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Probabilistic (logic) programming concepts. (English) Zbl 1346.68050
Summary: A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years.

MSC:
68N17 Logic programming
68N15 Theory of programming languages
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[1] Angelopoulos, N., & Cussens, J. (2004). On the implementation of MCMC proposals over stochastic logic programs. In M. Carro & J. F. Morales (Eds.), Proceedings of the colloquium on implementation of constraint and logic programming systems (CICLOPS-04). · Zbl 1179.68025
[2] Arora, N. S., de Salvo Braz, R., Sudderth, E. B., & Russell, S. J. (2010). Gibbs sampling in open-universe stochastic languages. In P. Grünwald & P. Spirtes (Eds.), Proceedings of the 26th conference on uncertainty in artificial intelligence (UAI-10) (pp. 30-39). AUAI Press.
[3] Bancilhon, F., Maier, D., Sagiv, Y., & Ullman, J. D. (1986). Magic sets and other strange ways to implement logic programs (extended abstract). In A. Silberschatz (Ed.), Proceedings of the 5th ACM SIGACT-SIGMOD symposium on principles of database systems (PODS-86) (pp. 1-15). ACM.
[4] Baral, C., Gelfond, M., & Rushton, J. N. (2004). Probabilistic reasoning with answer sets. In V. Lifschitz & I. Niemelä (Eds.), Proceedings of the 7th international conference on logic programming and nonmonotonic reasoning (LPNMR-04), Lecture Notes in Computer Science, (Vol. 2923, pp. 21-33). Springer. · Zbl 1122.68361
[5] Baral, C; Gelfond, M; Rushton, N, Probabilistic reasoning with answer sets, Theory and Practice of Logic Programming (TPLP), 9, 57-144, (2009) · Zbl 1170.68003
[6] Bellodi, E; Lamma, E; Riguzzi, F; Santos Costa, V; Zese, R, Lifted variable elimination for probabilistic logic programming, Theory and Practice of Logic Programming (TPLP), 14, 681-695, (2014) · Zbl 1309.68027
[7] Bragaglia, S., & Riguzzi, F. (2010). Approximate inference for logic programs with annotated disjunctions. In P. Frasconi & F. A. Lisi (Eds.), Revised papers of the 20th international conference on inductive logic programming (ILP-10), Lecture Notes in Computer Science (Vol. 6489, pp. 30-37). Springer. · Zbl 1329.68208
[8] Bröcheler, M., Mihalkova, L., & Getoor, L. (2010). Probabilistic similarity logic. In P. Grünwald & P. Spirtes (Eds.), Proceedings of the 26th conference on uncertainty in artificial intelligence (UAI-10) (pp. 73-82). AUAI Press. · Zbl 1379.68305
[9] Carlson, A., Betteridge, J., Kisiel, B., Settles, B., Hruschka, Jr., E. R., & Mitchell, T. M. (2010). Toward an architecture for never-ending language learning. In M. Fox & D. Poole (Eds.), Proceedings of the 24th AAAI conference on artificial intelligence (AAAI-10) (pp. 1306-1313). AAAI Press.
[10] Cohen, S. B., Simmons, R. J., & Smith, N. A. (2008). Dynamic programming algorithms as products of weighted logic programs. In M. Garcia de la Banda & E. Pontelli (Eds.), Proceedings of the 24th international conference on logic programming (ICLP-08), Lecture Notes in Computer Science (Vol. 5366, pp. 114-129). Springer. · Zbl 1185.68153
[11] Cohen, WW, WHIRL: A word-based information representation language, Artificial Intelligence, 118, 163-196, (2000) · Zbl 0938.68841
[12] Cussens, J. (2005). Integrating by separating: Combining probability and logic with ICL, PRISM and SLPs. APRIL II project report. · Zbl 0994.68025
[13] Dalvi, N. N., & Suciu, D. (2004). Efficient query evaluation on probabilistic databases. In M. A. Nascimento, M. T. Özsu, D. Kossmann, R. J. Miller, J. A. Blakeley & K. B. Schiefer (Eds.), Proceedings of the 30th international conference on very large databases (VLDB-04), (pp. 864-875). Morgan Kaufmann Publishers. · Zbl 0419.68082
[14] Dantsin, E. (1991). Probabilistic logic programs and their semantics. In A. Voronkov (Ed.), Proceedings of the first Russian conference on logic programming, Lecture Notes in Computer Science (Vol. 592, pp. 152-164). Springer.
