Argument Ranking with Categoriser Function

TL;DR

This paper investigates the categoriser function for argument ranking, addressing existence, uniqueness, and solution methods using fixed point techniques, and explores its properties and axioms satisfaction.

Contribution

It provides a detailed analysis of the categoriser function's mathematical properties and introduces a ranking semantics based on categoriser strength.

Findings

Addresses existence and uniqueness of solutions for cyclic argument systems

Uses fixed point techniques to find categoriser strength values

Shows the semantics satisfies key ranking axioms

Abstract

Recently, ranking-based semantics is proposed to rank-order arguments from the most acceptable to the weakest one(s), which provides a graded assessment to arguments. In general, the ranking on arguments is derived from the strength values of the arguments. Categoriser function is a common approach that assigns a strength value to a tree of arguments. When it encounters an argument system with cycles, then the categoriser strength is the solution of the non-linear equations. However, there is no detail about the existence and uniqueness of the solution, and how to find the solution (if exists). In this paper, we will cope with these issues via fixed point technique. In addition, we define the categoriser-based ranking semantics in light of categoriser strength, and investigate some general properties of it. Finally, the semantics is shown to satisfy some of the axioms that a ranking-based semantics should satisfy.