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Probabilistic reasoning with answer sets

Published online by Cambridge University Press:  01 January 2009

CHITTA BARAL ,
MICHAEL GELFOND  and
NELSON RUSHTON
CHITTA BARAL
Affiliation:
Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287-8809, USA (e-mail: [email protected])
MICHAEL GELFOND
Affiliation:
Department of Computer Science, Texas Tech University Lubbock, TX 79409, USA (e-mail: [email protected], [email protected])
NELSON RUSHTON
Affiliation:
Department of Computer Science, Texas Tech University Lubbock, TX 79409, USA (e-mail: [email protected], [email protected])
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Abstract

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several non-trivial examples and illustrate the use of P-log for knowledge representation and updating of knowledge. We argue that our approach to updates is more appealing than existing approaches. We give sufficiency conditions for the coherency of P-log programs and show that Bayes nets can be easily mapped to coherent P-log programs.

Keywords

Logic programminganswer setsprobabilistic reasoningAnswer Set Prolog
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 1 , January 2009 , pp. 57 - 144
Copyright
Copyright © Cambridge University Press 2009

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References

Apt, K. and Doets, K. 1994. A new definition of SLDNF resolution. Journal of Logic Programming. 18, 177–190.CrossRefGoogle Scholar
Bacchus, F. 1990. Representing and reasoning with uncertain knowledge. MIT Press, Boston, MA.Google Scholar
Bacchus, F., Grove, A., Halpern, J. and Koller, D. 1996. From statistical knowledge bases to degrees of belief. Artificial Intelligence. 87, 75–143.CrossRefGoogle Scholar
Balduccini, M., Gelfond, M., Nogueira, M., Watson, R. and Barry, M. 2001. An A-Prolog decision support system for the space shuttle - I. In Proc. of Practical Aspects of Declarative Languages, New York, NY, Springer, 169–183.Google Scholar
Balduccini, M., Gelfond, M., Nogueira, M. and Watson, R. 2002. Planning with the USA-Advisor. In 3rd NASA International workshop on Planning and Scheduling for.Google Scholar
Balduccini, M. and Gelfond, M. 2003. Logic programs with consistency-restoring rules. In International Symposium on Logical Formalization of Commonsense Reasoning, AAAI 2003 Spring Symposium Series. 9–18.Google Scholar
Baral, C. 2003. Knowledge representation, reasoning and declarative problem solving. Cambridge University Press.Google Scholar
Baral, C. and Gelfond, M. 1994. Logic Programming and Knowledge Representation. Journal of Logic Programming. 19 (20), 73–148.CrossRefGoogle Scholar
Baral, C., Gelfond, M. and Rushton, N. 2004. Probabilistic reasoning with answer sets. In Proc. of LPNMR7, Springer Berlin/Heidelberg, Volume 2923, 21–33.Google Scholar
Boutilier, C., Reiter, R. and Price, B. 2001. Symbolic Dynamic Programming for First-Order MDPs. In Proc. of IJCAI 01, Morgan Kaufmann, San Francisco, CA, 690–700.Google Scholar
Breese, J. 1990. Construction of belief and decision networks. Tech. rep., Technical Memorandom 90, Rockwell International Science Center, Palo Alto, CA.Google Scholar
Chen, W., Swift, T. and Warren, D. 1995. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming. 24 (3), 161–201.CrossRefGoogle Scholar
Citrigno, S., Eiter, T., Faber, W., Gottlob, G., Koch, C., Leone, N., Mateis, C., Pfeifer, G. and Scarcello, F. 1997. The dlv system: Model generator and application front ends. In Proc. of the 12th Workshop on Logic Programming, Bry, F., Freitag, B. and Seipel, D., Eds. LMU, Munich, 128–137.Google Scholar
Cussens, J. 1999. Loglinear models for first-order probabilistic reasoning. In Proc. of the Fifteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA, 126–133.Google Scholar
De Vos, M., and Vermeir, D. 2000. Dynamically ordered probabilistic choice logic programming. In Proc. of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS2000). Volume 1974 of LNCS, pages 227–239. Springer Verlag, London, UK.Google Scholar
Dekhtyar, A. and Dekhtyar, M. 2004. Possible worlds semantics for probabilistic logic programs. In ICLP. 137–148.CrossRefGoogle Scholar
Ferraris, P. and Lifschitz, V. 2005. Weight constraints as nested expressions. Theory and Practice of Logic Programming 5, 45–74.Google Scholar
Ferraris, P. and Lifschitz, V. 2005. Mathematical foundations of answer set programming. We Will Show Them! Essays in Honour of Dov Gabbay. King's College Publications. 615–664.Google Scholar
Gebser, M., Kaufmann, B., Neumann, A. and Schaub, T. 2007. CLASP: A conflict-driven answer set solver. In LPNMR'07. 260–265.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of the Fifth Int'l Conference and Symposium on Logic Programming, MIT Press, Cambridge, MA, 1070–1080.Google Scholar
Gelfond, M., Rushton, N. and Zhu, W. 2006. Combining logical and probabilistic reasoning. In Proc. of AAAI 06 Spring Symposium: Formalizing and Compiling Background Knowledge and Its Applications to Knowledge Representation and Question Answering, AAAI Press, Menlo Park, California, 50–55.Google Scholar
Getoor, L., Friedman, N., Koller, D. and Pfeffer, A. 2001. Learning probabilistic relational models. In Relational data mining. Springer, 307–335.CrossRefGoogle Scholar
