An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation Long Version
Lars Bengel, Giovanni Buraglio, Jan Maly, Kenneth Skiba
TL;DR
The paper tackles the limitation of traditional extension-based semantics which only distinguish arguments as skeptically accepted, credulously accepted, or rejected. It introduces a novel framework that blends extension-ranking semantics with social ranking functions, using the rank of a set and the lexicographic excellence operator ($\text{lex-cel}$) to produce a fine-grained, total or partial order over individual arguments, refining the standard acceptance categories. The authors establish sufficient and necessary conditions for a social-ranking operator to yield the desired $\sigma$-refinement, notably showing that Independence from the worst set together with Pareto-efficiency suffices for $\sigma$-C and the skeptical-credulous refinement, while Dominating set provides essential leverage for other principles. They demonstrate how the generalised approach can yield concrete argument rankings (e.g., $\text{lex-cel}_{\text{r-co}}$) that respect skeptical/credulous distinctions and further distinguish arguments within each class. By connecting social-ranking concepts with extension-ranking semantics, the work offers a flexible, principled framework for nuanced argument evaluation applicable to a range of semantics and potential real-world debates.
Abstract
In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property.