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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))


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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  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 for details about ProbLog concrete syntax.

  12. 12.

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

  13. 13.

    Download link of this implementation:

  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.


  1. Baroni, P., Giacomin, M.: Semantics of abstract argument systems. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 25–44. Springer, Boston (2009). doi:10.1007/978-0-387-98197-0_2

    Chapter  Google Scholar 

  2. Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93(1), 63–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Broda, K., Law, M.: PROBXHAIL: An Abductive-Inductive Algorithm for Probabilistic Inductive Logic Programming (2016)

    Google Scholar 

  4. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–357 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dung, P.M., Kowalski, R.A., Toni, F.: Dialectic proof procedures for assumption-based, admissible argumentation. Artif. Intell. 170(2), 114–159 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dung, P.M., Mancarella, P., Toni, F.: Computing ideal skeptical argumentation. Artif. Intell. 171(10–15), 642–674 (2007)

    Article  MATH  Google Scholar 

  7. Dung, P.M., Son, T.C., Thang, P.M.: Argumentation-based semantics for logic programs with first-order formulae. In: Baldoni, M., Chopra, A.K., Son, T.C., Hirayama, K., Torroni, P. (eds.) PRIMA 2016. LNCS (LNAI), vol. 9862, pp. 43–60. Springer, Cham (2016). doi:10.1007/978-3-319-44832-9_3

    Chapter  Google Scholar 

  8. Dung, P.M., Thang, P.M.: Towards (probabilistic) argumentation for jury-based dispute resolution. In: COMMA 2010, pp. 171–182 (2010)

    Google Scholar 

  9. Fierens, D., Van Den Broeck, G., Renkens, J., Shterionov, D., Gutmann, B., Thon, I., Janssens, G., De Raedt, L.: Inference and learning in probabilistic logic programs using weighted boolean formulas. Theory Pract. Logic Program. 15(3), 358–401 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gabbay, D.M., Rodrigues, O.: Probabilistic Argumentation: An Equational Approach, CoRR (2015)

    Google Scholar 

  11. Hung, N.D.: Inference procedures and engine for probabilistic argumentation. Int. J. Approx. Reason. 90, 163–191 (2017)

    Article  MathSciNet  Google Scholar 

  12. Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approx. Reason. 54(1), 47–81 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 1–16. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29184-5_1

    Chapter  Google Scholar 

  14. Poole, D.: Logic programming, abduction and probability. New Gen. Comput. 11(3), 377 (1993)

    Article  MATH  Google Scholar 

  15. Poole, D.: The independent choice logic and beyond. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic Inductive Logic Programming. LNCS, vol. 4911, pp. 222–243. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78652-8_8

    Chapter  Google Scholar 

  16. Sato, T.: A statistical learning method for logic programs with distribution semantics. In: Logic Programming, Proceedings of the Twelfth International Conference on Logic Programming, Tokyo, Japan, 13–16 June 1995, pp. 715–729 (1995)

    Google Scholar 

  17. Sato, T., Kameya, Y.: New advances in logic-based probabilistic modeling by PRISM. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic Inductive Logic Programming. LNCS, vol. 4911, pp. 118–155. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78652-8_5

    Chapter  Google Scholar 

  18. Thang, P.M.: Dialectical proof procedures for probabilistic abstract argumentation. In: Baldoni, M., Chopra, A.K., Son, T.C., Hirayama, K., Torroni, P. (eds.) PRIMA 2016. LNCS (LNAI), vol. 9862, pp. 397–406. Springer, Cham (2016). doi:10.1007/978-3-319-44832-9_27

    Chapter  Google Scholar 

  19. Thimm, M.: A probabilistic semantics for abstract argumentation. In: ECAI, vol. 242, pp. 750–755. ISO Press (2012)

    Google Scholar 

  20. Vennekens, J., Denecker, M., Bruynooghe, M.: Cp-logic: a language of causal probabilistic events and its relation to logic programming. Theory Pract. Logic Program. 9(3), 245–308 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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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.

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