[15] Maeyer, D; Renkens, J; Cloots, L; De, Raedt L; Marchal, K, Phenetic: network-based interpretation of unstructured gene lists in E. coli, Molecular BioSystems, 9, 1594-1603, (2013)
[16] Raedt, L; Kersting, K, Probabilistic logic learning, SIGKDD Explorations, 5, 31-48, (2003)
[17] De Raedt, L., Kimmig, A., & Toivonen, H. (2007). ProbLog: A probabilistic Prolog and its application in link discovery. In M. M. Veloso (Ed.), Proceedings of the 20th international joint conference on artificial intelligence (IJCAI-07), (pp. 2462-2467). Morgan Kaufmann Publishers. · Zbl 1209.68100
[18] Eisner, J., & Filardo, N. W. (2011). Dyna: Extending Datalog for modern AI. In O. de Moor, G. Gottlob, T. Furche & A. Sellers (Eds.), Datalog reloaded, Lecture Notes in Computer Science (Vol. 6702, pp. 181-220). Springer.
[19] Eisner, J., Goldlust, E., & Smith, N. (2005). Compiling Comp Ling: Weighted dynamic programming and the Dyna language. In C. Brew, L. F. Chien & K. Kirchhoff (Eds.), Proceedings of the human language technology conference and conference on empirical methods in natural language processing (HLT/EMNLP-05), (pp. 281-290). The Association for Computational Linguistics.
[20] Fierens, D., Blockeel, H., Bruynooghe, M., & Ramon, J. (2005). Logical Bayesian networks and their relation to other probabilistic logical models. In S. Kramer & B. Pfahringer (Eds.), Proceedings of the 15th international conference on inductive logic programming (ILP-05), Lecture Notes in Computer Science (Vol. 3625, pp. 121-135). Springer. · Zbl 1134.68507
[21] Fierens, D., Van den Broeck, G., Thon, I., Gutmann, B., & De Raedt, L. (2011). Inference in probabilistic logic programs using weighted CNFs. In F. G. Cozman & A. Pfeffer (Eds.), Proceedings of the 27th conference on uncertainty in artificial intelligence (UAI-11), (pp. 211-220). AUAI Press. · Zbl 0957.68013
[22] Fierens, D., Van den Broeck, G., Bruynooghe, M., & De Raedt, L. (2012). Constraints for probabilistic logic programming. In V. Mansinghka, D. Roy & N. Goodman (Eds.), Proceedings of the NIPS probabilistic programming workshop. · Zbl 1218.68169
[23] Fierens, D; Broeck, G; Renkens, J; Shterionov, D; Gutmann, B; Thon, I; etal., Inference and learning in probabilistic logic programs using weighted Boolean formulas, Theory and Practice of Logic Programming, 15, 358-401, (2013) · Zbl 1379.68062
[24] Flach, P. A. (1994). Simply logical: Intelligent reasoning by example. New York: John Wiley. · Zbl 0817.68049
[25] Fuhr, N. (1995). Probabilistic Datalog—A logic for powerful retrieval methods. In E. A. Fox, P. Ingwersen & R. Fidel (Eds.), Proceedings of the 18th annual international ACM SIGIR conference on research and development in information retrieval (SIGIR-95), (pp. 282-290). ACM Press.
[26] Fuhr, N, Probabilistic Datalog: implementing logical information retrieval for advanced applications, Journal of the American Society for Information Science (JASIS), 51, 95-110, (2000)
[27] Gerstenberg, T., & Goodman, N. D. (2012). Ping pong in Church: Productive use of concepts in human probabilistic inference. In N. Miyake, D. Peebles & R. P. Cooper (Eds.), Proceedings of the 34th annual conference of the cognitive science society (pp. 1590-1595). Cognitive Science Society.
