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Logic programming, abduction and probability

—A top-down anytime algorithm for estimating prior and posterior probabilities—

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Abstract

Probabilistic Horn abduction is a simple framework to combine probabilistic and logical reasoning into a coherent practical framework. The numbers can be consistently interpreted probabilistically, and all of the rules can be interpreted logically. The relationship between probabilistic Horn abduction and logic programming is at two levels. At the first level probabilistic Horn abduction is an extension of pure Prolog, that is useful for diagnosis and other evidential reasoning tasks. At another level, current logic programming implementation techniques can be used to efficiently implement probabilistic Horn abduction. This forms the basis of an “anytime” algorithm for estimating arbitrary conditional probabilities. The focus of this paper is on the implementation.

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References

  1. Apt, K. R. and Bezem, M., “Acyclic Programs,”New Generation Computing, 9, 3–4 pp. 335–363, 1991.

    Article  Google Scholar 

  2. Body, M. and Dean, T., “Solving Time-Dependent Planning Problems,” inProc. 11th International Joint Conf. on Artificial Intelligence, Detroit, MI, pp. 979–984, August 1989.

  3. Charniak, E. and Shimony, S. E., “Probabilistic Semantics for Cost Based Abduction,” inProc. 8th National Conference on Artificial Intelligence, Boston, pp. 106–111, July 1990.

  4. Clark, K. L., “Negation as Failure,” inLogic and Databases (H. Gallaire and J. Minker, eds.), Plenum Press, New York, pp. 293–322, 1978.

    Google Scholar 

  5. Console, L., Theseider Dupre, D. and Torasso, P., “On the Relationship between Abduction and Deduction,”Journal of Logic and Computation, 1, 5, pp. 661–690, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  6. Cox, P. T. and Pietrzykowski, T., “General Diagnosis by Abductive Inference,”Technical Report, CS8701, Computer Science, Technical University of Nove Scotia, Halifax, April 1987.

    Google Scholar 

  7. D’Ambrosio, B., “Real-Time Value-Driven Diagnosis,” inProc. Third International Workshop on the Principles of Diagnosis, Rosario, Washington, pp. 86–95, October 1992.

  8. de Kleer, J. and Williams, B. C., “Diagnosis with Behavioral Modes,” inProc. 11th International Joint Conf. on Artificial Intelligence, Detroit, pp. 1324–1330, August 1989.

  9. Finger, J. J. and Genesereth, M. R., “Residue: A Deductive Approach to Design Synthesis,”Technical Report, STAN-CS-85-1035, Department of Computer Science, Stanford University, Stanford, Cal., 1985.

    Google Scholar 

  10. Goebel, R., Furukawa, K. and Poole, D., “Using Definite Clauses and Integrity Constraints as the Basis for a Theory Formation Approach to Diagnostic Reasoning,” inProc. Third International Conference on Logic Programming, (E. Shapiro, ed.), London, pp. 211–222, July 1986.

  11. Inoue, K., “Consequence-Finding Based on Ordered Linear Resolution,” inProc. 12th International Joint Conf. on Artificial Intelligence, Sydney, Australia, pp. 158–164, August 1991.

  12. Inoue, K., “Linear Resolution for Consequence Finding,”Artificial Intelligence, 56, 2–3, pp. 301–353, August 1992.

    Article  MATH  MathSciNet  Google Scholar 

  13. Korf, K. E., “Depth-First Iterative Deepening: An Optimal Admissable Tree Search,”Artificial Intelligence, 27, 1, pp. 97–109, September 1985.

    Article  MATH  MathSciNet  Google Scholar 

  14. Lloyd, J. W.,Foundations of Logic Programming, Symbolic Computation Series, 2nd ed., Springer-Verlag, Berlin, 1987.

    Google Scholar 

  15. Naish, L., “Negation and Control in Prolog,”Lecture Notes in Computer Science 238, Springer-Verlag, 1986.

  16. Pearl, J.Heuristics, Addison-Wesley, Reading, MA, 1984.

    Google Scholar 

  17. Pearl, J.,Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA, 1988.

    Google Scholar 

  18. Pereira, F. C. N. and Shieber, S. M.,Prolog and Natural-Language Analysis, Center for the Study of Language and Information, 1987.

