On the graded acceptability of arguments in abstract and instantiated argumentation

摘要: Abstract The paper develops a formal theory of the degree justification arguments, which relies solely on structure an argumentation framework, and can be successfully interfaced with approaches to instantiated argumentation. is developed in three steps. First, introduces graded generalization two key notions underpinning Dung's semantics: self-defense conflict-freeness. This leads natural semantics, whereby standard extensions are weakened or strengthened depending level conflict-freeness they meet. investigates fixpoint these establishing existence results for them. Second, shows how semantics readily provide approach argument rankings, offering novel contribution recently growing research programme ranking-based semantics. Third, this ranking applied studied context frameworks, so doing shown account simple form accrual arguments within Dung paradigm. Finally, compared detail existing approaches.