One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support or positive dependency cycles. In this paper we introduce a new method to ensure acyclicity of arguments and present a family of extension-based semantics built on it, along with their classification w.r.t. cycles. Finally, we provide ADF versions of the properties known from the Dung setting.
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