We present a new approach to reasoning about the outcome of an argumentation framework, where an agent's reasoning with a framework and semantics is represented by an inference relation defined over a logical labeling language. We first study a monotonic type of inference which is, in a sense, more general than an acceptance function, but equally expressive. In order to overcome the limitations of this expressiveness, we study a non-monotonic type of inference which allows \emph{counterfactual} inferences. We precisely characterize the classes of frameworks distinguishable by the non-monotonic inference relation for the admissible semantics.