From Acceptance to Rejection in Abstract Argumentation

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.