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CP-logic: A language of causal probabilistic events and its relation to logic programming

Published online by Cambridge University Press:  01 May 2009

JOOST VENNEKENS ,
MARC DENECKER  and
MAURICE BRUYNOOGHE
JOOST VENNEKENS
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium (e-mail: [email protected], [email protected], [email protected])
MARC DENECKER
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium (e-mail: [email protected], [email protected], [email protected])
MAURICE BRUYNOOGHE
Affiliation:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium (e-mail: [email protected], [email protected], [email protected])
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Abstract

This paper develops a logical language for representing probabilistic causal laws. Our interest in such a language is two-fold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

Keywords

uncertaintycausalityprobabilistic logic programming
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 3 , May 2009 , pp. 245 - 308
Copyright
Copyright © Cambridge University Press 2009

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References

Bacchus, F. 1993. Using first-order probability logic for the construction of Bayesian networks. In Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, UAI'93, 219–226. Morgan Kaufmann, San Fransisco, USA.CrossRefGoogle Scholar
Baral, C., Gelfond, M. and Rushton, N. 2004. Probabilistic reasoning with answer sets. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-7). Lecture notes in artificial intelligence (LNAI), vol. 2923. Springer-Verlag NY, USA, 21–33.Google Scholar
Baral, C., Gelfond, M. and Rushton, N. In press. Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming 9 (1). Cambridge University Press.Google Scholar
Baral, C. and Hunsaker, M. 2007. Using the probabilistic logic programming language P-log for causal and counterfactual reasoning and non-naive conditioning. In Proceedings of IJCAI. Hyderabad, India.Google Scholar
Baral, C., Tran, N. and Tuan, L. 2002. Reasoning about actions in a probabilistic setting. In AAAI. Edmonton, Alberta, Canada.Google Scholar
Blockeel, H. and Meert, W. 2007. Towards learning non-recursive LPADs by transforming them into Bayesian networks. In Inductive Logic Programming, ILP'06, Revised Selected Papers. Lecture Notes in Computer Science, vol. 4455, 94–108. Springer-Verlag, New York.CrossRefGoogle Scholar
Breese, J. 1992. Construction of belief and decision networks. Computational Intelligence 8 (4), 624–647.CrossRefGoogle Scholar
Comley, J. W. and Dowe, D. L. 2003. General Bayesian networks and asymmetric languages. In Proceedings of the Second Hawaii International Conference on Statistics and Related fields. Honolulu, Hawaii, USA.Google Scholar
Cussens, J. 2000. Stochastic logic programs: Sampling, inference and applications. In Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Fransisco, USA, 115–122.Google Scholar
De Finetti, B. 1937. La prevision: ses lois logiques, ses sources subjectives. Annales de l'Institut Henri Poincaré 7, 1–68.Google Scholar
Dekhtyar, A. and Subrahmanian, V. S. 2000. Hybrid probabilistic programs. Journal of Logic Programming 43 (3), 187–250.CrossRefGoogle Scholar
Denecker, M. 1998. The well-founded semantics is the principle of inductive definition. In Logics in Artificial Intelligence (JELIA'98), Dix, J., Fariñas del Cerro, L., and Furbach, U., Eds. Lecture Notes in Artificial Intelligence, vol. 1489, Springer-Verlag NY, USA, 1–16.Google Scholar
Denecker, M. and Ternovska, E. 2008. A logic of non-monotone inductive definitions. Transactions On Computational Logic (TOCL), NY, USA. 9 (2), 1–52.CrossRefGoogle Scholar
Denecker, M. and Vennekens, J. 2007. Well-founded semantics and the algebraic theory of non-monotone inductive definitions. In Logic Programming and Nonmonotonic Reasoning, 9th International Conference, LPNMR 2007, Proceedings. Lecture Notes in Artificial Intelligence, vol. 4483, Springer, 84–96.Google Scholar
