  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.
