Abstract Argumentation Frameworks (Dung, 1995) are mainly concerned with the definition and study of the rational acceptance of arguments, based only on the way arguments interact. Usually, the acceptance of a given argument is given by the possibility of extending the analyzed argument to a set of “collectively acceptable” arguments. This set of collectively acceptable arguments must be internally coherent and defend itself from any external attack.
In this talk we focus on algorithmic and complexity issues related to this kind of argument acceptability. Work in progress and future directions are outlined.