[28] Getoor, L., Friedman, N., Koller, D., Pfeffer, A., & Taskar, B. (2007). Probabilistic relational models. In L. Getoor & B. Taskar (Eds.), An introduction to statistical relational learning (pp. 129-174). Cambridge, MA: MIT Press.
[29] Goodman, N. D., Mansinghka, V. K., Roy, D. M., Bonawitz, K., & Tenenbaum, J. B. (2008). Church: A language for generative models. In D. A. McAllester & P. Myllymäki (Eds.), Proceedings of the 24th conference on uncertainty in artificial intelligence (UAI-08), (pp. 220-229). AUAI Press.
[30] Gutmann, B., Jaeger, M., & De Raedt, L. (2010). Extending ProbLog with continuous distributions. In P. Frasconi & F. A. Lisi (Eds.), Proccedings of the 20th international conference on inductive logic programming (ILP-10), Lecture Notes in Computer Science (Vol. 6489, pp. 76-91). Springer. · Zbl 1329.68057
[31] Gutmann, B; Thon, I; Kimmig, A; Bruynooghe, M; Raedt, L, The magic of logical inference in probabilistic programming, Theory and Practice of Logic Programming (TPLP), 11, 663-680, (2011) · Zbl 1222.68060
[32] Haddawy, P. (1994). Generating Bayesian networks from probabilistic logic knowledge bases. In R. L. de Mántaras & D. Poole (Eds.), Proceedings of the 10th annual conference on uncertainty in artificial intelligence (UAI-94) (pp. 262-269). Morgan Kaufmann Publishers. · Zbl 1189.03039
[33] Heijden, M; Lucas, PJF, Describing disease processes using a probabilistic logic of qualitative time, Artificial Intelligence in Medicine, 59, 143-155, (2013)
[34] Hommersom, A., & Lucas, P. J. F. (2011). Generalising the interaction rules in probabilistic logic. In T. Walsh (Ed.), Proceedings of the 22nd international joint conference on artificial intelligence (IJCAI-11), (pp. 912-917). AAAI Press. · Zbl 1222.68060
[35] Hommersom, A., de Carvalho Ferreira, N., & Lucas, P. J. F. (2009). Integrating logical reasoning and probabilistic chain graphs. In W. L. Buntine, M. Grobelnik, D. Mladenic & J. Shawe-Taylor (Eds.), Proceedings of the European conference on machine learning and principles and practice of knowledge discovery in databases (ECML/PKDD-09), Lecture Notes in Computer Science (Vol. 5781, pp. 548-563). Springer.
[36] Huth, M., & Ryan, M. (2004). Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge: Cambridge University Press. · Zbl 1073.68001
[37] Jaeger, M. (1997). Relational Bayesian networks. In D. Geiger & P. P. Shenoy (Eds.), Proceedings of the 13th conference on uncertainty in artificial intelligence (UAI-97) (pp. 266-273). Morgan Kaufmann Publishers.
[38] Jaeger, M. (2008). Model-theoretic expressivity analysis. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), Probabilistic inductive logic programming-Theory and applications, Lecture Notes in Artificial Intelligence (Vol. 4911, pp. 325-339). Springer. · Zbl 1137.68591
[39] Kersting, K. (2012). Lifted probabilistic inference. In L. De Raedt, C. Bessière, D. Dubois, P. Doherty, P. Frasconi, F. Heintz & P. J. F. Lucas (Eds.), Proceedings of the 20th European conference on artificial intelligence (ECAI-12), Frontiers in Artificial Intelligence and Applications (Vol. 242, pp. 33-38). IOS Press.
