is used in a slightly different context.

Although various extension–based semantics for ADFs have already been proposed in the original paper [@inproc:adf], many of them were defined only for a particular ADF subclass called the bipolar and were not suitable for all types of situations. As a result, only three of them – conflict–free, model and grounded – remain. Moreover, the original formulations did not solve the problem of positive dependency cycles. Unfortunately, neither did the more recent work into labeling–based semantics [@tofix:newadf], even though they solve most of the problems of their predecessors. The aim of this paper is to address the issue of cycles and the lack of properly developed extension–based semantics. We introduce a family of such semantics and specialize them to handle the problem of support cycles, as their treatment seems to be the biggest difference among the available frameworks. Furthermore, a classification of our sub–semantics in the inside–outside fashion that we have described before is introduced. We also recall our previous research on admissibility in [@inproc:adm] and show how it fits into the new system. Our results also include which known properties, such as Fundamental Lemma, carry over from the Dung framework. Finally, we provide 