Abstract
We propose an extension of Poole’s independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This represents a conservative approach to probabilistic logic programming achieved by considering all the mass functions consistent with the probabilistic facts. This allows to model tasks for which independence among some probabilistic choices cannot be assumed, and a specific dependence model cannot be assessed. Preliminary tests on an object ranking application show that, despite the loose underlying assumptions, informative inferences can be extracted.
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Notes
- 1.
We use semicolons to separate the elements of an array and commas to separate the two bounds of an interval.
- 2.
Here we use the solver [12], freely available at http://psat.sourceforge.net.
- 3.
A XOR rewrites as a disjunction together with negations of pairwise conjunctions.
References
Andersen, K.A., Hooker, J.N.: Bayesian logic. Decis. Support Syst. 11(2), 191–210 (1994)
Apt, K.R., Bezem, M.: Acyclic programs. New Gener. Comput. 9(3), 335–363 (1991)
Augustin, T., Coolen, F., de Cooman, G., Troffaes, M.: Introduction to Imprecise Probabilities. Wiley, Hoboken (2014)
Carpenter, B., et al.: Stan: a probabilistic programming language. J. Stat. Softw. 20, 1–37 (2016)
Cozman, F., de Campos, C., da Rocha, J.C.: Probabilistic logic with independence. Int. J. Approx. Reason. 49(1), 3–17 (2008)
Cozman, F., di Ianni, L.: Probabilistic satisfiability and coherence checking through integer programming. Int. J. Approx. Reason. 58, 57–70 (2015)
Cozman, F., Mauá, D.: On the semantics and complexity of probabilistic logic programs. J. Artif. Intell. Res. 60, 221–262 (2017)
De Raedt, L.: Applications of probabilistic logic programming. In: International Conference on Inductive Logic Programming (2015)
De Raedt, L., Kimmig, A.: Probabilistic (logic) programming concepts. Mach. Learn. 100(1), 5–47 (2015)
De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: a probabilistic Prolog and its application in link discovery. In: International Joint Conference on Artificial Intelligence, pp. 2462–2467 (2007)
Fierens, D., et al.: Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theory Pract. Log. Program. 15(3), 358–401 (2015)
Finger, M., De Bona, G.: Probabilistic satisfiability: logic-based algorithms and phase transition. In: International Joint Conference on Artificial Intelligence, pp. 528–533 (2011)
Flesca, S., Furfaro, F., Parisi, F.: Consistency checking and querying in probabilistic databases under integrity constraints. J. Comput. Syst. Sci. 80(7), 1448–1489 (2014)
Fuhr, N.: Probabilistic datalog: a logic for powerful retrieval methods. In: International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 282–290. ACM (1995)
Fuhr, N.: Probabilistic datalog: implementing logical information retrieval for advanced applications. J. Assoc. Inf. Sci. Technol. 51(2), 95–110 (2000)
Fürnkranz, J., Hüllermeier, E.: Preference learning: an introduction. In: Fürnkranz, J., Hüllermeier, E. (eds.) Preference Learning, pp. 1–17. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14125-6_1
Georgakopoulos, G., Kavvadias, D., Papadimitriou, C.: Probabilistic satisfiability. J. Complex. 4(1), 1–11 (1988)
Haenni, R., Romeijn, J.W., Wheeler, G., Williamson, J.: Probabilistic Logics and Probabilistic Networks, vol. 350. Springer, Dordrecht (2010). https://doi.org/10.1007/978-94-007-0008-6
Janhunen, T.: Representing normal programs with clauses. In: European Conference on Artificial Intelligence, pp. 358–362. IOS Press (2004)
Levi, I.: The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. MIT press, Cambridge (1983)
Lukasiewicz, T.: Probabilistic logic programming. In: European Conference on Artificial Intelligence, pp. 388–392 (1998)
Lukasiewicz, T.: Probabilistic description logic programs. Int. J. Approx. Reason. 45(2), 288–307 (2007)
Michels, S., Hommersom, A., Lucas, P.J., Velikova, M.: A new probabilistic constraint logic programming language based on a generalised distribution semantics. Artif. Intell. 228, 1–44 (2015)
Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Inf. Comput. 101(2), 150–201 (1992)
Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)
Poole, D.: Probabilistic Horn abduction and Bayesian networks. Artif. Intell. 64(1), 81–129 (1993)
Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1), 7–56 (1997)
Sato, T.: A statistical learning method for logic programs with distribution semantics. In: International Conference on Logic Programming, pp. 715–729 (1995)
Vennekens, J., Verbaeten, S.: Logic programs with annotated disjunctions. Technical report CW 368, K.U.Leuven (2003)
Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic programs with annotated disjunctions. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 431–445. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27775-0_30
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Antonucci, A., Facchini, A. (2018). A Credal Extension of Independent Choice Logic. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_3
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