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An Argumentative Characterization of Disjunctive Logic Programming

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Progress in Artificial Intelligence (EPIA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11805))

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Abstract

This paper extends the result of Caminada and Schulz [6, 7] by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs. For this, we incorporate a previous work of ours (see [19, 20]), in which reasoning with assumption-based argumentation frameworks is based on certain core logics and the strict/defeasible assumptions may be arbitrary formulas in those logics. In our case, the core logic respects some inference rules for disjunction, which allows disjunctions in the heads of the programs’ rules to be handled properly.

This work is supported by the Israel Science Foundation (grant number 817/15). The first author is also partially supported by the Sofja Kovalevskaja award of the Alexander von Humboldt Foundation, funded by the German Ministry for Education and Research, the FCT projects RIVER (PTDC/CCI-COM/30952/2017) and NOVA LINCS (UID/CEC/04516/2013).

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Notes

  1. 1.

    In many presentations of assumption-based argumentation, extensions are required to be closed, i.e. they should contain any assumption they imply. Since the translation below will always give rise to the so-called flat ABFs (that is, ABFs for which a set of assumptions can never imply assumptions outside the set; See Note 3 below), closure of extensions is trivially satisfied.

  2. 2.

    Since the underlying language consists only of negated atoms or formulas of the form of program rules (see Definition 5), this definition indeed covers all the possible sets \(\mathcal{S}\) of \(\mathcal{L}\)-formulas.

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Authors and Affiliations

  1. Institute of Philosophy II, Ruhr University Bochum, Bochum, Germany

    Jesse Heyninck

  2. School of Computer Science, The Academic College of Tel-Aviv, Tel Aviv-Yafo, Israel

    Ofer Arieli

Authors
  1. Jesse Heyninck
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  2. Ofer Arieli
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Correspondence to Ofer Arieli .

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Editors and Affiliations

  1. INESC-TEC, University of Trás-os-Montes and Alto Douro, Vila Real, Portugal

    Paulo Moura Oliveira

  2. University of Minho, Braga, Portugal

    Paulo Novais

  3. LIACC/UP, University of Porto, Porto, Portugal

    Luís Paulo Reis

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Heyninck, J., Arieli, O. (2019). An Argumentative Characterization of Disjunctive Logic Programming. In: Moura Oliveira, P., Novais, P., Reis, L. (eds) Progress in Artificial Intelligence. EPIA 2019. Lecture Notes in Computer Science(), vol 11805. Springer, Cham. https://doi.org/10.1007/978-3-030-30244-3_44

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  • DOI: https://doi.org/10.1007/978-3-030-30244-3_44

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