论文标题
关于论证框架的首选扩展：具有幼稚集的徒
On the preferred extensions of argumentation frameworks: bijections with naive sets
论文作者
论文摘要
本文讨论了通过与另一个框架的幼稚集进行培养，以发现论证框架的首选扩展。首先，我们考虑了一个论证框架是天真的基础的情况：其天真的集合和首选扩展是相等的。认识到幼稚的论证框架很难，但是我们表明它对于具有界限的框架是可以进行的。接下来，我们在被允许关闭的论证框架的首选扩展（两个可接受的集合的交汇处）与在同一集参数集上的另一个框架的幼稚集之间进行两次培训。另一方面，我们证明识别可允许的论证框架是综合的。最后，我们介绍了不可还原的自我防御集的概念，因为那些不是他人的结合。事实证明，论证框架的首选扩展与其不可还原的自我抗辩集的框架的幼稚集之间存在了两者。因此，具有某些晶格属性的论证框架的首选扩展可以使用多项式延迟和多项式空间列出。
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.
