The equivalence zoo for Dung-style semantics

Notions of equivalence that are stronger than standard equivalence in the sense that they also take potential modifications of the available information into account have received considerable interest in non-monotonic reasoning. In this article, we focus on equivalence notions in argumentation. More specifically, we establish a number of new results about the relationships among various equivalence notions for Dung argumentation frameworks that are located between strong equivalence (Oikarinen and Woltran, 2011, Art. Intell, 175, 1985-2009) and standard equivalence. We provide the complete picture for this variety of equivalence relations (which we call the equivalence zoo) for stable, preferred, admissible and complete semantics.