[40] Kersting, K., & De Raedt, L. (2001). Bayesian logic programs. CoRR cs.AI/0111058. · Zbl 1006.68504
[41] Kersting, K., & De Raedt, L. (2008). Basic principles of learning Bayesian logic programs. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), Probabilistic inductive logic programming-Theory and applications, Lecture Notes in Artificial Intelligence (Vol. 4911, pp. 189-221). Springer. · Zbl 1137.68544
[42] Kersting, K; Raedt, L; Raiko, T, Logical hidden Markov models, Journal of Artificial Intelligence Research (JAIR), 25, 425-456, (2006) · Zbl 1182.68353
[43] Kimmig, A., Santos Costa, V., Rocha, R., Demoen, B., & De Raedt, L. (2008). On the efficient execution of ProbLog programs. In M. Garcia de la Banda & E. Pontelli (Eds.), Proceedings of the 24th international conference on logic programming (ICLP-08), Lecture Notes in Computer Science (Vol. 5366, pp. 175-189). Springer. · Zbl 1185.68162
[44] Kimmig, A., Gutmann, B., & Santos Costa, V. (2009). Trading memory for answers: Towards tabling ProbLog. In P. Domingos & K. Kersting (Eds.), Proceedings of the international workshop on statistical relational learning (SRL-2009).
[45] Kimmig, A., Van den Broeck, G., & De Raedt, L. (2011a). An algebraic Prolog for reasoning about possible worlds. In W. Burgard & D. Roth (Eds.), Proceedings of the 25th AAAI conference on artificial intelligence (AAAI-11) (pp. 209-214). AAAI Press.
[46] Kimmig, A; Demoen, B; Raedt, L; Santos Costa, V; Rocha, R, On the implementation of the probabilistic logic programming language problog, Theory and Practice of Logic Programming (TPLP), 11, 235-262, (2011) · Zbl 1220.68037
[47] Kimmig, A; Mihalkova, L; Getoor, L, Lifted graphical models: A survey, Machine Learning., 99, 1-45, (2015) · Zbl 1320.62016
[48] Koller, D., & Pfeffer, A. (1998). Probabilistic frame-based systems. In J. Mostow & C. Rich (Eds.), Proceedings of the 15th national conference on artificial intelligence (AAAI-98) (pp. 580-587). AAAI Press/MIT Press. · Zbl 1182.68353
[49] Lloyd, J. W. (1989). Foundations of Logic Programming (2nd ed.). Berlin: Springer. · Zbl 0547.68005
[50] Lodhi, H., & Muggleton, S. (2005). Modelling metabolic pathways using stochastic logic programs-based ensemble methods. In V. Danos & V. Schächter (Eds.), Revised selected papers of the international conference on computational methods in systems biology (CMSB-04), Lecture Notes in Computer Science (Vol. 3082, pp. 119-133). Springer. · Zbl 1088.68823
[51] Mansinghka, V. K., Kulkarni, T. D., Perov, Y. N., & Tenenbaum, J. B. (2013). Approximate Bayesian image interpretation using generative probabilistic graphics programs. In C. J. C. Burges, L. Bottou, Z. Ghahramani & K. Q. Weinberger (Eds.), Proceedings of the 27th annual conference on neural information processing systems (NIPS-13), Neural Information Processing Systems, (pp. 1520-1528).
[52] Mantadelis, T., & Janssens, G. (2011). Nesting probabilistic inference. In S. Abreu & V. Santos Costa (Eds.), Proceedings of the colloquium on implementation of constraint and logic programming systems (CICLOPS-11). · Zbl 1237.68190
[53] Milch, B., Marthi, B., Russell, S. J., Sontag, D., Ong, D. L., & Kolobov, A. (2005). BLOG: Probabilistic models with unknown objects. In L. P. Kaelbling & A. Saffiotti (Eds.), Proceedings of the 19th international joint conference on artificial intelligence (IJCAI-05) (pp. 1352-1359). NY: Professional Book Center.
