Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA frameworks (ABAFs) is that they are flat, i.e., each of the defeasible assumptions can only be assumed, but not derived. While it is known that flat ABAFs can be translated into abstract argumentation frameworks (AFs) as proposed by Dung, no translation exists from general, possibly non-flat ABAFs into any kind of abstract argumentation formalism. In this paper, we close this gap and show that bipolar AFs (BAFs) can instantiate general ABAFs. To this end we develop suitable, novel BAF semantics which borrow from the notion of deductive support. We investigate basic properties of our BAFs, including computational complexity, and prove the desired relation to ABAFs under several semantics. Finally, in order to support computation and explainability, we propose the notion of dispute trees for our BAF semantics.

翻译：基于假设的论辩（ABA）是一种著名的结构化论辩形式体系，其论辩和论辩间的攻击关系源于规则、可废止假设及其对立面。通常对ABA框架（ABAFs）施加的一个常见限制是它们必须是平坦的，即每个可废止假设只能被假设，而不能被推导。尽管已知平坦的ABAFs可以转化为Dung提出的抽象论辩框架（AFs），但目前尚未存在将一般性（可能非平坦的）ABAFs转化为任何类型抽象论辩形式体系的转化方法。本文填补了这一空白，证明双极AFs（BAFs）能够实例化一般的ABAFs。为此，我们发展了新颖且恰当的BAF语义，该语义借鉴了演绎支持的概念。我们研究了BAF的基本性质（包括计算复杂性），并证明了在多种语义下与ABAFs的期望关系。最后，为支持计算与可解释性，我们提出了针对BAF语义的争议树概念。