Any kind of dynamics in dynamic epistemic logic can be represented as an action model. Right? Wrong! In this contribution we prove that the update expressivity of communication patterns is incomparable to that of action models. Action models, as update mechanisms, were proposed by Baltag, Moss, and Solecki in 1998 and have remained the nearly universally accepted update mechanism in dynamic epistemic logics since then. Alternatives, such as arrow updates that were proposed by Kooi and Renne in 2011, have update equivalent action models. More recently, the picture is shifting. Communication patterns are update mechanisms originally proposed in some form or other by Agotnes and Wang in 2017 (as resolving distributed knowledge), by Baltag and Smets in 2020 (as reading events), and by Velazquez, Castaneda, and Rosenblueth in 2021 (as communication patterns). All these logics have the same expressivity as the base logic of distributed knowledge. However, their update expressivity, the relation between pointed epistemic models induced by such an update, was conjectured to be different from that of action model logic. Indeed, we show that action model logic and communication pattern logic are incomparable in update expressivity. We also show that, given a history-based semantics and when restricted to (static) interpreted systems, action model logic is (strictly) more update expressive than communication pattern logic. Our results are relevant for distributed computing wherein oblivious models involve arbitrary iteration of communication patterns.

翻译：在动态认知逻辑中，任何类型的动态过程都可以表示为行动模型。果真如此吗？不！本文证明，通信模式与行动模型的更新表达力是不可比较的。行动模型作为更新机制由Baltag、Moss和Solecki于1998年提出，此后一直是动态认知逻辑中近乎普遍接受的更新机制。其替代方案，如Kooi和Renne于2011年提出的箭头更新，则具有更新等价的行动模型。然而近年来，这一格局正在发生变化。通信模式作为更新机制，最初由Agotnes和Wang（2017年，作为消解分布式知识）、Baltag和Smets（2020年，作为阅读事件）以及Velazquez、Castaneda和Rosenblueth（2021年，作为通信模式）以不同形式提出。所有这些逻辑都具有与基础分布式知识逻辑相同的表达力。然而，它们的更新表达力——即此类更新所诱导的带标点认知模型之间的关系——曾被猜想与行动模型逻辑不同。事实上，我们证明行动模型逻辑与通信模式逻辑在更新表达力上是不可比较的。我们还证明，在基于历史的语义下且当限制于（静态）解释系统时，行动模型逻辑的更新表达力（严格）强于通信模式逻辑。我们的结果对分布式计算领域具有相关性，其中遗忘模型涉及通信模式的任意迭代。