State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn’s aboutness interpretation of fde, to the space of open sets of a spectral space. We show that these information structures induce so-called hype models which were recently developed by Leitgeb (2019). Conversely, we prove a representation theorem: roughly, hype models can be represented as induced by an information structure. Thus, the well-behaved logic hype is a sound and complete logic for reasoning about information in state spaces.As application of this framework, we investigate information fusion. We motivate two kinds of fusion. We define a groundedness and a separation property that allow a hype model to be closed under the two kinds of fusion. This involves a Dedekind–MacNeille completion and a fiber-space like construction. The proof-techniques come from pointless topology and universal algebra.

中文翻译：

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状态空间中的信息逻辑

在最一般的意义上，状态空间是包含信息的实体集。例子包括动力系统的状态、观察过程或可能世界。我们使用域理论来描述状态空间中正负信息的结构。我们提供了从动力系统轨迹空间到 Dunn 对fde, 到谱空间的开集空间。我们表明，这些信息结构会导致所谓的炒作Leitgeb (2019) 最近开发的模型。反过来，我们证明了一个表示定理：粗略地说，炒作模型可以表示为由信息结构诱导。因此，行为良好的逻辑炒作是在状态空间中推理信息的健全而完整的逻辑。作为该框架的应用，我们研究了信息融合。我们鼓励两种融合。我们定义了一个接地性和一个分离属性，它允许一个炒作两种融合下的模型要闭合。这涉及 Dedekind-MacNeille 完井和类似纤维空间的结构。证明技术来自无意义的拓扑和通用代数。