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Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

Published online by Cambridge University Press:  25 January 2012

FABRIZIO RIGUZZI  and
TERRANCE SWIFT
FABRIZIO RIGUZZI
Affiliation:
ENDIF – University of Ferrara, Via Saragat 1, I-44122 Ferrara, Italy (e-mail: fabrizio.riguzzi@unife.it)
TERRANCE SWIFT
Affiliation:
CENTRIA – Universidade Nova de Lisboa, Caparica, Portugal (e-mail: tswift@cs.suysb.edu)
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Abstract

Distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

Keywords

Probabilistic logic programmingTablingAnswer subsumptionLogic programs with annotated disjunctionProgram transformation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Issue 2: 25th Annual GULP Conference , March 2013 , pp. 279 - 302
Copyright
Copyright © Cambridge University Press 2012

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References

Baselice, S., Bonatti, P. and Criscuolo, G. 2009. On finitely recursive programs. Theory and Practice of Logic Programming 9, 2, 213–238.Google Scholar
Calimeri, F., Cozza, S., Ianni, G. and Leone, N. 2008. Computable functions in ASP: Theory and implementation. In Proc. of International Conference on Logic Programming, de la Banda, M. Garcia and Pontelli, E., Eds. LNCS, vol. 5366. Springer, 407–424.CrossRefGoogle Scholar
Chen, W. and Warren, D. S. 1996. Tabled evaluation with delaying for general logic programs. Journal of the Association for Computing Machinery 43, 1, 20–74.Google Scholar
De Raedt, L., Demoen, B., Fierens, D., Gutmann, B., Janssens, G., Kimmig, A., Landwehr, N., Mantadelis, T., Meert, W., Rocha, R., Costa, V. S., Thon, I. and Vennekens, J. 2008. Towards digesting the alphabet-soup of statistical relational learning. In Proc. of the NIPS2008 Workshop on Probabilistic Programming, 13 December 2008, Whistler, Canada.Google Scholar
De Raedt, L., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic prolog and its application in link discovery. In Proc. of the International Joint Conference on Artificial Intelligence, Veloso, M., Ed. IJCAI, 2462–2467.Google Scholar
Fuhr, N. 2000. Probabilistic datalog: Implementing logical information retrieval for advanced applications. Journal of the American Society of Information Sciences 51, 2, 95–110.Google Scholar
Kameya, Y. and Sato, T. 2000. Efficient EM learning with tabulation for parameterized logic programs. In Proc. of the International Conference on Computational Logic, Lloyd, J., Dahl, V., Furbach, U., Kerber, M., Lau, K., Palamidessi, K., Pereira, L. M., Sagiv, Y. and Stuckey, P., Eds. LNCS, vol. 1861. Springer, 269–284.Google Scholar
Kimmig, A., Demoen, B., De Raedt, L., Costa, V. S. and Rocha, R. 2011. On the implementation of the probabilistic logic programming language problog. Theory and Practice of Logic Programming 11, Special Issue 2–3, 235–262.CrossRefGoogle Scholar
Kimmig, A., Gutmann, B. and SantoCosta, V. Costa, V. 2009. Trading memory for answers: Towards tabling ProbLog. In Proc. of the International Workshop on Statistical Relational Learning, 2–4 July 2009, Leuven, Belgium.Google Scholar
Kolmogorov, A. N. 1950. Foundations of the Theory of Probability. Chelsea Publishing Company, New York.Google Scholar
Mantadelis, T. and Janssens, G. 2010. Dedicated tabling for a probabilistic setting. In Proc. of the Technical Communications of the International Conference on Logic Programming, Hermenegildo, M. and Schaub, T., Eds. LIPIcs, vol. 7. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 124–133.Google Scholar
Meert, W., Struyf, J. and Blockeel, H. 2009. CP-Logic theory inference with contextual variable elimination and comparison to BDD based inference methods. In Proc. of the International Conference on Inductive Logic Programming, De Raedt, L., Ed. LNCS, vol. 5989. Springer, 96–109.Google Scholar
Poole, D. 1997. The independent choice logic for modelling multiple agents under uncertainty. Artificial Intelligence 94, 1–2, 7–56.Google Scholar
Poole, D. 2000. Abducing through negation as failure: Stable models within the independent choice logic. Journal of Logic Programming 44, 1–3, 5–35.Google Scholar
Przymusinski, T. 1989. Every logic program has a natural stratification and an iterated least fixed point model. In Proc. of the Symposium on Principles of Database Systems, Silberschatz, A., Ed. ACM Press, 11–21.Google Scholar
Riguzzi, F. 2007. A top down interpreter for LPAD and CP–logic. In Proc. of the Congress of the Italian Association for Artificial Intelligence, Basili, R. and Pazienza, M. T., Eds. LNAI, vol. 4733. Springer, 109–120.Google Scholar
Riguzzi, F. 2008. Inference with logic programs with annotated disjunctions under the well founded semantics. In Proc. of International Conference on Logic Programming, de la Banda, M. Garcia and Pontelli, E., Eds. LNCS, vol. 5366. Springer, 667–771.CrossRefGoogle Scholar
Riguzzi, F. and Swift, T. 2011. The PITA system: Tabling and answer subsumption for reasoning under uncertainty. Theory and Practice of Logic Programming, International Conference on Logic Programming, Special Issue 11, 4–5, 433–449.Google Scholar
Sagonas, K., Swift, T. and Warren, D. S. 2000. The limits of fixed-order computation. Theoretical Computer Science 254, 1–2, 465–499.CrossRefGoogle Scholar
Sato, T. 1995. A statistical learning method for logic programs with distribution semantics. In Proc. of the International Conference on Logic Programming, Sterling, L., Ed. MIT Press, 715–729.Google Scholar
Sato, T. and Kameya, Y. 1997. Prism: A language for symbolic-statistical modeling. In Proc. of the International Joint Conference on Artificial Intelligence, Pollack, M., Ed. IJCAI, 1330–1339.Google Scholar
Swift, T. 1999a. A new formulation of tabled resolution with delay. In Recent Advances in Artifiial Intelligence, Barahona, P. and Alferes, J. J., Eds. LNAI, vol. 1695. Springer, 163–177.Google Scholar
Swift, T. 1999b. Tabling for non-monotonic programming. Annals of Mathematics and Artificial Intelligence 25, 3–4, 201–240.CrossRefGoogle Scholar
Tamaki, H. and Sato, T. 1986. OLDU resolution with tabulation. In Proc. of the International Conference on Logic Programming, Shapiro, E., Ed. LNCS, vol. 225. Springer, 84–98.Google Scholar
Thayse, A., Davio, M. and Deschamps, J. P. 1978. Optimization of multivalued decision algorithms. In Proc. of the International Symposium on Multiple-Valued Logic. IEEE Computer Society Press, 171–178.Google Scholar
Valiant, L. G. 1979. The complexity of enumeration and reliability problems. SIAM Journal on Computing 8, 3, 410–421.Google Scholar
van Gelder, A. 1989. The alternating fixpoint of logic programs with negation. In Proc. of the Symposium on Principles of Database Systems, Silberschatz, A., Ed. ACM, 1–10.Google Scholar
van Gelder, A., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of the Association for Computing Machinery 38, 3, 620–650.CrossRefGoogle Scholar
Vennekens, J. and Verbaeten, S. 2003. Logic Programs with Annotated Disjunctions. Technical Report CW386, K. U. Leuven, Belgium.Google Scholar
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In Proc. of the International Conference on Logic Programming, Demoen, B. and Lifschitz, V., Eds. LNCS, vol. 3131. Springer, 195–209.Google Scholar
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