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A Generalization of Probabilistic Argumentation with Dempster-Shafer Theory

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KI 2017: Advances in Artificial Intelligence (KI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10505))

Abstract

One of the first (and key) steps in analyzing an argumentative exchange is to reconstruct complete arguments from utterances which may carry just enthymemes. In this paper, using legal argument from analogy, we argue that in this reconstruction process interpreters may have to deal with a kind of uncertainty that can be appropriately represented in Dempster-Shafer (DS) theory rather than classical probability theory. Hence we generalize and relax existing frameworks of Probabilistic Argumentation (PAF), which are currently based on classical probability theory, by what we refer to as DS-based Argumentation framework (DSAF). Concretely, we first define a DSAF form and semantics by generalizing existing PAF form and semantics. We then present a method to translate existing proof procedures for standard Abstract Argumentation into DSAF inference procedures. Finally we provide a Prolog-based implementation of the resulted DSAF inference procedures.

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Notes

  1. 1.

    Conventionally, arguments are shown as nodes and attacks as directed edges.

  2. 2.

    http://ict.siit.tu.ac.th/~hung/dsafengine/appendix.pdf.

  3. 3.

    Preferred/grounded.

  4. 4.

    As discussed in [6], not all PAF proposals adopt this distribution semantics. For example the PAF proposals of [7, 8, 20] define their semantics in terms of some rational conditions on Probabilistic Distribution Function (PDF) \(f: Arg \rightarrow [0,1]\), for f(A) to represent some value of argument A, which may not relate to the acceptability of A. In fact f(A) has been given diverse interpretations, from the truth of A, the reliability of A, the probability of A being effective, the belief degree put into A, to whatever measure that can be attached to A as an argument [7].

  5. 5.

    For \(X \in Arg\), \(Attack_{X} \triangleq \{Y \in Arg \mid (Y,X) \in Att\}\) and \(Attacked_{X} \triangleq \{Y \in Arg \mid (X,Y) \in Att\}\).

  6. 6.

    Note that \(W_{sem}(A) \subseteq W(A)\).

  7. 7.

    Other legal academics give different reconstructions of A, e.g. Brewer [1].

  8. 8.

    In this section we always refer to an arbitrary but fixed DSAF framework \(\mathcal D = (\mathcal F, \mathcal W, m)\) with \(\mathcal F = (Arg, Att)\) if not explicitly stated otherwise.

  9. 9.

    Because of the lack of space, we present only the computation of \(Bl_{sem}(A)\). Note that our Prolog-based implementation can compute both \(Bl_{pr}(A)\) and \(Pl_{pr}(A)\).

  10. 10.

    Recall that \(X \in 2^{\mathcal W}\) is a focal element of m iff \(m(X) > 0\).

  11. 11.

    In this case \(Follow_{\mathcal F}(t,sl)\) is a singleton set.

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Acknowledgment

This work was partially funded by: (1) Center of Excellence in Intelligent Informatics, Speech and Language Technology and Service Innovation (CILS), Thammasat University; and (2) Intelligent Informatics and Service Innovation (IISI), SIIT, Thammasat University.

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Authors and Affiliations

  1. Sirindhorn International Institute of Technology, Pathum Thani, Thailand

    Nguyen Duy Hung

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  1. Nguyen Duy Hung
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Correspondence to Nguyen Duy Hung .

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Editors and Affiliations

  1. Fakultät für Informatik, Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. FB Informatik, TU Darmstadt, Darmstadt, Hessen, Germany

    Johannes Fürnkranz

  3. FB Informatik, Universität Koblenz, Koblenz, Rheinland-Pfalz, Germany

    Matthias Thimm

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Hung, N.D. (2017). A Generalization of Probabilistic Argumentation with Dempster-Shafer Theory. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds) KI 2017: Advances in Artificial Intelligence. KI 2017. Lecture Notes in Computer Science(), vol 10505. Springer, Cham. https://doi.org/10.1007/978-3-319-67190-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-67190-1_12

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