On Conflict-free Labellings – Realizability, Construction and Patterns of Redundancy

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.