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The Matrix Approach for Abstract Argumentation Frameworks

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Theory and Applications of Formal Argumentation (TAFA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9524))

Abstract

Matrices and the operation of dual interchange are introduced into the study of Dung’s argumentation frameworks. It is showed that every argumentation framework can be represented by a matrix, and the basic extensions (such as admissible, stable, complete) can be determined by sub-blocks of its matrix. In particular, an efficient approach for determining the basic extensions has been developed using two types of standard matrix. Furthermore, we develop the topic of matrix reduction along two different lines. The first one enables to reduce the matrix into a less order matrix playing the same role for the determination of extensions. The second one enables to decompose an extension into several extensions of different sub-argumentation frameworks. It makes us not only solve the problem of determining grounded and preferred extensions, but also obtain results about dynamics of argumentation frameworks.

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Notes

  1. 1.

    strictly speaking, it should be denoted by \(M_{AF}(i_{1}, i_{2}, ..., i_{n})\).

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Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, China

    Yuming Xu

  2. IRIT, University of Toulouse, Toulouse, France

    Claudette Cayrol

Authors
  1. Yuming Xu
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  2. Claudette Cayrol
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Corresponding author

Correspondence to Claudette Cayrol .

Editor information

Editors and Affiliations

  1. King's College London, London, United Kingdom

    Elizabeth Black

  2. Strand Building;Strand Campus, King's College London, London, United Kingdom

    Sanjay Modgil

  3. Department of Computing Science, University of Aberdeen, Aberdeen, United Kingdom

    Nir Oren

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© 2015 Springer International Publishing Switzerland

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Xu, Y., Cayrol, C. (2015). The Matrix Approach for Abstract Argumentation Frameworks. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2015. Lecture Notes in Computer Science(), vol 9524. Springer, Cham. https://doi.org/10.1007/978-3-319-28460-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-28460-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28459-0

  • Online ISBN: 978-3-319-28460-6

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