Dynamic reasoning environments are among the key aspects in formal argumentation research. Presumably the best understood problem is the so-called enforcement problem which asks, generally speaking, whether a given argumentation framework can be modified in a way that a certain desired outcome is ensured. However, enforcement research primarily focuses on the acceptance of arguments or sets thereof. This paper aims to explore the dual problem and investigates means to reject certain unreasonable viewpoints. To achieve this, we use labelling semantics on abstract argumentation frameworks (AFs), since they provide a clearly defined notion of rejection. We consider different kinds of updates for our given AF and provide results on existence as well as minimality of syntactic and semantic changes. For the latter, we define the new concept of consensus preservation, formalizing the intuition that formerly acceptable opinions should remain acceptable in the adapted framework. Lastly we discuss how these two notions of minimizing change interact.

The paper deals with the topic of realizability in abstract argumentation. More precisely, we consider the most basic kind of labellings, so-called conflict-free labellings. The understanding of these labellings is essential as any mature labelling-based semantics selects its output among these labellings. We show how to decide whether a given set of labellings is the conflict-free outcome of a certain Dungean framework. To this end we introduce several new criteria like L-tightness, reject-witness and reject-compositionality. These properties play a decisive role in the central characterization theorem. Moreover, we present a construction method, showing how to realize a conflict-free realizable labelling-set. Finally, we study the representational freedom in case of such labellings. This leads to an uniqueness result for a certain sub-class and a surprising connection to strong equivalence in case of extension-based semantics.