Getoor, L. and Taskar, B. 2007. Statistical Relational Learning. MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Halpern, J. 1990. An analysis of first-order logics of probability. Artificial Intelligence. 46, 311–350.CrossRefGoogle Scholar
Halpern, J. 2003. Reasoning about Uncertainty. MIT Press, Cambridge, MA.Google Scholar
Hilborn, R. and Mangel, M. 1997. The Ecological Detective. Princeton University Press.Google Scholar
Iwan, G. and Lakemeyer, G. 2002. What observations really tell us. In CogRob'02.CrossRefGoogle Scholar
Jr, H. E. K. and Teng, C. M. 2001. Uncertain Inference. Cambridge University Press.Google Scholar
Kersting, K. and De Raedt, L. 2007. Bayesian logic programs: Theory and Tool. In An Introduction to Statistical Relational Learning. Getoor, L. and Taskar, B., Eds. MIT Press, Cambridge, MA.Google Scholar
Koller, D. 1999. Probabilistic relational models. In ILP99. 3–13.CrossRefGoogle Scholar
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. and Scarcello, F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic. 7 (3), 499–562.CrossRefGoogle Scholar
Lierler, Y. 2005. Cmodels - SAT-based disjunctive answer set solver. In Proc. of Logic Programming and Non Monotonic Reasoning, Volume 3662 of LNCS, Springer, Berlin/Heidelberg, 447–451.CrossRefGoogle Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transaction on Computational Logic. 2, 526–541.CrossRefGoogle Scholar
Lifschitz, V., Tang, L. and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence. 25 (3–4), 369–389.CrossRefGoogle Scholar
Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Proc. of the Eleventh Int'l Conf. on Logic Programming, Van Hentenryck, P., Ed. 23–38.Google Scholar
Lin, F. and Zhao, Y. 2004. ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence. 157 (1–2), 115–137.CrossRefGoogle Scholar
Lukasiewicz, T. 1998. Probabilistic logic programming. In Proe. of European Conference on Artificial Intelligence. 388–392.Google Scholar
Muggleton, S. 1995. Stochastic logic programs. In Proc. of the 5th International Workshop on Inductive Logic Programming, De Raedt, L., Ed. Department of Computer Science, Katholieke Universiteit Leuven, 29.Google Scholar
Nelson, D. 1949. Constructible falsity. Journal of Symbolic logic. 14, 16–26.CrossRefGoogle Scholar
Ng, R. T. and Subrahmanian, V. S. 1992. Probabilistic logic programming. Information and Computation. 101 (2), 150–201.CrossRefGoogle Scholar
Ng, R. T. and Subrahmanian, V. S. 1994. Stable semantics for probabilistic deductive databases. Information and Computation. 110 (1), 42–83.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
Niemelä, I. and Simons, P. 1997. Smodels – an implementation of the stable model and well-founded semantics for normal logic programs. In Proc. 4th international conference on Logic programming and non-monotonic reasoning, Dix, J., Furbach, U., and Nerode, A., Eds. Springer, 420–429.CrossRefGoogle Scholar
Nilsson, N. 1986. Probabilistic logic. Artificial Intelligence. 28, 71–87.Google Scholar
Paskin, M. 2002. Maximum entropy probabilistic logic. Tech. Rep. UCB/CSD-01-1161, Computer Science Division, University of California, Berkeley, CA.Google Scholar
Pasula, H. and Russell, S. 2001. Approximate Inference for First-order Probabilistic Languages. IJCAI-01, Seattle, WA, 2001, 741–748.Google Scholar
Pearl, J. 2000. Causality. Cambridge University Press, New York, NY.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
Poole, D. 2000. Abducing through negation as failure: Stable models within the independent choice logic. Journal of Logic Programming. 44, 5–35.CrossRefGoogle Scholar
Reiter, R. 1978. On closed world data bases. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Plenum Press, New York, 119–140.Google Scholar
Richardson, M. and Domingos, P. 2006. Markov logic networks. Machine Learning. 62, 107–136.CrossRefGoogle Scholar
Riezler, S. 1998. Probabilistic constraint logic programming. Ph.D. thesis, University of Tubingen, Tubingen, Germany.Google Scholar
Costa, V. S., Page, D., Qazi, M. and Cussens, J. 2003. CLP(BN): Constraint logic programming for probabilistic knowledge. In Proceedings of the Nineteenth International Conference on Uncertainty in AI (UAI-2003), Morgan Kaufmann, San Francisco, CA.Google Scholar
Sato, T. 1995. A statistical learning method for logic programs with distribution semantics. In Proc. of the 12th International Conference on Logic Programming (ICLP95), MIT Press, Cambridge, MA, 715–729.Google Scholar
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence. 138 (1–2), 181–234.CrossRefGoogle Scholar
Vennekens, J., Denecker, M. and Bruynooge, M. 2006. Extending the role of causality in probabilistic modeling. http://www.cs.kuleuven.ac.be/~joost/#research.Google Scholar
Vennekens, J. 2007. Algebraic and Logical Study of Constructive Processes in Knowledge representation Ph.D Dissertation. K.U. Leuven. Belgium.Google Scholar
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In Proc. of International Conference on Logic Programming. 431–445.CrossRefGoogle Scholar
Wang, P. 2004. The limitation of Bayesianism. Artificial Intelligence. 158 (1), 97–106.CrossRefGoogle Scholar
Wellman, M., Breese, J. and Goldman, R. 1992. From knowledge bases to decision models. Knowledge Engineering Review. 35–53.CrossRefGoogle Scholar