On the Difference between Assumption-based Argumentation and Abstract Argumentation

In the current paper, we re-examine the connection between abstract argumentation and assumption-based argumentation. These two formalisms are often claimed to be equivalent in the sense that (a) evaluating an assumption based argumentation framework directly with the dedicated semantics, and (b) first constructing the corresponding abstract argumentation framework and then applying the corresponding abstract argumentation semantics, produce the same outcome. Although this holds for several semantics, in this work we show that there exist well-studied admissibility-based semantics (semi-stable and eager) under which equivalence does not hold.