[54] Moldovan, B., Thon, I., Davis, J., & De Raedt, L. (2013). MCMC estimation of conditional probabilities in probabilistic programming languages. In L. C. van der Gaag (Ed.), Proceedings of the 12th European conference on symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU-13), Lecture Notes in Computer Science (Vol. 7958, pp. 436-448). Springer. · Zbl 06195172
[55] Mørk, S; Holmes, I, Evaluating bacterial gene-finding HMM structures as probabilistic logic programs, Bioinformatics, 28, 636-642, (2012)
[56] Muggleton, S; Raedt, L (ed.), Stochastic logic programs, 254-264, (1996), Amsterdam
[57] Natarajan, S., Tadepalli, P., Altendorf, E., Dietterich, T. G., Fern, A., & Restificar, A. C. (2005). Learning first-order probabilistic models with combining rules. In L. De Raedt & S. Wrobel (Eds.), Proceedings of the 22nd international conference on machine learning (ICML-05), ACM International conference proceeding series (Vol. 119, pp. 609-616). ACM.
[58] Nitti, D., De Laet, T., & De Raedt, L. (2013). A particle filter for hybrid relational domains. In N. Amato (Ed.), Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS-13) (pp. 2764-2771). IEEE.
[59] Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. Burlington: Morgan Kaufmann Publishers. · Zbl 0746.68089
[60] Pfeffer, A. (2001). IBAL: A probabilistic rational programming language. In B. Nebel (Ed.), Proceedings of the 17th international joint conference on artificial intelligence (IJCAI-01), (pp. 733-740). Morgan Kaufmann Publishers. · Zbl 0994.68025
[61] Pfeffer, A. (2009). Figaro: An object-oriented probabilistic programming language. Charles River Analytics: Technical report.
[62] Poole, D. (1992). Logic programming, abduction and probability. In Proceedings of the international conference on fifth generation computing systems (FGCS-92) (pp. 530-538). IOS Press. · Zbl 0862.68018
[63] Poole, D, Probabilistic Horn abduction and Bayesian networks, Artificial Intelligence, 64, 81-129, (1993) · Zbl 0792.68176
[64] Poole, D. (1995). Exploiting the rule structure for decision making within the independent choice logic. In P. Besnard & S. Hanks (Eds.), Proceedings of the eleventh annual conference on uncertainty in artificial intelligence (UAI-95) (pp. 454-463). Morgan Kaufmann Publishers.
[65] Poole, D, Abducing through negation as failure: stable models within the independent choice logic, Journal of Logic Programming, 44, 5-35, (2000) · Zbl 0957.68013
[66] Poole, D. (2003). First-order probabilistic inference. In G. Gottlob & T. Walsh (Eds.), Proceedings of the 18th international joint conference on artificial intelligence (IJCAI-03) (pp. 985-991). Morgan Kaufmann Publishers.
[67] Poole, D. (2008). The independent choice logic and beyond. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), Probabilistic inductive logic programming-Theory and applications, Lecture Notes in Artificial Intelligence (Vol. 4911, pp. 222-243). Springer. · Zbl 1137.68596
[68] Poole, D. (2010). Probabilistic programming languages: Independent choices and deterministic systems. In R. Dechter, H. Geffner & J. Halpern (Eds.), Heuristics, probability and causality: A tribute to Judea Pearl (pp. 253-269). NY: College Publications. · Zbl 1216.68070
[69] Poon, H., & Domingos, P. (2006). Sound and efficient inference with probabilistic and deterministic dependencies. In Y. Gil & R. J. Mooney (Eds.), Proceedings of the 21st national conference on artificial intelligence (AAAI-06) (pp. 458-463). AAAI Press.
[70] Renkens, J; Broeck, G; Nijssen, S, K-optimal: A novel approximate inference algorithm for problog, Machine Learning, 89, 215-231, (2012) · Zbl 1260.68067
[71] Renkens, J., Kimmig, A., Van den Broeck, G., & De Raedt, L. (2014). Explanation-based approximate weighted model counting for probabilistic logics. In C. E. Brodley & P. Stone (Eds.), Proceedings of the 28th AAAI conference on artificial intelligence (AAAI-14) (pp. 2490-2496). AAAI Press.
