An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation Long Version

TL;DR

This paper introduces a new family of argument-ranking semantics using social ranking functions to refine argument acceptance classifications, supported by necessary and sufficient conditions for their application.

Contribution

It proposes a novel argument-ranking semantics based on social ranking functions, enhancing the classification of arguments in abstract argumentation.

Findings

Defines necessary and sufficient conditions for social ranking functions to produce refined argument rankings.

Provides a formal framework linking social ranking methods to argumentation semantics.

Enhances the granularity of argument acceptance and rejection classifications.

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.