The Poison Game is a two-player game played on a graph in which one player can influence which edges the other player is able to traverse. It operationalizes the notion of existence of credulously admissible sets in an argumentation framework or, in graph-theoretic terminology, the existence of non-trivial semi-kernels. We develop a modal logic (poison modal logic, PML) tailored to represent winning positions in such a game, thereby identifying the precise modal reasoning that underlies the notion of credulous admissibility in argumentation. We study model-theoretic and decidability properties of PML, and position it with respect to recently studied logics at the cross-road of modal logic, argumentation, and graph games.
翻译:毒玩游戏是一个双玩游戏, 玩家可以在其中影响另一个玩家能够穿越的边缘的图形上玩。 它可以将存在可信可接受组的概念运用到一个论证框架中, 或者用图形理论术语, 非三边半内核的存在。 我们开发了一个模式逻辑( poison modal 逻辑, PML ), 以代表游戏中获胜的位置, 从而确定精确的模式推理, 其基础是可信可接受性的概念。 我们研究PML 模型理论和可变性特性, 并将其定位于最近研究的逻辑在模式逻辑、 参数和图形游戏交叉路口的交叉位置 。