A labelling approach for ideal and stage semantics

In this document, we describe the concepts of ideal semantics and stage semantics for abstract argumentation in terms of argument labellings. The difference between the traditional extensions approach and the labelling approach is that where the former only identifies the sets of accepted arguments, the latter also identifies the rejected arguments as well as the arguments that are neither accepted nor rejected. So far, the labellings approach has been successfully applied to complete, grounded, preferred, stable and semi-stable semantics, as well as to the concept of admissibility. In the current paper, we continue this line of research by showing that ideal semantics and stage semantics can also be described in terms of argument labellings.