In this paper, we propose a generalisation of Dung's abstract argumentation framework that allows representing higher-order attacks and supports, that is attacks or supports whose targets are other attacks or supports. We follow the necessary interpretation of the support, based on the intuition that the acceptance of an argument requires the acceptance of each supporter. We propose semantics accounting for acceptability of arguments and validity of interactions, where the standard notion of extension is replaced by a triple of a set of arguments, a set of attacks and a set of supports. Our framework is a conservative generalisation of Argumentation Frameworks with Necessities (AFN). When supports are ignored, Argumentation Frameworks with Recursive Attacks are recovered.
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