We discuss repeatable experiments about which various agents may have different information. This information can vary from a full probabilistic description of the experiment in the sense that the probabilities of all outcomes are known to the agent, to having no information whatsoever, except the collection of possible outcomes. We argue that belief functions are very suitable for modeling the type of information we have in mind. We redevelop and rederive various notions of conditional belief functions, using a viewpoint of relative frequencies. We call the two main forms of conditioning contingent and necessary conditioning, respectively. The former is used when the conditioning event may also have not occurred, whereas the latter is used when it turns out that the event on which we condition occurs necessarily. Our approach unifies various notions in the literature into one conceptual framework, namely, the updated belief functions of Fagin and Halpern, the unnormalized conditional belief function of Smets, and the notions of updating and focusing as used by Dubois and Prade. We show that the original Dempster–Shafer definition of conditional belief functions cannot be interpreted directly in our framework. We give a number of examples illustrating our interpretation, as well as the differences between the various notions of conditioning.

中文翻译：

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用置信函数重新审视条件概率

我们讨论了关于各种代理可能具有不同信息的可重复实验。该信息可以从对实验的完整概率描述（即代理已知所有结果​​的概率）到除了可能结果的集合之外没有任何信息。我们认为信念函数非常适合对我们想到的信息类型进行建模。我们使用相对频率的观点重新开发和重新推导条件信念函数的各种概念。我们分别将两种主要形式的条件反射称为偶然条件反射和必要条件反射。前者用于条件事件可能还没有发生时，而后者用于我们条件化的事件必然发生时。我们的方法将文献中的各种概念统一到一个概念框架中，即 Fagin 和 Halpern 的更新信念函数、Smets 的非规范化条件信念函数，以及 Dubois 和 Prade 使用的更新和聚焦概念。我们表明，条件置信函数的原始 Dempster-Shafer 定义不能在我们的框架中直接解释。我们给出了许多例子来说明我们的解释，以及各种条件反射概念之间的差异。我们表明，条件置信函数的原始 Dempster-Shafer 定义不能在我们的框架中直接解释。我们给出了许多例子来说明我们的解释，以及各种条件反射概念之间的差异。我们表明，条件置信函数的原始 Dempster-Shafer 定义不能在我们的框架中直接解释。我们给出了许多例子来说明我们的解释，以及各种条件反射概念之间的差异。