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Capturing Bipolar Argumentation in Non-flat Assumption-Based Argumentation

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PRIMA 2017: Principles and Practice of Multi-Agent Systems (PRIMA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10621))

Abstract

Bipolar Argumentation Frameworks (BAFs) encompass both attacks and supports among arguments. We study different semantic interpretations of support in BAFs, particularly necessary and deductive support, as well as argument coalitions and a recent proposal by Gabbay. We analyse the relationship of these different notions of support in BAFs with the semantics of a well established structured argumentation formalism, Assumption-Based Argumentation (ABA), which predates BAFs. We propose natural mappings from BAFs into a restricted class of (non-flat) ABA frameworks, which we call bipolar, and prove that the admissible and preferred semantics of these ABA frameworks correspond to the admissible and preferred semantics of the various approaches to BAFs. Motivated by the definition of stable semantics for BAFs, we introduce a novel set-stable semantics for ABA frameworks, and prove that it corresponds to the stable semantics of the various approaches to BAFs. Finally, as a by-product of modelling various approaches to BAFs in bipolar ABA, we identify precise semantic relationships amongst all approaches we consider.

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Notes

  1. 1.

    We added the prefix n-, for ‘necessary’, for ease of reference.

  2. 2.

    We added the prefix d-, for ‘deductive’, for ease of reference. These notions are not to be confused with the ones bearing the same names in [9].

  3. 3.

    Gabbay calls it simply an extension; we use G-admissible for ease of reference.

  4. 4.

    The names ‘d-coalition’ and ‘meta framework’, respectively, are used in [11].

  5. 5.

    Note that \(\Rightarrow ^{-1}\) is irreflexive and transitive too; this condition is required to ensure that \(\mathcal {N}\) is a well-defined AFN (see Sect. 4.1).

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Authors and Affiliations

  1. Department of Computing, Imperial College London, London, UK

    Kristijonas Čyras, Claudia Schulz & Francesca Toni

Authors
  1. Kristijonas Čyras
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  2. Claudia Schulz
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  3. Francesca Toni
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Corresponding authors

Correspondence to Kristijonas Čyras or Claudia Schulz .

Editor information

Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Bo An

  2. Universidade Federal Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil

    Ana Bazzan

  3. Universidade Nova de Lisboa, Caparica, Portugal

    João Leite

  4. Université Côte d’Azur, Sophia Antipolis, France

    Serena Villata

  5. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Leendert van der Torre

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Čyras, K., Schulz, C., Toni, F. (2017). Capturing Bipolar Argumentation in Non-flat Assumption-Based Argumentation. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds) PRIMA 2017: Principles and Practice of Multi-Agent Systems. PRIMA 2017. Lecture Notes in Computer Science(), vol 10621. Springer, Cham. https://doi.org/10.1007/978-3-319-69131-2_23

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  • DOI: https://doi.org/10.1007/978-3-319-69131-2_23

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