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Inference and Learning in Probabilistic Argumentation

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Multi-disciplinary Trends in Artificial Intelligence (MIWAI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10607))

Abstract

Inference for Probabilistic Argumentation has been focusing on computing the probability that a given argument or proposition is acceptable. In this paper, we formalize such tasks as computing marginal acceptability probabilities given some evidence and learning probabilistic parameters from a dataset. We then show that algorithms for them can be composed by finely joining a basic PA inference algorithm and existing algorithms for the corresponding tasks in Probabilistic Logic Programming or even Bayesian networks.

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Notes

  1. 1.

    credulous/grounded/stable semantics. There are many other semantics. For a review, readers are referred to, e.g. [1].

  2. 2.

    For convenience, define \(head(r) = l_0\) and \(body(r) = \{l_1,\dots l_n\}\).

  3. 3.

    Elements of \(\lnot \mathcal A_p = \{ \lnot x \mid x \in \mathcal A_p\}\) are called negative probabilistic assumptions.

  4. 4.

    G is a directed acyclic graph over \(\mathcal X = \{X_1, \dots , X_m\}\) and \(\varTheta \) is a set of conditional probability tables (CPTs), one CPT \(\varTheta _{X\mid par(X)}\) for each \(X \in \mathcal X\).

  5. 5.

    Probabilistic parameters are made up for the sake of illustrations and so is the dependency of burglaries on earthquakes.

  6. 6.

    We shall make use of usual notations in FOL such as atoms, literals, Herbrand base, interpretations, etc. without precise definitions.

  7. 7.

    When discussing a PABA inference task, we always refer to an arbitrary but fixed PABA framework \(\mathcal P = (\mathcal A_p, \mathcal N, \mathcal F)\) if not explicitly stated otherwise.

  8. 8.

    That is, a partial world is interpreted as a conjunction of probabilistic assumptions, while a frame is interpreted as a disjunction of partial worlds (In other words, a DNF over probabilistic assumptions).

  9. 9.

    Note that \(\mathcal F_{s'}\) is the ABA framework obtained from \(\mathcal F\) by adding a set of facts \(\{p \leftarrow \mid p \in s'\}\).

  10. 10.

    Note that if \(s = s_1 \cup \dots \cup s_n\) is inconsistent, then s is not a partial world and hence \(s \not \in \mathcal S\).

  11. 11.

    Readers are referred to http://problog.readthedocs.io/en/latest/cli.html for details about ProbLog concrete syntax.

  12. 12.

    obj(.) maps evidences to sentences of the underlying language.

  13. 13.

    Download link of this implementation: http://ict.siit.tu.ac.th/~hung/Prengine/2.0.

  14. 14.

    Prolog-based PLP languages using SLDNF resolution such as ProbLog fail to learn this dataset because SLDNF resolution does not terminate if queried ?-bark, howl.

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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. Universiti Teknologi Brunei, Gadong, Brunei Darussalam

    Somnuk Phon-Amnuaisuk

  2. Universiti Teknologi Brunei, Gadong, Brunei Darussalam

    Swee-Peng Ang

  3. Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Soo-Young Lee

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Hung, N.D. (2017). Inference and Learning in Probabilistic Argumentation. In: Phon-Amnuaisuk, S., Ang, SP., Lee, SY. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2017. Lecture Notes in Computer Science(), vol 10607. Springer, Cham. https://doi.org/10.1007/978-3-319-69456-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-69456-6_1

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  • Online ISBN: 978-3-319-69456-6

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