Abstract
We present a novel approach that uses an iterative deepening algorithm in order to perform probabilistic logic inference for ProbLog, a probabilistic extension of Prolog. The most used inference method for ProbLog is exact inference combined with tabling. Tabled exact inference first collects a set of SLG derivations which contain the probabilistic structure of the ProbLog program including the cycles. At a second step, inference requires handling these cycles in order to create a non-cyclic Boolean representation of the probabilistic information. Finally, the Boolean representation is compiled to a data structure where inference can be performed in linear time. Previous work has illustrated that there are two limiting factors for ProbLog’s exact inference. The first factor is the target compilation language and the second factor is the handling of the cycles. In this paper, we address the second factor by presenting an iterative deepening algorithm which handles cycles and produces solutions to problems that previously ProbLog was not able to solve. Our experimental results show that our iterative deepening approach gets approximate bounded values in almost all cases and in most cases we are able to get the exact result for the same or one lower scaling factor.
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Notes
- 1.
MetaProbLog is an implementation of the ProbLog semantics and can be found at: www.dcc.fc.up.pt/metaproblog. Other implementations are ProbLog1 and ProbLog2 and can be found at: http://dtai.cs.kuleuven.be/problog.
- 2.
Q1 = p(hgnc_983,hgnc_620), \(\overline{Q1}\) = p(hgnc_620,hgnc_983),
Q2 = p(hgnc_582,hgnc_620), \(\overline{Q2}\) = p(hgnc_620,hgnc_582),
Q3 = p(hgnc_983,hgnc_582) and \(\overline{Q3}\) = p(hgnc_582,hgnc_983).
References
Akers, S.B.: Binary decision diagrams. IEEE Trans. Comput. 27(6), 509–516 (1978)
Bragaglia, S., Riguzzi, F.: Approximate inference for logic programs with annotated disjunctions. In: Frasconi, P., Lisi, F.A. (eds.) ILP 2010. LNCS, vol. 6489, pp. 30–37. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21295-6_7
Chen, W., Warren, D.S.: Tabled evaluation with delaying for general logic programs. J. ACM 43(1), 20–74 (1996)
Côrte-Real, J., Mantadelis, T., de Castro Dutra, I., Rocha, R.: SkILL - a stochastic inductive logic learner. In: International Conference on Machine Learning and Applications (ICMLA), pp. 555–558 (2015)
Costa, V.S., Rocha, R., Damas, L.: The YAP prolog system. Theory Pract. Logic Program. (TPLP) 12(1–2), 5–34 (2012)
Darwiche, A.: SDD: a new canonical representation of propositional knowledge bases. In: International Joint Conference on Artificial Intelligence (IJCAI), vol. 2, pp. 819–826 (2011)
Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Reason. (JAIR) 17, 229–264 (2002)
Kimmig, A., Demoen, B., De Raedt, L., Santos Costa, V., Rocha, R.: On the implementation of the probabilistic logic programming language ProbLog. Theory Pract. Logic Program. (TPLP) 11(2–3), 235–262 (2011)
Lierler, Y., Maratea, M.: Cmodels-2: SAT-based answer set solver enhanced to non-tight programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS, vol. 2923, pp. 346–350. Springer, Heidelberg (2003). doi:10.1007/978-3-540-24609-1_32
Mantadelis, T., Janssens, G.: Dedicated tabling for a probabilistic setting. In: International Conference on Logic Programming (ICLP). Leibniz International Proceedings in Informatics (LIPIcs), vol. 7, pp. 124–133 (2010)
Mantadelis, T., Rocha, R., Kimmig, A., Janssens, G.: Preprocessing Boolean formulae for BDDs in a probabilistic context. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS, vol. 6341, pp. 260–272. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15675-5_23
Mantadelis, T., Shterionov, D., Janssens, G.: Compacting Boolean formulae for inference in probabilistic logic programming. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds.) LPNMR 2015. LNCS, vol. 9345, pp. 425–438. Springer, Cham (2015). doi:10.1007/978-3-319-23264-5_35
Pfeffer, A.: IBAL: a probabilistic rational programming language. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 733–740 (2001)
Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1–2), 107–136 (2006)
Riguzzi, F., Swift, T.: The PITA system: tabling and answer subsumption for reasoning under uncertainty. Comput. Res. Repository abs/1107.4747 (2011)
Sato, T., Kameya, Y.: PRISM: a language for symbolic-statistical modeling. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 1330–1339 (1997)
Shterionov, D., Janssens, G.: Implementation and performance of probabilistic inference pipelines. In: Pontelli, E., Son, T.C. (eds.) PADL 2015. LNCS, vol. 9131, pp. 90–104. Springer, Cham (2015). doi:10.1007/978-3-319-19686-2_7
Vlasselaer, J., Van den Broeck, G., Kimmig, A., Meert, W., De Raedt, L.: Anytime inference in probabilistic logic programs with Tp-compilation. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 1852–1858 (2015)
Acknowledgments
We want to thank the anonymous reviewers for their valuable comments. This work is partially funded by the ERDF through the COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, and by National Funds through the FCT as part of project UID/EEA/50014/2013.
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Mantadelis, T., Rocha, R. (2017). Using Iterative Deepening for Probabilistic Logic Inference. In: Lierler, Y., Taha, W. (eds) Practical Aspects of Declarative Languages. PADL 2017. Lecture Notes in Computer Science(), vol 10137. Springer, Cham. https://doi.org/10.1007/978-3-319-51676-9_14
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