一句话：用 Cayley 群表示认知框架，给出带公共知识的多主体模态逻辑的 van Benthem 式刻画与多尺度局部性分析。
论文研究带群体公共知识模态的多主体认知模态逻辑，目标是获得 van Benthem 风格的模型论刻画。公共知识模态具有不动点特征，其派生可及关系涉及可达性与传递闭包，使相关 Kripke 框架类成为非初等类，超出经典模型论范围，也给模型论博弈分析带来新挑战。作者在局部性技术之外，为适配的 Cayley 群建立结构理论：将智能体对应到生成元集合，使每个认知框架都可在互模拟意义下由具特定无环性质的 Cayley 群表示，从而按不同智能体联盟的距离测度进行多粒度局部性分析。关键结果是：将经典一阶逻辑的互模拟不变性刻画推广到有限或任意公共知识 Kripke 框架类。
We investigate multi-agent epistemic modal logic with common knowledge modalities for groups of agents and obtain van Benthem style model-theoretic characterisations, in terms of bisimulation invariance of classical first-order logic over the non-elementary classes of (finite or arbitrary) common knowledge Kripke frames. The fixpoint character of common knowledge modalities and the rôle that reachability and transitive closures play for the derived accessibility relations take our analysis beyond classical model-theoretic terrain and technically pose a novel challenge to the analysis of model-theoretic games. Over and above the more familiar locality-based techniques we exploit a specific structure theory for specially adapted Cayley groups: through the association of agents with sets of generators, all epistemic frames can be represented up to bisimilarity by suitable Cayley groups with specific acyclicity properties; these support a locality analysis at different levels of granularity as induced by distance measures w.r.t. various coalitions of agents.