Independence in Relational Languages with Finite Domains
Resumo
Este artigo introduz uma linguagem de primeira-ordem restrita que combina sentenças lógicas e asserções probabilísticas em domínios finitos. Neste esforço preliminar para construir um instrumento geral de representação de conhecimento, apresentamos a linguagem e um algoritmo de inferência baseado em proposicionalização e redução para programação multilinear.Referências
Andersen, K. A. and Hooker, J. N. (1994). Bayesian logic. Decision Support Systems, 11:191–210.
Chandru, V. and Hooker, J. (1999). Optimization methods for logical inference. John Wiley & Sons Inc.
R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and Expert Systems. Springer-Verlag, New York, 1999.
Cozman, F. G., de Campos, C. P., and da Rocha, J. C. F. (2006). Probabilistic logic with strong independence. In Brazilian Symposium on Artificial Intelligence.
Cozman, F. G., de Campos, C. P., and da Rocha, J. C. F. (2007). Probabilistic logic with independence. International Journal of Approximate Reasoning, accepted for publication.
de Campos, C. P. and Cozman, F. G. (2004). Inference in credal networs using multilinear programming. In Onaindia, E. and Staab, S., editors, Proceedings of the Second Starting AI Researchers’ Symposium (STAIRS), pages 50–61, Amsterdam, The Netherlands. IOS Press.
de Salvo Braz, R., Amir, E., and Roth, D. (2006). Lifted first-order probabilistic inference. In International Joint Conference in Artificial Intelligence (IJCAI).
Getoor, L., Friedman, N., Koller, D., and Taskar, B. (2001). Learning probabilistic models of relational structure. In International Conference on Machine Learning, pages 170–177.
Giugno, R. and Lukasiewicz, T. (2002). P-SHOQ(D): A probabilistic extension of SHOQ(D) for probabilistic ontologies in the semantic web. In Flesca, S., Greco, S., Leone, N., and Ianni, G., editors, Proceedings of the 8th European Conference on Logics in Artificial Intelligence (JELIA), volume 2424, pages 86–97, Cosenza, Italy. Lecture Notes in Artificial Intelligence, Springer.
Halpern, J. Y. (2003). Reasoning about uncertainty. MIT Press, Cambridge, Massachusetts.
Hansen, P. and Jaumard, B. (1996). Probabilistic satisfiability. Technical Report G-96-31, Les Cahiers du GERAD, École Polytechique de Montréal.
Jaeger, M. (1997). Relational Bayesian networks. In Geiger, D. and Shenoy, P. P., editors, Conference on Uncertainty in Artificial Intelligence, pages 266–273, San Francisco, California. Morgan Kaufmann.
Jaeger, M. (2001). Complex probabilistic modeling with recursive relational bayesian networks. Annals of Mathematics and Artificial Intelligence, 32:179–220.
Lakshmanan, L. V. S. and Sadri, F. (1994). Probabilistic deductive databases. In Symposium on Logic Programming, pages 254–268.
Lukasiewicz, T. (1998). Probabilistic logic programming. In European Conference on Artificial Intelligence, pages 388–392.
Lukasiewicz, T. (2001). Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2(3):289–339.
Nerode, A. and Shore, R. A. (1997). Logic for Applications (2nd ed.). Springer-Verlag, New York.
Ng, R. and Subrahmanian, V. S. (1992). Probabilistic logic programming. Information and Computation, 101(2):150–201.
Ngo, L. and Haddawy, P. (1997). Answering queries from context-sensitive probabilistic knowledge bases. Theoretical Computer Science, 171(1–2):147–177.
Nilsson, N. J. (1986). Probabilistic logic. Artificial Intelligence, 28:71–87.
Ognjanović, Z. (2006). Discrete linear-time probabilistic logics: Completeness, decidability and complexity. Journal of Logic Computation, 16(2):257–285.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, California, 1988.
Poole, D. (2003). First-order probabilistic inference. In International Joint Conference on Artificial Intelligence (IJCAI), pages 985–991.
