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, an important role is played by a recursive schema in the definition of extensions. This paper proves that all the semantics encompassed by Dung's framework adhere to this property, not previously considered in the literature, which we call SCC-recursiveness. We argue that this notion plays a general role in the definition and computation of argumentation semantics.
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