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International Workshop on Theorie and Applications of Formal Argumentation

TAFA 2013: Theory and Applications of Formal Argumentation pp 158–175Cite as

The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8306))

Abstract

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given.

  • The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set).

  • The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument.

  • The Center problem asks whether, given two extensions of distance k, whether there is a “center” extension that is of distance at most k − 1 from both given extensions.

We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results cover several different semantics, including admissible, complete, preferred, semi-stable and stable semantics.

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Author information

Authors and Affiliations

  1. CNRS, LAMSADE, Paris, France

    Eun Jung Kim

  2. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Sebastian Ordyniak

  3. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Stefan Szeider

Authors
  1. Eun Jung Kim
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  2. Sebastian Ordyniak
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  3. Stefan Szeider
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Editor information

Editors and Affiliations

  1. Department of Informatics, King’s College London, Strand, WC2R 2LS, London, UK

    Elizabeth Black

  2. King’s College London, Strand, WC2R 2LS, London, UK

    Sanjay Modgil

  3. Department of Computing Science, University of Aberdeen, AB24 3UE, Aberdeen, UK

    Nir Oren

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Kim, E.J., Ordyniak, S., Szeider, S. (2014). The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2013. Lecture Notes in Computer Science(), vol 8306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54373-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-54373-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54372-2

  • Online ISBN: 978-3-642-54373-9

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