zbMATH — the first resource for mathematics

P-log: refinement and a new coherency condition. (English) Zbl 07093482
Summary: This paper focuses on the investigation and improvement of knowledge representation language P-log that allows for both logical and probabilistic reasoning. We refine the definition of the language by eliminating some ambiguities and incidental decisions made in its original version and slightly modify the formal semantics to better match the intuitive meaning of the language constructs. We also define a new class of coherent (i.e., logically and probabilistically consistent) P-log programs which facilitates their construction and proofs of correctness. There are a query answering algorithm, sound for programs from this class, and a prototype implementation which, due to their size, are not included in the paper. They, however, can be found in the dissertation of the first author.
60 Probability theory and stochastic processes
68 Computer science
CP-logic; PRISM; ProbLog
Full Text: DOI
[1] Balai, E.: Investigating and Extending P-log. Ph.D. thesis, Texas Tech University (2017)
[2] Balai, E., Gelfond, M.: On the relationship between P-log and LPMLN. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9-15 July 2016, pp. 915-921. http://www.ijcai.org/Abstract/16/134 (2016)
[3] Balai, E., Gelfond, M.: Refining and generalizing P-log - preliminary report. In: Proceedings of the 10th Workshop on Answer Set Programming and Other Computing Paradigms co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning, ASPOCP@LPNMR 2017, Espoo, Finland, July 3, 2017. http://ceur-ws.org/Vol-1868/p6.pdf (2017)
[4] Balai, E., Gelfond, M., Zhang, Y.: Towards answer set programming with sorts. In: Logic Programming and Nonmonotonic Reasoning, 12th International Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proceedings, pp. 135-147 (2013) · Zbl 1405.68042
[5] Balduccini, M.: Answer set solving and non-herbrand functions. In: Proceedings of the 14th International Workshop on Non-Monotonic Reasoning (NMR’2012)(Jun 2012) (2012) · Zbl 1248.68468
[6] Balduccini, M., Gelfond, M.: Logic programs with consistency-restoring rules. In: International Symposium on Logical Formalization of Commonsense Reasoning, AAAI 2003 Spring Symposium Series, pp. 9-18 (2003)
[7] Baral, C., Gelfond, M., Rushton, N.: Probabilistic Reasoning with Answer Sets. in: International Conference on Logic Programming and Nonmonotonic Reasoning, pp. 21-33. Springer (2004) · Zbl 1122.68361
[8] Baral, C.; Gelfond, M.; Rushton, N., Probabilistic reasoning with answer sets, Theory Pract. Logic Program., 9, 57-144, (2009) · Zbl 1170.68003
[9] Baral, C., Hunsaker, M.: Using the probabilistic logic programming language P-log for causal and counterfactual reasoning and non-naive conditioning. In: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6-12, 2007, pp. 243-249 (2007)
[10] Bartholomew, M., Lee, J.: Stable models of multi-valued formulas: partial versus total functions. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, July 20-24, 2014. http://www.aaai.org/ocs/index.php/KR/KR14/paper/view/8020 (2014)
[11] Cabalar, P.: Partial functions and equality in answer set programming. In: Logic Programming, 24th International Conference, ICLP 2008, Udine, Italy, December 9-13 2008, Proceedings, pp. 392-406. https://doi.org/10.1007/978-3-540-89982-2_36 (2008) · Zbl 1185.68149
[12] Cozman, FG; Mauá, DD, On the semantics and complexity of probabilistic logic programs, J. Artif. Intell. Res., 60, 221-262, (2017) · Zbl 1418.68027
[13] Raedt, L.; Kimmig, A., Probabilistic (logic) programming concepts, Mach. Learn., 100, 5-47, (2015) · Zbl 1346.68050
[14] Dix, J.; Gottlob, G.; Marek, VW, Reducing disjunctive to non-disjunctive semantics by shift-operations, Fundam. Inform., 28, 87-100, (1996) · Zbl 0863.68088
[15] Fierens, D.; den Broeck, G.; Renkens, J.; Shterionov, D.; Gutmann, B.; Thon, I.; Janssens, G.; Raedt, L., Inference and learning in probabilistic logic programs using weighted boolean formulas, Theory Pract. Logic Program., 15, 358-401, (2015) · Zbl 1379.68062
[16] Gelfond, M., Kahl, Y.: Knowledge Representation, Reasoning, and the Design of Intelligent Agents: The Answer-set Programming Approach. Cambridge University Press, Cambridge (2014)
[17] Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 15-19, 1988, vol. 2, pp. 1070-1080 (1988)
[18] Gelfond, M.; Lifschitz, V., Classical negation in logic programs and disjunctive databases, N. Gener. Comput., 9, 365-386, (1991) · Zbl 0735.68012
[19] Gelfond, M., Rushton, N.: Causal and Probabilistic Reasoning in P-log. In: Dechter, R., Geffner, H., Halpern, J. (eds.) A Tribute to Judea Pearl, pp. 337-359, College Publications (2010) · Zbl 1218.68167
[20] Gelfond, M.; Zhang, Y., Vicious circle principle and logic programs with aggregates, TPLP, 14, 587-601, (2014) · Zbl 1309.68032
