The usual $\mathbf{S}{\mathbf{5}}_{\mathbf{n}}$ epistemic model for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so-called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.

通常 $\mathbf{小号}{\mathbf{5}}_{\mathbf{ñ}}$多智能体系统的认知模型基于Kripke框架，Kripke框架是一个图形，其边缘用不区分两种状态的智能体标记。我们建议通过考虑对偶，简单复杂模型来揭示此结构中隐含的高维信息。我们使用动态认知逻辑（DEL）来研究在一组主体彼此通信之后，认知简单化复杂模型如何变化。我们专注于代表所谓的即时快照的动作模型异步代理的通信模式，因为它是分布式可计算性的核心（但我们的设置适用于其他通信模式）。从最初的认知复合体到应用了行动模型后的拓扑复合体之间保留着拓扑不变性，这些拓扑不变性决定了主体在交流后获得的知识。最后，我们描述了如何将分布式任务规范建模为DEL动作模型，并表明拓扑不变量确定任务是否可解决。因此，我们提供了DEL与分布式可计算性拓扑理论之间的桥梁，该理论研究了共享内存或消息传递体系结构中的任务可解决性。