  19. Plaisted, D. A., “The Occur-Check Problem in Prolog,”New Generation Computing, 2, pp. 309–322, 1984.

    Article  MATH  Google Scholar 

  20. Poole, D., “A Logical Framework for Default Reasoning,”Artificial Intelligence, 36, 1, pp. 27–47, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  21. Poole, D., “Representing Knowledge for Logic-Based Diagnosis,” inInternational Conference on Fifth Generation Computing Systems, Tokyo, Japan, pp. 1282–1290, November 1988.

  22. Poole, D., “Compiling a Default Reasoning System into Prolog,”New Generation Computing, 9, 1, pp. 3–38, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  23. Poole, D., “Representing Bayesian Networks within Probabilistic Horn Abduction,”in Proc. Seventh Conf. on Uncertainty in Artificial Intelligence, Los Angeles, pp. 271–278, July 1991.

  24. Poole, D., “Representing Diagnostic Knowledge for Probabilistic Horn Abduction,” inProc. 12th International Joint Conf. on Artificial Intelligence, Sydney, pp. 1129–1135, August 1991.

  25. Poole, D., “Probabilistic Horn Abduction and Bayesian Networks,”Technical Report, 92-20, Department of Computer Science, University of British Columbia, August 1992, to appear,Artificial Intelligence, 1993.

  26. Poole, D., “Search for Computing Posterior Probabilities in Bayesian Natworks,”Technical Report, 92-24, Department of Computer Science, University of British Columbia, September 1992.

  27. Poole, D., Goebel, R. and Aleliunas, R., “Theorist: A Logical Reasoning System for Defaults and Diagnosis,” inThe Knowledge Frontier: Essays in the Representation of Knowledge (N. Cercone and G. McCalla, eds.), Springer-Verlag, New York, NY, pp. 331–352, 1987.

    Google Scholar 

  28. Pople, Jr. H. E., “On the Mechanization of Abductive Logic,” inProc. 3rd International Joint Conf. on Artificial Intelligence, Stanford, pp. 147–152, August 1973.

  29. Reiter, R. and de Kleer, J., “Foundations of Assumption-Based Truth Maintenance Systems: Preliminary Report,” inProc. 6th National Conference on Artificial Intelligence, Seattle, pp. 183–188, July 1987.

  30. Sattar, A. and Goebel, R., “Using Crucial Literals to Select Better Theories,”Computational Intelligence, 7, 1, pp. 11–22, February 1991.

    Article  MathSciNet  Google Scholar 

  31. Shanahan, M., “Prediction is Deduction, but Explanation Is Abduction,” inProc. 11th International Joint Conf. on Artificial Intelligence, Detroit, Mich., pp. 1055–1060, August, 1989.

  32. Sterling, L. and Shapiro, E.,The Art of Prolog, MIT Press, Cambridge, MA, 1986.

    MATH  Google Scholar 

  33. Stickel, M. E., “A Prolog-Like Inference System for Computing Minimum-Cost Abductive Explanations in Natural Language Interpretations,”Technical Note, 451, SRI International, Menlo Park, CA, September, 1988.

    Google Scholar 

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Authors and Affiliations

  1. Department of British Columbia, University of British Colubmia, V6T 1Z2, Vancouver, B. C., Canada

    David Poole

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  1. David Poole
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David Poole, Ph. D.: He is an associate professor in the Department of Computer Science at the University of British Columbia, and a Scholar of the Canadian Institute for Advanced Research. He obtained his Ph. D. from the Australian National University in 1984, was part of the Logic Programming and AI Group at the University of Waterloo from 1984–1988, and has been at the University of British Columbia since 1988. He was an invited visiting researcher at ICOT in 1989, and is a member of the Editorial Board of New Generation Computing. His main research interests are automated logical and probabilistic reasoning for diagnosis, common sense reasoning and decision making. He pioneered assumption-based logical reasoning, co-developed the system “Theorist” which has been used for both default and abductive reasoning, and has combined these ideas with probabilistic representations and algorithms.

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Poole, D. Logic programming, abduction and probability. New Gener Comput 11, 377–400 (1993). https://doi.org/10.1007/BF03037184

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  • DOI: https://doi.org/10.1007/BF03037184

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