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An Axiomatic Approach to Support in Argumentation

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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

In the context of bipolar argumentation (argumentation with two kinds of interaction, attacks and supports), we present an axiomatic approach for taking into account a special interpretation of the support relation, the necessary support. We propose constraints that should be imposed to a bipolar argumentation system using this interpretation. Some of these constraints concern the new attack relations, others concern acceptability. We extend basic Dung’s framework in different ways in order to propose frameworks suitable for encoding these constraints. By the way, we propose a formal study of properties of necessary support.

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Notes

  1. 1.

    if and only if.

  2. 2.

    such that.

  3. 3.

    with respect to.

  4. 4.

    This is an abuse of language since, stricly speaking, this is an edge-labeled graph (with two labels) rather than a directed graph.

  5. 5.

    Irreflexivity has also been considered for instance in [21, 22].

  6. 6.

    Note that if \(c {\mathbf{R}_{\text{ sup }}}b\) and \(c {\mathbf{R}_{\text{ att }}}b\), as an extension must be conflict-free, there is no extension containing both c and b, so the constraint trivially holds. Some works, as for instance [10], exclude the case when \(c {\mathbf{R}_{\text{ sup }}}b\) and \(c {\mathbf{R}_{\text{ att }}}b\).

  7. 7.

    Due to Proposition 1, coherent may be replaced by conflict-free.

  8. 8.

    Note that enforcing coherence makes the set C useless due to Proposition 2.

  9. 9.

    Note that it is an argumentation system in dung’s sense.

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Authors and Affiliations

  1. IRIT-UPS, Toulouse, France

    Claudette Cayrol & Marie-Christine Lagasquie-Schiex

Authors
  1. Claudette Cayrol
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  2. Marie-Christine Lagasquie-Schiex
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Correspondence to Marie-Christine Lagasquie-Schiex .

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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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Cayrol, C., Lagasquie-Schiex, MC. (2015). An Axiomatic Approach to Support in Argumentation. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-28460-6_5

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