In argumentation theory, Dung's abstract framework provides a unifying view of several alternative semantics based on the notion of extension. Recently, a new semantics has been introduced to solve the problems related to counterintuitive results produced by literature proposals. In this semantics, extensions can be decomposed and constructed along the strongly connected components of the defeat graph. This paper proves that this property holds also in the context of all semantics encompassed by Dung's framework, showing that strongly connected components may play a general role in the definition and computation of argumentation semantics.
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