H.D. Sherali and W.P. Adams. A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Academic Publishers, 1999.
Chandru, V. and Hooker, J. (1999). Optimization methods for logical inference. John Wiley & Sons Inc.
R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and Expert Systems. Springer-Verlag, New York, 1999.
Cozman, F. G., de Campos, C. P., and da Rocha, J. C. F. (2006). Probabilistic logic with strong independence. In Brazilian Symposium on Artificial Intelligence.
Cozman, F. G., de Campos, C. P., and da Rocha, J. C. F. (2007). Probabilistic logic with independence. International Journal of Approximate Reasoning, accepted for publication.
de Campos, C. P. and Cozman, F. G. (2004). Inference in credal networs using multilinear programming. In Onaindia, E. and Staab, S., editors, Proceedings of the Second Starting AI Researchers’ Symposium (STAIRS), pages 50–61, Amsterdam, The Netherlands. IOS Press.
de Salvo Braz, R., Amir, E., and Roth, D. (2006). Lifted first-order probabilistic inference. In International Joint Conference in Artificial Intelligence (IJCAI).
Getoor, L., Friedman, N., Koller, D., and Taskar, B. (2001). Learning probabilistic models of relational structure. In International Conference on Machine Learning, pages 170–177.
Giugno, R. and Lukasiewicz, T. (2002). P-SHOQ(D): A probabilistic extension of SHOQ(D) for probabilistic ontologies in the semantic web. In Flesca, S., Greco, S., Leone, N., and Ianni, G., editors, Proceedings of the 8th European Conference on Logics in Artificial Intelligence (JELIA), volume 2424, pages 86–97, Cosenza, Italy. Lecture Notes in Artificial Intelligence, Springer.
Halpern, J. Y. (2003). Reasoning about uncertainty. MIT Press, Cambridge, Massachusetts.
Hansen, P. and Jaumard, B. (1996). Probabilistic satisfiability. Technical Report G-96-31, Les Cahiers du GERAD, École Polytechique de Montréal.
Jaeger, M. (1997). Relational Bayesian networks. In Geiger, D. and Shenoy, P. P., editors, Conference on Uncertainty in Artificial Intelligence, pages 266–273, San Francisco, California. Morgan Kaufmann.
Jaeger, M. (2001). Complex probabilistic modeling with recursive relational bayesian networks. Annals of Mathematics and Artificial Intelligence, 32:179–220.
Lakshmanan, L. V. S. and Sadri, F. (1994). Probabilistic deductive databases. In Symposium on Logic Programming, pages 254–268.
Lukasiewicz, T. (1998). Probabilistic logic programming. In European Conference on Artificial Intelligence, pages 388–392.
Lukasiewicz, T. (2001). Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2(3):289–339.
Nerode, A. and Shore, R. A. (1997). Logic for Applications (2nd ed.). Springer-Verlag, New York.
Ng, R. and Subrahmanian, V. S. (1992). Probabilistic logic programming. Information and Computation, 101(2):150–201.
Ngo, L. and Haddawy, P. (1997). Answering queries from context-sensitive probabilistic knowledge bases. Theoretical Computer Science, 171(1–2):147–177.
Nilsson, N. J. (1986). Probabilistic logic. Artificial Intelligence, 28:71–87.
Ognjanović, Z. (2006). Discrete linear-time probabilistic logics: Completeness, decidability and complexity. Journal of Logic Computation, 16(2):257–285.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, California, 1988.
Poole, D. (2003). First-order probabilistic inference. In International Joint Conference on Artificial Intelligence (IJCAI), pages 985–991.
H.D. Sherali and W.P. Adams. A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Academic Publishers, 1999.
Publicado
30/06/2007
Como Citar
LUNA, José E. Ochoa; CAMPOS, Cassio P. de; COZMAN, Fabio G..
Independence in Relational Languages with Finite Domains. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 6. , 2007, Rio de Janeiro/RJ.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2007
.
p. 1421-1429.
ISSN 2763-9061.
