A recent line of research has developed around logics of belief based on information confirmed by a reliable source. In this paper, we provide a finer analysis and extension of this framework, where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature. We combine Belnap-Dunn logic and non-standard probabilities to account for potentially contradictory information within a two-layer modal logical framework to account for belief. The bottom layer is to be that of evidence represented by probabilistic information provided by sources available to an agent. The modalities connecting the bottom layer to the top layer, are that of belief of the agent based on the information from the sources in terms of (various kinds of) aggregation. The top layer is to be the logic of thus formed beliefs.

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如何对不一致的概率信息进行推理？

最近的一系列研究围绕基于可靠来源确认的信息的信念逻辑展开。在本文中，我们对该框架进行了更精细的分析和扩展，其中确认来自多个可能相互冲突的来源并且具有概率性质。我们结合 Belnap-Dunn 逻辑和非标准概率来解释两层模态逻辑框架内潜在的矛盾信息，以解释信念。底层是由代理可用资源提供的概率信息表示的证据。将底层连接到顶层的模态是基于（各种）聚合的来源信息的代理的信念。顶层是这样形成的信念的逻辑。