-
Views
-
Cite
Cite
João Alcântara, Renan Cordeiro, Bipolar Argumentation Frameworks with a dual relation between defeat and defence, Journal of Logic and Computation, Volume 35, Issue 2, March 2025, exae006, https://doi.org/10.1093/logcom/exae006
Close - Share Icon Share
Abstract
Bipolar Argumentation Frameworks (|$\textit{BAF}$|s) extend Dung’s Abstract Argumentation Frameworks (|$\textit{AAF}$|s) by incorporating an explicit notion of support between arguments. However, there is a price to pay: the semantics for |$\textit{BAF}$|s often involve more intricate definitions and computational procedures than those for |$\textit{AAF}$|s. In this paper, we establish a dual relation between defeat and defence. Taking profit from this dual perspective, we define conflict-free sets, acceptability, extension-based and labelling-based semantics as in |$\textit{AAF}$|s. We also show that our definitions collapse into the corresponding concepts proposed for |$\textit{AAF}$|s when the support relation is ignored. In particular, we prove the semantics |$\beta $|-admissible, |$\beta $|-complete, |$\beta $|-grounded, |$\beta $|-preferred, |$\beta $|-stable and |$\beta $|-semi-stable defined here for |$\textit{BAF}$|s are generalisations of the corresponding semantics for |$\textit{AAF}$|s. Besides generalising |$\textit{AAF}$|s semantics to |$\textit{BAF}$|s, our approach also preserves some of their most remarkable results, including Dung’s Fundamental Lemma.
