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Generalizing stable semantics by preferences

Different proposals have been made in the literature for refining Dung's argumentation framework by preferences between arguments. The idea is to ignore an attack if the attacked argument is stronger than its attacker. Acceptability semantics are then applied on the remaining attacks. Unfortunately, these proposals may return some unintended results, in particular, when the attack relation is asymmetric. 
 
In this paper, we propose a new approach in which preferences are taken into account at the semantics level. In case preferences are not available or do not conflict with the attacks, the extensions of the new semantics coincide with those of the basic ones. Besides, in our approach, the extensions (under a given semantics) are the maximal elements of a dominance relation on the powerset of the set of arguments. Throughout the paper, we focus on stable semantics. We provide a full characterization of its dominance relations; and we refine it with preferences.