This paper deals with the problem of finding the preferred extensions of an argumentation framework by means of a bijection with the naive sets of another framework. First, we consider the case where an argumentation framework is naive-bijective: its naive sets and preferred extensions are equal. Recognizing naive-bijective argumentation frameworks is hard, but we show that it is tractable for frameworks with bounded in-degree. Next, we give a bijection between the preferred extensions of an argumentation framework being admissible-closed (the intersection of two admissible sets is admissible) and the naive sets of another framework on the same set of arguments. On the other hand, we prove that identifying admissible-closed argumentation frameworks is coNP-complete. At last, we introduce the notion of irreducible self-defending sets as those that are not the union of others. It turns out there exists a bijection between the preferred extensions of an argumentation framework and the naive sets of a framework on its irreducible self-defending sets. Consequently, the preferred extensions of argumentation frameworks with some lattice properties can be listed with polynomial delay and polynomial space.

翻译：本文研究了通过另一框架的朴素集合与论证框架的优先扩展建立双射关系的问题。首先，我们考虑论证框架是朴素双射的情形：其朴素集合与优先扩展相等。识别朴素双射论证框架是困难的，但我们证明对于有界入度框架该问题是可处理的。其次，我们给出了满足可接受闭性质（两个可接受集的交集仍是可接受的）的论证框架的优先扩展与同一论证集上另一框架的朴素集合之间的双射。另一方面，我们证明识别可接受闭论证框架是coNP完全的。最后，我们引入不可约自守集的概念，即那些不能表示为其他集合之并的集合。结果表明，论证框架的优先扩展与其在不可约自守集上构建的框架的朴素集合之间存在双射。因此，具有某种格性质的论证框架的优先扩展可以在多项式延迟和多项式空间内枚举。