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How to Manage Supports in Incomplete Argumentation

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Foundations of Information and Knowledge Systems (FoIKS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14589))

Abstract

The growing interest in generalizations of Dung’s abstract argumentation frameworks has recently led to the simultaneous and independent discovery of a combination of two of these generalizations: Bipolar Argumentation Frameworks (BAFs), where a relation representing supports between arguments is added, and Incomplete Argumentation Frameworks (IAFs), where the existence of arguments and attacks may be uncertain, resulting in the so-called Incomplete Bipolar Abstract Argumentation Frameworks (IBAFs). This paper digs deeper into such a combination by: (i) providing a thoughtful analysis of the existing notions of completion (the hypothetical removal of uncertainty used in IBAFs to reason about argument acceptability); (ii) proposing, motivating and studying new notions of completion; (iii) throwing new complexity results on argument acceptability problems associated with IBAFs; (iv) encoding these reasoning problems into a lightweight version of dynamic logic.

The second author benefited from the support of the project AGGREEY ANR-22-CE23-0005 of the French National Research Agency (ANR).

The third author gratefully acknowledges funding from the project PID2020-117871GB-I00 of the Spanish Ministry of Science and Innovation.

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Notes

  1. 1.

    Case 1 (resp. 2) is also called “super-mediated” (resp. “supported”) attack in the literature.

  2. 2.

    These conditions have been first introduced in a very general approach by [13] then reused in the deductive case by [25]. Nevertheless, due to the duality between deductive and necessary supports, they can be trivially extended to the necessary case.

  3. 3.

    We are aware that we use the word “necessary” with two different meanings. We choose not to deviate from the standard terminology in the literature. However it will be clear from the context if we mean “necessary support” or “necessary in all the completions”.

  4. 4.

    Note that this constraint could be relaxed by permitting \(\mathcal {R}^?\) and \(\mathcal {S}^?\) to have a (possibly) non-empty intersection. It will be the subject of future work.

  5. 5.

    This principle can be straightforwardly adapted to necessary support by the mentioned duality.

  6. 6.

    As usual, sceptical reasoning is trivial with \(\sigma = \textsf{ad}\) since the empty set is always an admissible set.

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Acknowledgments

We want to acknowledge our colleague Sylvie Doutre for the very rich exchanges about the topic of this paper.

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Authors and Affiliations

  1. Université Paul Sabatier, IRIT, Toulouse, France

    Marie-Christine Lagasquie-Schiex

  2. Université Paris Cité, LIPADE, 75006, Paris, France

    Jean-Guy Mailly

  3. Complutense University of Madrid, Madrid, Spain

    Antonio Yuste-Ginel

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  1. Marie-Christine Lagasquie-Schiex
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Correspondence to Antonio Yuste-Ginel .

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  1. Leibniz University Hannover, Hanover, Germany

    Arne Meier

  2. TU Wien, Wien, Austria

    Magdalena Ortiz

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Lagasquie-Schiex, MC., Mailly, JG., Yuste-Ginel, A. (2024). How to Manage Supports in Incomplete Argumentation. In: Meier, A., Ortiz, M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2024. Lecture Notes in Computer Science, vol 14589. Springer, Cham. https://doi.org/10.1007/978-3-031-56940-1_18

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