Realisability of Ranking-based Semantics

In this work, we discuss the realisability problem for ranking-based semantics in the area of abstract argumentation. So, for a given ranking and ranking-based semantics, we want to find an AF s.t. the selected ranking-based semantics induces our ranking when applied to the AF. We show that this question can be answered trivially with yes for a number of ranking-based semantics, i.e. for every ranking we can find such an AF. In addition to the discussion about the realisability problem, we also introduce a new equivalence notion for argumentation frameworks. We call two AFs ranking equivalent if they have the same ranking for a ranking-based semantics.