[72] Richardson, M; Domingos, P, Markov logic networks, Machine Learning, 62, 107-136, (2006)
[73] Riguzzi, F, Extended semantics and inference for the independent choice logic, Logic Journal of the IGPL, 17, 589-629, (2009) · Zbl 1189.03039
[74] Riguzzi, F. (2013a). cplint Manual. https://sites.google.com/a/unife.it/ml/cplint/cplint-manual
[75] Riguzzi, F, MCINTYRE: A Monte Carlo system for probabilistic logic programming, Fundamenta Informaticae, 124, 521-541, (2013)
[76] Riguzzi, F, Speeding up inference for probabilistic logic programs, The Computer Journal, 57, 347-363, (2014)
[77] Riguzzi, F; Swift, T, The PITA system: tabling and answer subsumption for reasoning under uncertainty, Theory and Practice of Logic Programming (TPLP), 11, 433-449, (2011) · Zbl 1218.68169
[78] Roy, D., Mansinghka, V., Winn, J., McAllester, D., Tenenbaum, D. (Eds.) (2008) . Probabilistic programming, NIPS Workshop.
[79] Russell, S. J., & Norvig, (2003). Artificial intelligence: A modern approach (2nd ed.). Upper Saddle River: Prentice Hall. · Zbl 0835.68093
[80] Santos Costa, V., & Paes, A. (2009). On the relationship between PRISM and CLP( BN). In P. Domingos & K. Kersting (Eds.), Proceedings of the international workshop on statistical relational learning (SRL-2009).
[81] Santos Costa, V., Page, D., Qazi, M., & Cussens, J. (2003). CLP( BN): Constraint logic programming for probabilistic knowledge. In C. Meek & U. Kjærulff (Eds.), Proceedings of the 19th conference on uncertainty in artificial intelligence (UAI-03) (pp. 517-524). Morgan Kaufmann Publishers. · Zbl 1170.68003
[82] Santos Costa, V., Page, D., & Cussens, J. (2008). CLP( BN): Constraint logic programming for probabilistic knowledge. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), Probabilistic inductive logic programming-Theory and applications, Lecture Notes in Artificial Intelligence (Vol. 4911, pp. 156-188). Springer. · Zbl 1137.68342
[83] Sato, T. (1995). A statistical learning method for logic programs with distribution semantics. In L. Sterling (Ed.), Proceedings of the 12th international conference on logic programming (ICLP-95) (pp. 715-729). MIT Press. · Zbl 1189.03039
[84] Sato, T. (2011). A general MCMC method for Bayesian inference in logic-based probabilistic modeling. In T. Walsh (Ed.), Proceedings of the 22nd international joint conference on artificial intelligence (IJCAI-11) (pp. 1472-1477). AAAI Press.
[85] Sato, T., & Kameya, Y. (1997). PRISM: A language for symbolic-statistical modeling. In M. E. Pollack (Ed.), Proceedings of the 15th international joint conference on artificial intelligence (IJCAI-97) (pp. 1330-1339). Morgan Kaufmann Publishers.
[86] Sato, T; Kameya, Y, Parameter learning of logic programs for symbolic-statistical modeling, Journal of Artificial Intelligence Research (JAIR), 15, 391-454, (2001) · Zbl 0994.68025
[87] Sato, T., Kameya, Y., & Zhou, N. F. (2005). Generative modeling with failure in PRISM. In L. P. Kaelbling & A. Saffiotti (Eds.), Proceedings of the 19th international joint conference on artificial intelligence (IJCAI-05) (pp. 847-852). Professional Book Center. · Zbl 1179.68025
[88] Sato, T; Kameya, Y; Kurihara, K, Variational Bayes via propositionalized probability computation in PRISM, Annals of Mathematics and Artificial Intelligence, 54, 135-158, (2008) · Zbl 1178.68591
[89] Skarlatidis, A; Artikis, A; Filippou, J; Paliouras, G, A probabilistic logic programming event calculus, Theory and Practice of Logic Programming (TPLP), 15, 213-245, (2015) · Zbl 1379.68305
[90] Sneyers, J; Meert, W; Vennekens, J; Kameya, Y; Sato, T, CHR(PRISM)-based probabilistic logic learning, Theory and Practice of Logic Programming (TPLP), 10, 433-447, (2010) · Zbl 1209.68100
[91] Stuhlmueller, A., Tenenbaum, J. B., & Goodman, N. D. (2010). Learning structured generative concepts. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd annual conference of the cognitive science society (pp. 2296-2301). Cognitive Science Society.
