Assumption-based Argumentation (ABA) is a well-established form of structured argumentation. ABA frameworks with an underlying atomic language are widely studied, but their applicability is limited by a representational restriction to ground (variable-free) arguments and attacks built from propositional atoms. In this paper, we lift this restriction and propose a novel notion of constrained ABA (CABA), whose components, as well as arguments built from them, may include constrained variables, ranging over possibly infinite domains. We define non-ground semantics for CABA, in terms of various notions of non-ground attacks. We show that the new semantics conservatively generalise standard ABA semantics.

翻译：假设论证（ABA）是一种成熟的结构化论证形式。基于原子语言的ABA框架已被广泛研究，但其适用性受到表示限制的制约，即仅能处理由命题原子构成的无变量（基础）论证与攻击。本文中，我们突破了这一限制，提出了一种新颖的约束ABA（CABA）概念，其构成组件及由此构建的论证均可包含约束变量，这些变量的取值范围可覆盖可能无限的域。我们针对CABA定义了非基础语义，该语义基于多种非基础攻击的概念。我们证明，新语义在保守意义上推广了标准ABA语义。