An action language-based formalisation of an abstract argumentation framework

TL;DR

This paper introduces a new formal framework for abstract argumentation that incorporates the order of argument enunciation, enabling unique outcome determination and addressing properties like termination and completeness.

Contribution

It presents an action language-based formalisation that models argument order, providing a novel approach to derive unique dialogue outcomes in abstract argumentation.

Findings

The framework ensures termination and correctness.

It guarantees a unique extension for dialogues considering argument order.

A modified transformation verifies a specific completeness property.

Abstract

An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome of this dialogue. In this paper, we propose a new framework for modelling abstract argumentation graphs, a model that incorporates the order of enunciation of arguments. By taking this order into account, we have the means to deduce a unique outcome for each dialogue, called an extension. We also establish several properties, such as termination and correctness, and discuss two notions of completeness. In particular, we propose a modification of the previous transformation based on a "last enunciated last updated" strategy, which verifies the second form of completeness.