In this article, we start with a two-player game that models communication under adverse circumstances in everyday life and study it from the perspective of a modal logic of graphs, where links can be deleted locally according to definitions available to the adversarial player. We first introduce a new language, semantics and some typical validities. We then formulate a new type of first-order translation for this modal logic and prove its correctness. Then, a novel notion of bisimulation is proposed that leads to a characterization theorem for the logic as a fragment of first-order logic, and a further investigation is made of its expressive power against hybrid modal languages. Next, we discuss how to axiomatize this logic of link deletion, using dynamic-epistemic logics as a contrast. Finally, we show that our new modal logic lacks both the tree model property and the finite model property and that its satisfiability problem is undecidable.

中文翻译：

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丢失连接：可删除链接的模态逻辑

在本文中，我们从一个两人游戏开始，该游戏在日常生活中的不利条件下对通讯进行建模，并从图的模态逻辑的角度进行研究，其中可以根据对抗性玩家可用的定义在本地删除链接。我们首先介绍一种新的语言，语义和一些典型的有效性。然后，我们为此模态逻辑制定一种新型的一阶翻译，并证明其正确性。然后，提出了一种新的双仿真概念，该概念导致了作为一阶逻辑片段的逻辑的定理定理，并进一步研究了其对混合模态语言的表达能力。接下来，我们讨论如何使用动态流行病逻辑作为对比来合理化链接删除的这种逻辑。最后，