Credulous Acceptability, Poison Games and Modal Logic

The Poison Game is a two-player game in which players alternatively move a token on a graph's nodes and such that one player can influence which edges the other player is able to traverse. It operationalizes the notion of existence of credulously acceptable arguments in an argumentation framework or, equivalently, 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 acceptability in argumentation. We study model-theoretic and decidability properties of PML, and position it with respect to recently studied logics at the crossroad of modal logic, argumentation, and graph games.