On Undisputed Sets in Abstract Argumentation

We introduce the notion of an undisputed set for abstract argumentation frameworks, which is a conflict-free arguments, such that its reduct contains no non-empty admissible set. show sets, and stronger strongly provide meaningful approach to weaken admissibility deal with problem attacks from self-attacking in similar manner as recently introduced weak admissibility. investigate properties our new semantical notions certain relationships classical semantics, particular sets are generalisation preferred extensions stable extensions. also computational complexity standard reasoning tasks these they lie on second third level polynomial hierarchy, respectively.