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Progressive Inference Algorithms for Probabilistic Argumentation

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PRIMA 2018: Principles and Practice of Multi-Agent Systems (PRIMA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11224))

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Abstract

We develop a progressive inference approach for Probabilistic Argumentation, and then implement obtained algorithms for three standard semantics: the credulous, the ideal, and the skeptical preferred semantics. Like their exact counterparts, these algorithms can be destined to compute the exact answers, however while doing so, they can output immediate answers increasingly close to the exact ones.

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Notes

  1. 1.

    PABA and ABA are formally defined in Sect. 2.

  2. 2.

    Shorthands for \({{\varvec{b}}}urglary, {{\varvec{e}}}arthquake, {{\varvec{p1}}}\_alarm, {{\varvec{p2}}}\_alarm, {{\varvec{p3}}}\_alarm\) respectively.

  3. 3.

    The dependency of burglaries on earthquakes as well as parameter values are made up for the sake of illustrations.

  4. 4.

    credulous/grounded/ideal semantics.

  5. 5.

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

  6. 6.

    Note that any admissible set of assumptions is a subset of some preferred set of assumptions; and any preferred set of assumptions is also admissible.

  7. 7.

    An ABA \({\mathcal {F}}\) is finitary if for each node in the dependency graph of \({\mathcal {F}}\), there is a finite number of nodes reachable from it; and positively acyclic if in the dependency graph of \({\mathcal {F}}\), there is no infinite directed path consisting solely non-assumption nodes.

  8. 8.

    A probabilistic assumption is an element of \({\mathcal {A}}_p \cup \lnot {\mathcal {A}}_p\). A proposition not in \({\mathcal {A}}_p \cup \lnot {\mathcal {A}}_p\) is called a non-probabilistic proposition.

  9. 9.

    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 \(X \in \mathcal X\).

  10. 10.

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

  11. 11.

    We use Problog [8] syntax.

  12. 12.

    We have developed sound translation schemes for the ideal semantics and skeptical preferred semantics. However they can not be presented here due to lack of space.

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Acknowledgment

This work is supported by SIIT Young Researcher Grant, contract no SIIT 2017-YRG-NH02.

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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. School of Computing and Information Systems, University of Melbourne, Melbourne, Australia

    Tim Miller

  2. Department of Computer Science, University of Aberdeen, Aberdeen, UK

    Nir Oren

  3. Artificial Intelligence Research Center (AIRC), National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Yuko Sakurai

  4. Artificial Intelligence Research Center (AIRC), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan

    Itsuki Noda

  5. University of Otago, Dunedin, New Zealand

    Bastin Tony Roy Savarimuthu

  6. Computer Science Department, New Mexico State University, Las Cruces, USA

    Tran Cao Son

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Hung, N.D. (2018). Progressive Inference Algorithms for Probabilistic Argumentation. In: Miller, T., Oren, N., Sakurai, Y., Noda, I., Savarimuthu, B.T.R., Cao Son, T. (eds) PRIMA 2018: Principles and Practice of Multi-Agent Systems. PRIMA 2018. Lecture Notes in Computer Science(), vol 11224. Springer, Cham. https://doi.org/10.1007/978-3-030-03098-8_23

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  • DOI: https://doi.org/10.1007/978-3-030-03098-8_23

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  • Online ISBN: 978-3-030-03098-8

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