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Ranking of Arguments Using Social Ranking Choice

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2024)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 1174))

Abstract

In argumentation theory, semantics defined by Dung evaluate subsets of arguments by classifying each into two categories: accepted or rejected. This makes some applications (like online debate) more complex since many accepted arguments can be returned without any insight into the strength of each argument. Conversely to extension-based semantics, ranking-based semantics allow us to determine the strength of acceptability of each argument. However, this approach does not evaluate sets of arguments but each argument individually. In this paper, our goal is to classify the arguments more precisely than just accepting or rejecting them and, therefore, to find a total pre-order of arguments. For this purpose, we will present a method to, first, rank subsets of arguments using extension-based semantics and, then, apply power indices of social choice to this ranking to find a pre-order of arguments. Our approach has the advantage of combining extension-based semantics and lexicographic social ranking. Indeed, given two arguments, it allows us to state which one is more plausible than the other and if they are jointly acceptable or not.

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Notes

  1. 1.

    Because a appears two times in \(\Sigma _1\), zero time in \(\Sigma _2\), one time in \(\Sigma _3\), etc.

  2. 2.

    For instance in order to say that \(a \succeq c\), we compare the two vectors \(\theta \)(a) and \(\theta \)(c) in a lexicographic way (2=2, 0=0, 1=1 but 3>2).

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Acknowledgement

Amélie Leroy, Meltem Öztürk and Gabriella Pigozzi acknowledge financial support from the project THEMIS ANR20-CE23-0018 of the French National Research Agency (ANR).

Author information

Authors and Affiliations

  1. Université Paris Dauphine, PSL Research University, Lamsade, 75016, Paris, France

    Amélie Leroy, Meltem Öztürk & Gabriella Pigozzi

  2. LIMICS (INSERM UMRS 1142), Université Paris 13, Sorbonne Paris Cité, 93017, Bobigny, France

    Karima Sedki

  3. UPMC Université Paris 6, Sorbonne Universités, Paris, France

    Karima Sedki

Authors
  1. Amélie Leroy
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  2. Meltem Öztürk
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  3. Gabriella Pigozzi
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  4. Karima Sedki
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Corresponding author

Correspondence to Karima Sedki .

Editor information

Editors and Affiliations

  1. LIP6, BC169, Sorbonne Université, Paris, France

    Marie-Jeanne Lesot

  2. Departamento de Engenharia Mecânica, University of Lisbon, Lisbon, Portugal

    Susana Vieira

  3. Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

    Marek Z. Reformat

  4. INESC-ID,Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    João Paulo Carvalho

  5. INESC-ID, Av. das Forças Armadas, 1649-026, ISCTE - University Institute of Lisbon, Lisboa, Portugal

    Fernando Batista

  6. LIP6, BC169, Place Jussieu 4, 75005, Sorbonne University, Paris, France

    Bernadette Bouchon-Meunier

  7. Machine Intelligence Institute, 715 North Avenue, Iona Collage, NEW ROCHELLE, NY, USA

    Ronald R. Yager

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Leroy, A., Öztürk, M., Pigozzi, G., Sedki, K. (2024). Ranking of Arguments Using Social Ranking Choice. In: Lesot, MJ., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2024. Lecture Notes in Networks and Systems, vol 1174. Springer, Cham. https://doi.org/10.1007/978-3-031-74003-9_23

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