Solid Semantics for Abstract Argumentation Frameworks and the Preservation of Solid Semantic Properties

In this paper, we propose solid admissibility that is a strengthened version of Dung’s admissibility to obtain the most acceptable set of arguments. Besides, other solid extensions based on solid admissibility are defined. Such extensions not only include all defenders of its elements but also exclude all arguments indirectly attacked and indirectly defended by some argument(s). Furthermore, we characterize solid extensions with propositional formulas. Using these formulas, we aggregate solid extensions by using approaches from judgment aggregation. Especially, although no quota rule preserves Dung’s admissibility for any argumentation framework, we show that there exist quota rules that preserve solid admissibility for any argumentation framework.