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Validation of Labelling Algorithms for Abstract Argumentation Frameworks: The Case of Listing Stable Extensions

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Artificial Intelligence and Soft Computing (ICAISC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13588))

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Abstract

An abstract argumentation framework (af for short) is a pair (A, R) where A is a set of abstract arguments and \(R\subseteq A \times A\) is the attack relation. Let \(H=(A,R)\) be an af, \(S \subseteq A\) be a set of arguments and \(S^+ = \{y \mid \exists x\in S \text { with }(x,y)\in R\}\). Then, S is a stable extension in H if and only if \(S^+ = A{\setminus } S\). In this paper, we present a thorough, formal validation of a known labelling algorithm for listing all stable extensions in a given af.

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Authors and Affiliations

  1. Department of Computer Science, German Jordanian University, Amman, Jordan

    Samer Nofal, Amani Abu Jabal, Abdullah Alfarrarjeh & Ismail Hababeh

Authors
  1. Samer Nofal
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  2. Amani Abu Jabal
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  3. Abdullah Alfarrarjeh
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  4. Ismail Hababeh
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Corresponding author

Correspondence to Samer Nofal .

Editor information

Editors and Affiliations

  1. Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Nofal, S., Abu Jabal, A., Alfarrarjeh, A., Hababeh, I. (2023). Validation of Labelling Algorithms for Abstract Argumentation Frameworks: The Case of Listing Stable Extensions. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2022. Lecture Notes in Computer Science(), vol 13588. Springer, Cham. https://doi.org/10.1007/978-3-031-23492-7_36

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  • DOI: https://doi.org/10.1007/978-3-031-23492-7_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23491-0

  • Online ISBN: 978-3-031-23492-7

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