General directionality and the local behavior of argumentation semantics

In abstract argumentation, the directionality principle conveys the intuition that, for an unattacked set, the choice of arguments that are part of an extension should only depend on the restriction of the framework to that set. Furthermore, having made such a choice, one should be able to select arguments from the rest of the framework so as to get an extension. In this paper we show how this idea can be generalized and used for formulating SCC-recursiveness as a stronger version of directionality. We argue that such properties characterize the information that is needed for computing the extensions of an argumentation semantics. We provide a formal approach for describing and comparing directionality-like properties. Our model provides a clear distinction between SCC-recursive semantics that use defense information and those that do not use it.