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Explanations of Non-monotonic Inference in Admissibility-Based Abstract Argumentation

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Logic and Argumentation (CLAR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13040))

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Abstract

In this paper, we introduce a formal framework for explaining change of inference in abstract argumentation, in particular in the context of iteratively drawing inferences from a sequence of normal expansions, with a focus on admissible set-based semantics. We then conduct a formal analysis, showing that given an initial argumentation framework and an extension that has been inferred from it, we can guarantee the existence of explanation arguments for the violation of monotony when inferring an extension from a normal expansion of the initial argumentation framework.

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Notes

  1. 1.

    The exception among the four semantics that Dung introduces in his seminal paper is stable semantics, which is not universally defined.

  2. 2.

    In this example, the behavior of \(\mathcal{R}\)’s inference function coincides with preferred semantics [13], to be defined later.

  3. 3.

    We focus on normal expansions because we consider it a reasonable assumption that in an argumentation context, dynamic scenarios are modeled by adding arguments to an argumentation framework without deleting arguments (instead, arguments can be defeated) and without changing the attack relations between existing arguments.

  4. 4.

    https://maven.apache.org/.

  5. 5.

    https://gradle.org/.

  6. 6.

    Let us highlight that we make use of normal expansions and not of the change operations for abstract argumentation frameworks that were introduced by Cayrol et al. [7] because the latter do not support the addition of arbitrarily many arguments as part of a single operation, which makes Baumann’s and Brewka’s normal expansions slightly more convenient in our case.

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Acknowledgments

We thank the anonymous reviewers for their thoughtful and useful feedback. This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.

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Authors and Affiliations

  1. Umeå University, Umeå, Sweden

    Timotheus Kampik

  2. Ericsson Research, Stockholm, Sweden

    Kristijonas Čyras

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  1. Timotheus Kampik
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  2. Kristijonas Čyras
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Correspondence to Timotheus Kampik .

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Editors and Affiliations

  1. Department of Information Engineering, University of Brescia, Brescia, Italy

    Pietro Baroni

  2. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  3. Department of Philosophy (Zhuhai), Sun Yat-sen University, Zhuhai, China

    Yὶ N. Wáng

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Kampik, T., Čyras, K. (2021). Explanations of Non-monotonic Inference in Admissibility-Based Abstract Argumentation. In: Baroni, P., Benzmüller, C., Wáng, Y.N. (eds) Logic and Argumentation. CLAR 2021. Lecture Notes in Computer Science(), vol 13040. Springer, Cham. https://doi.org/10.1007/978-3-030-89391-0_12

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  • DOI: https://doi.org/10.1007/978-3-030-89391-0_12

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