[92] Suciu, D., Olteanu, D., Ré, C., & Koch, C. (2011). Probabilistic databases, Synthesis lectures on data management (Vol. 16). Burlington: Morgan & Claypool Publishers. · Zbl 0938.68841
[93] Thon, I; Landwehr, N; Raedt, L, Stochastic relational processes: efficient inference and applications, Machine Learning, 82, 239-272, (2011) · Zbl 1237.68169
[94] Valiant, LG, The complexity of enumeration and reliability problems, SIAM Journal on Computing, 8, 410-421, (1979) · Zbl 0419.68082
[95] Van den Broeck, G., Thon, I., van Otterlo, M., & De Raedt, L. (2010). DTProbLog: A decision-theoretic probabilistic Prolog. In M. Fox & D. Poole (Eds.), Proceedings of the 24th AAAI conference on artificial intelligence (AAAI-10) (pp. 1217-1222). AAAI Press.
[96] Van den Broeck, G., Taghipour, N., Meert, W., Davis, J., & De Raedt, L. (2011). Lifted probabilistic inference by first-order knowledge compilation. In T. Walsh (Ed.), Proceedings of the 22nd international joint conference on artificial intelligence (IJCAI-11) (pp. 2178-2185). AAAI Press.
[97] Van den Broeck, G., Meert, W., & Darwiche, A. (2014). Skolemization for weighted first-order model counting. In C. Baral, G. D. Giacomo & T. Eiter (Eds.), Proceedings of the 14th international conference on principles of knowledge representation and reasoning (KR-14) (pp. 111-120). AAAI Press.
[98] Vennekens, J. (2007). Algebraic and logical study of constructive processes in knowledge representation. PhD thesis, K.U. Leuven.
[99] Vennekens, J., Verbaeten, S., & Bruynooghe, M. (2004). Logic programs with annotated disjunctions. In: B. Demoen & V. Lifschitz (Eds.), Proceedings of the 20th international conference on logic programming (ICLP-04), Lecture Notes in Computer Science (Vol. 3132, pp. 431-445). Springer. · Zbl 1104.68391
[100] Vennekens, J., Denecker, M., & Bruynooghe, M. (2006). Representing causal information about a probabilistic process. In M. Fisher, W. van der Hoek, B. Konev & A. Lisitsa (Eds.), Proceedings of the 10th European conference on logics in artificial intelligence (JELIA-06), Lecture Notes in Computer Science (Vol. 4160, pp. 452-464). Springer. · Zbl 1152.68621
[101] Vennekens, J; Denecker, M; Bruynooghe, M, CP-logic: A language of causal probabilistic events and its relation to logic programming, Theory and Practice of Logic Programming (TPLP), 9, 245-308, (2009) · Zbl 1179.68025
[102] Wang, W. Y., Mazaitis, K., & Cohen, W. W. (2013). Programming with personalized PageRank: A locally groundable first-order probabilistic logic. In Q. He, A. Iyengar, W. Nejdl, J. Pei & R. Rastogi (Eds.), Proceedings of the 22nd ACM international conference on information and knowledge management (CIKM-13) (pp. 2129-2138). ACM.
[103] Warren, DS, Memoing for logic programs, Communications of the ACM (CACM), 35, 93-111, (1992)
[104] Wellman, MP; Breese, JS; Goldman, RP, From knowledge bases to decision models, The Knowledge Engineering Review, 7, 35-53, (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.