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Identifying Necessary and Sufficient Conditions for the Enforcement Problem of Argumentation Frameworks

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PRIMA 2022: Principles and Practice of Multi-Agent Systems (PRIMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13753))

Abstract

In the dynamics research of argumentation frameworks (AFs), the enforcement problem deals with changing an AF for the purpose of ensuring that a certain set of desired arguments becomes (part of) an extension. In this paper we focus on expansions of an AF where solely the addition of new arguments and attacks is allowed and the original framework remains unchanged. Existing results about the enforcement problem under strong and normal expansion are all sufficient conditions. We argue that necessary and sufficient conditions are essential concerning the solvability of the enforcement problem. Specifically, two necessary and sufficient conditions are identified for the non-strict enforcement in respectively the odd-length cycle free and the even-length cycle free AFs under strong expansion. This result can be used to determine that when new arguments satisfying the condition are unavailable, enforcing the desired set simply becomes unsolvable.

This work was supported in part by funding from the National Natural Science Foundation of China (61621003).

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Authors and Affiliations

  1. Key Laboratory of MADIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Huan Zhang & Songmao Zhang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Huan Zhang

Authors
  1. Huan Zhang
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  2. Songmao Zhang
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Correspondence to Huan Zhang .

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Editors and Affiliations

  1. Özyeğin University, Istanbul, Turkey

    Reyhan Aydoğan

  2. Universitat Politècnica de València, Valencia, Spain

    Natalia Criado

  3. Université Paris-Dauphine, Paris, France

    Jérôme Lang

  4. Universitat Politècnica de València, Valencia, Spain

    Victor Sanchez-Anguix

  5. King's College London, London, UK

    Marc Serramia

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Zhang, H., Zhang, S. (2023). Identifying Necessary and Sufficient Conditions for the Enforcement Problem of Argumentation Frameworks. In: Aydoğan, R., Criado, N., Lang, J., Sanchez-Anguix, V., Serramia, M. (eds) PRIMA 2022: Principles and Practice of Multi-Agent Systems. PRIMA 2022. Lecture Notes in Computer Science(), vol 13753. Springer, Cham. https://doi.org/10.1007/978-3-031-21203-1_44

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  • DOI: https://doi.org/10.1007/978-3-031-21203-1_44

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  • Online ISBN: 978-3-031-21203-1

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