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The Distribution Semantics of Extended Argumentation

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Knowledge and Systems Sciences (KSS 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 780))

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Abstract

The distribution semantics is a de facto approach for integrating logic programming with probability theory, and recently has been applied for the standard abstract argumentation framework. In this paper, we define the distribution semantics for extended argumentation frameworks, and moreover derive inference procedures from existing proof procedures of such extended argumentation frameworks. While doing so we focus on extended argumentation frameworks with attacks on attacks and the inductive defense semantics thereof. However our results can be easily obtained for other extended frameworks and semantics.

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Notes

  1. 1.

    Arguments and attacks are shown as nodes and directed edges respectively.

  2. 2.

    Not all PAF proposals use the distribution semantics (detailed in the paper body).

  3. 3.

    Each argument is annotated with possible worlds it occurs.

  4. 4.

    An attack (C, B) where B is an argument is shown by an arrow \(C \rightarrow B\). An attack \((B,\gamma )\) where \(\gamma \) is an attack is shown by an arrow from B to the arrow showing \(\gamma \).

  5. 5.

    Download link: http://ict.siit.tu.ac.th/~hung/peafengine.

  6. 6.

    preferred/grounded.

  7. 7.

    The PAF proposals of [8, 11, 19] define their semantics in terms of 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.

  8. 8.

    i-preferred/i-grounded.

  9. 9.

    Since \(X \in Att\), the proponent can attack src(X) or X. He should not attack src(X) if this is an argument he moved previously.

  10. 10.

    If \(src(\alpha ) \in SP_i\), then the proponent does not need to re-defend \(src(\alpha )\).

  11. 11.

    An EAF (Arg, Att) is bounded if for each \(X \in Arg \cup Att\), \(Attack_X\) is finite.

  12. 12.

    To compute i-grounded semantics, dispute derivations have to be equipped with slightly different filtering mechanisms which we do not explore here.

  13. 13.

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

  14. 14.

    In this case \(Follow(t, sl) = \{t'\}\) and \(t \xrightarrow [\mathcal O:Attack_X]{\mathcal P:X} t'\).

  15. 15.

    Note that \(W_{src(\alpha )}\) is the set of possible worlds containing \(src(\alpha )\).

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Acknowledgment

This work was funded by Center of Excellence in Intelligent Informatics, Speech and Language Technology and Service Innovation; and Intelligent Informatics and Service Innovation, 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. Tsinghua University, Beijing, China

    Jian Chen

  2. Thammasat University, Bangkadi Muang Pathumthani, Thailand

    Thanaruk Theeramunkong

  3. National Electronics and Computer Technology Center, Pathumthani, Thailand

    Thepachai Supnithi

  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Xijin Tang

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Hung, N.D. (2017). The Distribution Semantics of Extended Argumentation. In: Chen, J., Theeramunkong, T., Supnithi, T., Tang, X. (eds) Knowledge and Systems Sciences. KSS 2017. Communications in Computer and Information Science, vol 780. Springer, Singapore. https://doi.org/10.1007/978-981-10-6989-5_17

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  • DOI: https://doi.org/10.1007/978-981-10-6989-5_17

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