是一种语境理论，量子概率不允许进行认知（无知）解释。通过询问上下文和非经典概率之间可能的联系，我们表明可以选择一类 TμMP 理论，其中将概率作为 Kolmogorovian 概率在（微观）上下文集上的经典平均值引入，这赋予它们认知解释。表征 TμMP 的条件与经典力学 (CM)、统计力学 (SM) 和 QM 兼容，因此我们假设这些理论属于 TμMP。在 CM 和 SM 的情况下，这个假设是无关紧要的，因为它们中作为 TμMP 成员引入的所有概念都简化为标准概念。在 QM 的情况下，它导致将量子概率解释为 Kolmogorovian 框架中的一个派生概念，解释了为什么它是非 Kolmogorovian 的，并为其提供了认知解释。这些结果在之前的一篇论文中是预料到的，但它们是在不涉及单个对象的一般框架中获得的，这表明即使仅采用 QM 的最小（统计）解释以避免以下问题来自标准的量子测量理论。