De Raedt, L., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic Prolog and its application in link discovery. In Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI'07, 2462–2467.Google Scholar
Fierens, D., Blockeel, H., Bruynooghe, M. and Ramon, J. 2005. Logical Bayesian networks and their relation to other probabilistic logical models. In Proceedings of the 15th International Conference on Inductive Logic Programming, ILP'05. Lecture Notes in Computer Science, vol. 3625, Springer NY, USA, 121–135.CrossRefGoogle Scholar
Finzi, A. and Lukasiewicz, T. 2003. Structure-based causes and explanations in the independent choice logic. In Proceedings of the 19h Conference on Uncertainty in Artificial Intelligence, UAI'03. Acapolco, Mexico.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–387.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1993. Representing action and change by logic programs. Journal of Logic Programming 17 (2–4), 301–322.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1998. Action languages. Linköping Electronic Articles in Computer and Information Science 3, 16.Google Scholar
Getoor, L., Friedman, N., Koller, D. and Pfeffer, A. 2001. Learning probabilistic relational models. In Relational Data Mining, Dzeroski, S. and Lavrac, N., Eds. Springer-Verlag NY, USA, 7–34.Google Scholar
Ghahramani, Z. 1998. Learning dynamic Bayesian networks. In Adaptive Processing of Sequences and Data Structures. Lecture Notes in Artificial Intelligence. Springer-Verlag NY, USA, 168–197.CrossRefGoogle Scholar
Giunchiglia, E. and Lifschitz, V. 1998. An action language based on causal explanation: Preliminary report. In Proceedings of AAAI 98. Madison, Wisconsin, USA.Google Scholar
Halpern, J. and Pearl, J. 2001a. Causes and explanations: A structural model approach – Part I: Causes. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, UAI'01. Madison, Wisconsin, USA.Google Scholar
Halpern, J. and Pearl, J. 2001b. Causes and explanations: A structural model approach – Part II: Explanations. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, UAI'01. Madison, Wisconsin, USA.Google Scholar
Jaeger, M. 1997. Relational Bayesian networks. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97). Providence, Rhode Island, USA.Google Scholar
Kakas, A. C., Kowalski, R. and Toni, F. 1992. Abductive logic programming. Journal of Logic and Computation 2 (6), 719–770.CrossRefGoogle Scholar
Kersting, K. and De Raedt, L. 2000. Bayesian logic programs. In Proceedings of the Work-in-Progress Track at the 10th International Conference on Inductive Logic Programming, Cussens, J. and Frisch, A., Eds. 138–155.Google Scholar
Kersting, K. and De Raedt, L. 2001. Bayesian logic programs. Tech. Rep. 151, Institute for Computer Science, University of Freiburg, Germany.CrossRefGoogle Scholar
Kersting, K. and De Raedt, L. 2007. Bayesian logic programming: Theory and tool. In An Introduction to Statistical Relational Learning, Getoor, L. and Taskar, B., Eds. MIT Press. 291–322.CrossRefGoogle Scholar
Lakshmanan, L. V. S. and Sadri, F. 1994. Probabilistic deductive databases. In Proceedings of the International Symposium on Logic Programming, ILPS'94, Bruynooghe, M., Ed. MIT Press, Cambridge, MA, USA, 254–268.Google Scholar
Lifschitz, V. and Turner, H. 1999. Representing transition systems by logic programs. In LPNMR. El Paso, TX, USA.Google Scholar
Lukasiewicz, T. 2001. Fixpoint characterizations for many-valued disjunctive logic programs. In Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'01). Lecture Notes in Artificial Intelligence, vol. 2173. Springer-Verlag NY, USA, 336–350.Google Scholar
Martin-Löf, P. 1982. Constructive mathematics and computer programming. In Proceedings of the Sixth International Congress of Logic, Methodology, and Philosophy of Science. 153–175.Google Scholar
McCain, N. 1997. Causality in commonsense reasoning about actions. Ph.D. Thesis, University of Texas at Austin.Google Scholar
