Cogent argument extensions are weakly admissible but not vice versa

TL;DR

The paper investigates two non-admissible argumentation semantics, cogency and weak admissibility, within Dung frameworks. It formalizes both notions and proves a containment result: $Cog(F) \subseteq ad^{w}(F)$, while the reverse inclusion can fail, demonstrated through concrete counterexamples. The findings indicate that cogency is more skeptical than weak admissibility, and the work clarifies the implications for selecting semantics in argumentation analysis. This contributes to understanding the trade-offs between skepticism and credulity in non-admissible semantics and informs semantic choices in AF reasoning.

Abstract

In this research note, we show the relationship between two non-admissible argumentation framework semantics: cogent and weakly admissible semantics. We prove that, while cogent extensions are weakly admissible, the converse is not true.