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A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation

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PRIMA 2019: Principles and Practice of Multi-Agent Systems (PRIMA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11873))

Abstract

Computing acceptability semantics of abstract argumentation frameworks is receiving increasing attention. Large-scale instances, with a clustered structure, have shown particularly difficult to compute. This paper presents a distributed algorithm, AFDivider, that enumerates the acceptable sets under several labelling-based semantics. This algorithm starts with cutting the argumentation framework into clusters thanks to a spectral clustering method, before computing simultaneously in each cluster parts of the labellings. This algorithm is proven to be sound and complete for the stable, complete and preferred semantics, and empirical results are presented.

Supported by the ANR-11-LABEX-0040-CIMI project of the CIMI International Centre for Mathematics and Computer Science in Toulouse.

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Notes

  1. 1.

    International Competition on Computational Models of Argumentation (ICCMA) http://argumentationcompetition.org/.

  2. 2.

    The density in an argumentation graph is the ratio “number of existing attacks” over “number of potential attacks” (this last number is equal to \(n^2\) with n being the number of arguments).

  3. 3.

    According to [23], the set of arguments is not necessarily finite. Nevertheless, in this paper, it is reasonable to assume that it is finite.

  4. 4.

    There exist algorithms, such as Krylov-Schur method, able to compute eigenvectors from smallest to greatest eigenvalue and to stop at any wanted step (e.g. the number of vectors found). With such an algorithm it is not necessary to find all the solutions as we are interested only in the small eigenvalues.

  5. 5.

    Given n observations, a KMeans algorithm aims to partition the n observations into k subsets such that the distance between the elements inside each subset is minimized. Here we have \(n=5\) and \(k=2\).

  6. 6.

    To highlight the necessity of the maximality check, let us take as minimal example the AF defined by \(\langle \{a,b\}, \{(a,b),(b,a)\} \rangle \) and a partition of it in which each argument is in a different cluster. For each cluster, we will have three possible labellings as the inward attack source may be labelled \({\texttt {\textit{in}}}\), \({\texttt {\textit{out}}}\) or \({{\texttt {\textit{und}}}}\) in the other cluster. The reunifying phase will thus admit the labelling \(\{(a, {{\texttt {\textit{und}}}}), (b,{{\texttt {\textit{und}}}})\}\) which is not a preferred labelling.

  7. 7.

    amador-transit_20151216_1706.gml.80.apx and basin-or-us.gml.20.apx are instances which come from real data of the traffic domain.

  8. 8.

    Note that Pyglaf is also multi-core. Moreover, when we compare Pyglaf and AFDivider, we use a computer with the same number of cores. So the fact that there is a more important parallelization in AFDivider (so more threads) is not what explains the difference in runtime for the preferred semantics.

  9. 9.

    For an overview on the different AF splitting possibilities see [8].

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Authors and Affiliations

  1. IRIT, UT1-UT3, Toulouse, France

    Sylvie Doutre, Mickaël Lafages & Marie-Christine Lagasquie-Schiex

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  1. Sylvie Doutre
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  2. Mickaël Lafages
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  3. Marie-Christine Lagasquie-Schiex
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Correspondence to Marie-Christine Lagasquie-Schiex .

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Editors and Affiliations

  1. Università degli Studi di Torino, Turin, Italy

    Matteo Baldoni

  2. Utrecht University, Utrecht, The Netherlands

    Mehdi Dastani

  3. Zhejiang University, Hangzhou, China

    Beishui Liao

  4. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Yuko Sakurai

  5. University of Texas at Dallas, Richardson, TX, USA

    Rym Zalila Wenkstern

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Doutre, S., Lafages, M., Lagasquie-Schiex, MC. (2019). A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham. https://doi.org/10.1007/978-3-030-33792-6_6

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  • DOI: https://doi.org/10.1007/978-3-030-33792-6_6

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