McCain, N. and Turner, H. 1996. Causal theories of action and change. In Proceedings of the Thirteenth National Conference on Artificial Intelligence and the Eighth Innovative Applications of Artificial Intelligence Conference (13th AAAI/8th IAAI). AAAI Press, Menlo Park, CA, USA, 460–465.Google Scholar
Meert, W., Struyf, J. and Blockeel, H. 2007. Learning ground CP-logic theories by means by Bayesian network techniques. In Proceedings of the 6th International Workshop on Multi-Relational Data Mining. 93–104.Google Scholar
Muggleton, S. 2000. Learning stochastic logic programs. Electronic Transactions in Artificial Intelligence 5 (041), 141–153.Google Scholar
Ng, R. T. and Subrahmanian, V. S. 1992. Probabilistic logic programming. Information and Computation 101 (2), 150–201.CrossRefGoogle Scholar
Ngo, L. and Haddawy, P. 1997. Answering queries from context-sensitive probabilistic knowledge bases. Theoretical Computer Science 171 (1–2), 147–177.CrossRefGoogle Scholar
Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Fransisco, USA.Google Scholar
Pearl, J. 2000. Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge, England.Google Scholar
Pinto, J. and Reiter, R. 1993. Temporal reasoning in logic programming: A case for the situation calculus. In Proceedings of the International Conference on Logic Programming. 203–221. MIT Press Cambridge, MA, USA.Google Scholar
Poole, D. 1993. Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64 (1), 81–129.CrossRefGoogle Scholar
Poole, D. 1997. The Independent Choice Logic for modelling multiple agents under uncertainty. Artificial Intelligence 94 (1–2), 7–56.CrossRefGoogle Scholar
Przymusinski, T. C. 1991. Stable semantics for disjunctive programs. New Generation Computing 3/4, 401–424.CrossRefGoogle Scholar
Riguzzi, F. 2004. Learning logic programs with annotated disjunctions. In 14th Internation Conference on Inductive Logic Programming (ILP2004), Porto, 6–8 September 2004, Srinivasan, A. and King, R., Eds. Springer-Verlag, Heidelberg, Germany, 270–287.CrossRefGoogle Scholar
Riguzzi, F. 2007. A top down interpreter for LPAD and CP-logic. In The 14th RCRA Workshop Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion. Rome, Italy.Google Scholar
Sakama, C. and Inoue, K. 1994. An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of automated reasoning 13 (1), 145–172.CrossRefGoogle Scholar
Santos Costa, V., Page, D., Qazi, M. and Cussens, J. 2003. CLP(BN): Constraint logic programming for probabilistic knowledge. In Proceedings of the Nineteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-2003). Morgan Kaufmann, San Fransisco, USA. 517–524.Google Scholar
Sato, T. and Kameya, Y. 1997. PRISM: A language for symbolic-statistical modeling. In Proceedings of the International Joint Conferences on Artificial Intelligence, IJCAI'97, 1330–1335. Morgan Kauffmann, San Fransisco, USA.Google Scholar
Shafer, G. 1996. The Art of Causal Conjecture. MIT Press, San Fransisco, USA.CrossRefGoogle Scholar
Tran, N. and Baral, C. 2004. Encoding probabilistic causal model in probabilistic action language. In AAAI. San Jose, California, USA.Google Scholar
Van Belleghem, K., Denecker, M. and De Schreye, D. 1997. On the relation between situation calculus and event calculus. Journal of Logic Programming (Special Issue on Reasoning about Actions and Change), 31 (1–3), 3–37.CrossRefGoogle Scholar
Van Gelder, A., Ross, K. and Schlipf, J. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38 (3), 620–650.CrossRefGoogle Scholar
Venn, J. 1866. The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability. Macmillan, London, UK.Google Scholar
Vennekens, J., Denecker, M. and Bruynooghe, M. 2006. Representing causal information about a probabilistic process. In Logics in Artificial Intelligence, 10th European Conference, JELIA'06, Proceedings. Lecture Notes in Computer Science, vol. 4160. Springer NY, USA, 452–464.Google Scholar
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In Logic Programming, 20th International Conference, ICLP'04, Proceedings. Lecture Notes in Computer Science, vol. 3132. Springer NY, USA, 431–445.Google Scholar