Level n arguments
An argument is ultimately undefeated if there is a level such that it is in at that level and all higher levels.
An argument is ultimately defeated if there is a level such that it is not in at that level nor at any higher level.
An argument is provisionally defeated if it is neither ultimately defeated nor ultimately undefeated.
? Cf. Pollock. See also Dung’s work for the basic properties of level n arguments