[21] Gelfond, M., Zhang, Y.: Vicious circle principle and formation of sets in ASP based languages. In: Logic Programming and Nonmonotonic Reasoning, 14Th International Conference, LPNMR (2017) · Zbl 06769658
[22] Halpern, J.Y.: A modification of the Halpern-Pearl definition of causality. In: Proceedings of the 24th International Conference on Artificial Intelligence, IJCAI’15, pp. 3022-3033. AAAI Press. http://dl.acm.org/citation.cfm?id=2832581.2832671 (2015)
[23] Halpern, JY; Pearl, J., Causes and explanations: a structural-model approach. Part I: Causes, Br. J. Philos. Sci., 56, 843-887, (2005) · Zbl 1092.03003
[24] Jaynes, E. T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003) · Zbl 1045.62001
[25] Kersting, K., Raedt, L.D.: Bayesian logic programs. In: Inductive Logic Programming, 10th International Conference, ILP 2000, Work-in-progress reports, London, UK, July 2000, Proceedings. http://ceur-ws.org/Vol-35/07-KerstingDeRaedt.ps (2000)
[26] Lee, J., Wang, Y.: Weighted rules under the stable model semantics. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, South Africa, April 25-29, 2016, pp. 145-154. http://www.aaai.org/ocs/index.php/KR/KR16/paper/view/12901 (2016)
[27] Lee, J., Yang, Z.: LPMLN, weak constraints, and p-log. in: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, pp. 1170-1177, San Francisco, California, USA (2017)
[28] Lifschitz, V., Turner, H.: Splitting a logic program. In; Logic Programming, Proceedings of the Eleventh International Conference on Logic Programming, Santa Marherita Ligure, Italy, June 13-18, 1994, pp. 23-37 (1994)
[29] Lukasiewicz, T.: Probabilistic Logic Programming. In: ECAI, pp. 388-392 (1998)
[30] Lukasiewicz, T., Probabilistic description logic programs, Int. J. Approx. Reason., 45, 288-307, (2007) · Zbl 1122.68027
[31] De Morais, E.M., Finger, M.: Probabilistic Answer Set Programming. In: Brazilian Conference on Intelligent Systems, BRACIS 2013, Fortaleza, CE, Brazil, 19-24 October, 2013, pp. 150-156. https://doi.org/10.1109/BRACIS.2013.33 (2013)
[32] Muggleton, S.; etal., Stochastic logic programs, Advances in Inductive Logic Programming, 32, 254-264, (1996)
[33] Ng, R.; Subrahmanian, VS, Probabilistic logic programming, Inf. Comput., 101, 150-201, (1992) · Zbl 0781.68038
[34] Ngo, L.; Haddawy, P., Answering queries from context-sensitive probabilistic knowledge bases, Theor. Comput. Sci., 171, 147-177, (1997) · Zbl 0874.68280
[35] Oikarinen, E., Janhunen, T.: Modular equivalence for normal logic programs. In: ECAI, vol. 6, pp. 412-416 (2006)
[36] Pearl, J.: Reasoning with cause and effect. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 99, Stockholm, Sweden, July 31 - August 6, 1999. vol. 2, 1450 pages, pp 1437-1449 (1999)
[37] Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000) · Zbl 0959.68116
[38] Pereira, L. M., Saptawijaya, A.: Programming Machine Ethics, 1st edn. Springer Publishing Company, Incorporated, Berlin (2016)
[39] Poole, D., Probabilistic horn abduction and bayesian networks, Artif. Intell., 64, 81-129, (1993) · Zbl 0792.68176
[40] Poole, D., The independent choice logic for modelling multiple agents under uncertainty, Artif. Intell., 94, 7-56, (1997) · Zbl 0902.03017
[41] Raedt, L.D., Kimmig, A., Toivonen, H.: Problog: A probabilistic prolog and its application in link discovery. In: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6-12, 2007, pp. 2462-2467 . http://ijcai.org/Proceedings/07/Papers/396.pdf (2007)
[42] Sato, T.: A statistical learning method for logic programs with distribution semantics. In: Inproceedings of the 12th International Conference on Logic Programming (ICLP’95), pp. 715-729. MIT Press (1995)
[43] Sato, T., Kameya, Y.: PRISM: A language for symbolic-statistical modeling. In: Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, IJCAI 97, Nagoya, Japan, August 23-29, 1997, vol. 2, pp. 1330-1339. http://ijcai.org/Proceedings/97-2/Papers/078.pdf (1997)
[44] 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, 245-308, (2009) · Zbl 1179.68025
[45] Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic programs with annotated disjunctions. In: Logic Programming, 20th International Conference, ICLP 2004, Saint-Malo, France, September 6-10, 2004, Proceedings, pp. 431-445. https://doi.org/10.1007/978-3-540-27775-0_30 (2004) · Zbl 1104.68391
[46] Wellman, MP; Henrion, M., Explaining ’explaining away’, IEEE Trans. Pattern Anal. Mach. Intell., 15, 287-292, (1993) · Zbl 0760.68068
[47] Zhang, S., Stone, P.: Corpp: Commonsense reasoning and probabilistic planning, as applied to dialog with a mobile robot. In: Proceedings of the 29th Conference on Artificial Intelligence (AAAI) (2015)
[48] Zhu, W.: Plog: Its Algorithms and Applications. Ph.D. thesis, Texas Tech University (2012)
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.