Structural Analysis of Extension-Based Argumentation Semantics with Joint Acceptability

Dung’s abstract argumentation provides us with a general framework to deal with argumentation. For extension-based semantics, the central issue is how to determine the extensions w.r.t. various semantics. Motivated by the acceptability and reinstatement criterion, we propose the notions of J-acceptability and J-reinstatement. Correspondingly, we introduce the J-complete semantics which reveals the gap between complete semantics and preferred semantics. It is shown that acceptability together with J-acceptability forms the foundation of extension-based semantics. For example, any admissible set can be built starting from a conflict-free collection of initial sets by iteratively applying some functions based on acceptability and J-acceptability. This novel idea enables to give a clear description of the extensions of the standard semantics.

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