Graphical Analysis of Abstract Argumentation Frameworks via Boolean Networks

Van-Giang Trinh, Belaid Benhamou, Vincent Risch

2025

Abstract

Abstract Argumentation Frameworks (AFs) are the key formalism of abstract argumentation, which is one of the main directions in argumentation research. An AF is mainly studied by means of its extensions, defined as subsets of arguments. In this work, we define a Boolean Network (BN) encoding for AFs, where BNs are a simple and efficient mathematical formalism that has a long history of research. We then show that the attack graph of an AF coincides with the influence graph of its encoded BN, and in particular preferred and stable extensions of this AF one-to-one correspond to minimal trap spaces and fixed points of the encoded BN, respectively. We also define a new concept for BNs called complete trap space, then show that complete trap spaces (resp. the percolation of the special trap space where all variables are free) in BNs one-to-one correspond (resp. corresponds) to complete extensions (resp. the grounded extension) in AFs. This connection opens the promising application to graphical analysis of AFs, which is an interesting line of research with many useful applications. More specifically, we use it to explore many new results relating extensions of an AF and (positive or negative) cycles in its attack graph. In particular, we show new upper bounds based on positive feedback vertex sets for the numbers of stable, preferred, and complete extensions.

Paper Citation

in Harvard Style

Trinh V., Benhamou B. and Risch V. (2025). Graphical Analysis of Abstract Argumentation Frameworks via Boolean Networks. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART; ISBN 978-989-758-737-5, SciTePress, pages 745-756. DOI: 10.5220/0013346400003890

in Bibtex Style

@conference{icaart25,
author={Van-Giang Trinh and Belaid Benhamou and Vincent Risch},
title={Graphical Analysis of Abstract Argumentation Frameworks via Boolean Networks},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART},
year={2025},
pages={745-756},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013346400003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART
TI - Graphical Analysis of Abstract Argumentation Frameworks via Boolean Networks
SN - 978-989-758-737-5
AU - Trinh V.
AU - Benhamou B.
AU - Risch V.
PY - 2025
SP - 745
EP - 756
DO - 10.5220/0013346400003890
PB - SciTePress