The relation between (a fragment of) assumption-based argumentation (ABA) and logic programs (LPs) under stable model semantics is well-studied. However, for obtaining this relation, the ABA framework needs to be restricted to being flat, i.e., a fragment where the (defeasible) assumptions can never be entailed, only assumed to be true or false. Here, we remove this restriction and show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called set-stable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.

翻译：（假设基础论证（ABA）的一个片段与稳定模型语义下的逻辑程序（LPs）之间的关系已得到充分研究。然而，为建立此关系，ABA框架需限制为平坦形式，即其中（可撤销的）假设永不能被推导，仅能被假定为真或假。本文去除了这一限制，证明了非平坦ABA与头部含失败即否定的逻辑程序之间的对应关系。随后，我们将此结果扩展至所谓集合稳定ABA语义，该语义最初针对非平坦ABA的片段（称为双极ABA）定义。我们展示了如何为头部含失败即否定的逻辑程序定义集合稳定语义，并证明了其与集合稳定ABA语义的对应关系。）