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.

翻译：近年来，拓扑语义在认知逻辑中的应用日益受到关注，其在建模证据、信念程度及自指现象等方面展现出重要价值。本文提出一种能够表达公共知识及其多种推广形式的多拓扑动态认知逻辑，并证明其在闭包空间上具有有限模型性质，但在康托尔导空间上不具备该性质。后一结论通过嵌入带“过去”算子的线性时序逻辑版本得以证明，而该时序逻辑本身不具备有限模型性质。