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Verification in Attack-Incomplete Argumentation Frameworks

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Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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Abstract

We tackle the problem of expressing incomplete knowledge about the attack relation in abstract argumentation frameworks. In applications, incomplete argumentation frameworks may arise as intermediate states in an elicitation process, when merging different beliefs about an argumentation framework’s state, or in cases where the complete information cannot be fully obtained. To this end, we employ a model introduced by Cayrol et al. [10] and analyze the question of whether certain justification criteria are possibly (or necessarily) fulfilled, i.e., whether they are fulfilled in some (or in every) completion of the incomplete argumentation framework. We formally extend the definition of existing criteria to these incomplete argumentation frameworks and provide characterization and complexity results for variants of the verification problem.

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Notes

  1. 1.

    Besides four faculties of HHU Düsseldorf and the Fachhochschule für öffentliche Verwaltung NRW, the practice partners of this project include registered societies, limited liability companies, and the municipal councils of Köln, Bonn, and Münster, among others. We refer to the website http://www.fortschrittskolleg.de for more details.

  2. 2.

    Other models of incomplete-information settings in voting include dynamic social choice with evolving preferences [29] and online manipulation in sequential elections [21].

  3. 3.

    In addition to these semantics we also use conflict-freeness and admissibility as criteria. While these are generally not considered to be semantics, we will not always explicitly distinguish between semantics and basic properties for the sake of conciseness.

  4. 4.

    Unlike the concepts of credulous and skeptical acceptance in the related literature, which denote membership of arguments in, respectively, some and all extensions of a specific argumentation framework, our notions of properties holding possibly and necessarily describe criteria holding in, respectively, some and all argumentation frameworks (i.e., completions), and are therefore settled one level of abstraction higher.

  5. 5.

    A set of arguments is \( RI \) -preferred if it is maximal among all necessarily admissible sets, where \( R \widehat{=} \mathscr {R}^{+}\) and \( I \widehat{=} \mathscr {R}^{?}\) in our notation.

  6. 6.

    For formal definitions of these criteria, see their work [10].

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Acknowledgments

We thank the anonymous reviewers for their helpful comments. This work was supported in part by an NRW grant for gender-sensitive universities and the project “Online Participation,” both funded by the NRW Ministry for Innovation, Science, and Research.

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Authors and Affiliations

  1. Heinrich-Heine-Universität Düsseldorf, 40225, Düsseldorf, Germany

    Dorothea Baumeister, Daniel Neugebauer & Jörg Rothe

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  1. Dorothea Baumeister
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  2. Daniel Neugebauer
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Correspondence to Daniel Neugebauer .

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  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Baumeister, D., Neugebauer, D., Rothe, J. (2015). Verification in Attack-Incomplete Argumentation Frameworks. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_21

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