Equilibrium States in Numerical Argumentation Networks

TL;DR

This paper introduces an iterative algorithm for finding equilibrium states in numerical argumentation networks, ensuring convergence to extensions compatible with initial argument values.

Contribution

It proposes a novel iteration formula for numerical argumentation networks and thoroughly investigates its properties and connections to existing techniques.

Findings

The iteration formula converges to compatible extensions.

The method outperforms existing approaches in certain scenarios.

The approach bridges numerical and non-numerical argumentation techniques.

Abstract

Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed by others are thoroughly investigated in this paper.