The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the postcondition-free case. As upper bounds, it is shown that either 1 atom, 3 agents and preconditions of modal depth 18 or 1 atom, 7 agents and preconditions of modal depth 3 suffice for Turing completeness.

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动态认知逻辑的收敛性，连续性，重复性和图灵完备性

本文从拓扑的角度分析了动态认知逻辑。主要贡献包括一个框架，在该框架中，动态认知逻辑满足了拓扑动态系统的要求，从而使离散动态逻辑与动态系统的连续映射相接。该设置基于逻辑收敛的概念，这在逻辑上等同于Stone拓扑的收敛。提出了一个灵活的，参数化的度量标准系列，这些度量标准可以诱导Stone拓扑，用作分析辅助。我们显示了由动作模型变换相对于Stone拓扑连续诱发的地图，并给出了有关所述地图的重复行为的结果。在递归结果中，我们显示了由有限作用模型引起的映射可能具有无数个递归点，即使在有限输入模型上启动也是如此。若干重复结果借鉴了图灵完备的一类动作模型，为此，本文在无后置条件的情况下提供了证明。作为上限，表明1个原子，3个主体和模态深度为18的先决条件或1个原子，7个主体和模态深度为3的先决条件就足以满足图灵完整性。