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：假设基论证（ABA）与稳定模型语义下的逻辑程序（LP）之间的关系已得到充分研究。然而，为建立此关系，ABA框架需限制为平坦框架，即（可废止）假设永远无法被蕴涵、仅能被假定为真或假的片段。本文移除此限制，展示了非平坦ABA与头部包含失败否定的LP之间的对应关系。随后，我们将此结果扩展至所谓的集合稳定ABA语义——该语义最初为称为双极ABA的非平坦ABA片段而定义。我们展示了如何为头部包含失败否定的LP定义集合稳定语义，并证明其与集合稳定ABA语义的对应关系。