In his seminal 1995 paper, Dung laid the foundations of abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack.

This paper provides a solution to this problem. More precisely, we introduce alternative foundations for abstract argumentation, namely weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. We also conduct an analysis of the relationship of our concepts with similar concepts found in the literature. We show that weak admissibility, although defined in entirely different terms, is in fact equivalent to a notion of acceptability which was defined by Kakas and Mancarella yet never studied in depth.

The new semantics presented here overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.¹

在他 1995 年的开创性论文中，Dung 奠定了抽象论证的基础，这是目前知识表示的主要研究领域。他指出，所有传统语义背后的弄巧成拙的论点存在一个问题。如果一个论点通过奇怪的攻击循环直接或间接地攻击自己，就会发生自我挫败，除非该循环被某个从外部攻击循环的论点打破。受此类论点代表自相矛盾或自相矛盾的论点这一事实的启发，他要求提供合理的语义，以克服此类论点确实可能使他们攻击的任何论点无效的问题。

本文为这个问题提供了一个解决方案。更准确地说，我们引入了抽象论证的替代基础，即弱可接受性和弱辩护。在展示了这些关键概念与经典案例中的兼容之后，我们引入了经典 Dung 风格语义的新版本，包括完整的、首选的和接地的语义。我们对这些新概念进行了严格的研究，包括相互关系以及与它们的 Dung 风格对应物的关系。我们还对我们的概念与文献中的类似概念之间的关系进行了分析。我们证明了弱可接纳性，虽然用完全不同的术语定义，但实际上等同于由 Kakas 和 Mancarella 定义但从未深入研究过的可接受性概念。

这里提出的新语义克服了自毁论据的问题，它们在语义上对自攻论元的句法删除不敏感，这是自毁论的一种特殊情况。¹