How to Argue for Anything: Enforcing Arbitrary Sets of Labellings using AFs

We contribute to the investigation of possible outcomes of argumentation under semantics formulated using argumentation frameworks (AFs). In particular, we study this question for the labelling-based formulation of such semantics, generalizing previous work which has focused on extensions. In this paper, we restrict attention to the preferred and semi-stable semantics, showing that as long as we have a sufficient number of fresh arguments available, we can in fact argue for anything. That is, for any set of finite labellings there is an AF that enforces exactly this set as the outcome of argumentation.