提出可表达共同知识的多拓扑程序动态逻辑，揭示其在不同空间中的性质差异。
Common Knowledge Always, Forever
- 构建支持共同知识表达的多拓扑程序动态逻辑系统
- 证明该系统在闭包空间具有有限模型性质，但在康托导出空间不具有
- 适用于逻辑、认知建模与形式语义研究者
近年来，认知逻辑的拓扑语义受到越来越多关注，已被用于建模证据、信念程度及自指等。本文引入一种可表达共同知识及其多种推广的多拓扑程序动态逻辑（polytopological PDL），并证明其在闭包空间中具有有限模型性质，但在康托导出空间中不具有。后一结论通过将带有‘过去’时态的线性时序逻辑的一种变体嵌入该系统而得出，而该时序逻辑本身不具备有限模型性质。
原文摘要 · Abstract (English)
There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property.
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