Skip to main content
SpringerLink
Log in

Statistical Abduction with Tabulation

  • Chapter
  • First Online:
Book cover Computational Logic: Logic Programming and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2408))

Abstract

We propose statistical abduction as a first-order logical framework for representing, inferring and learning probabilistic knowledge. It semantically integrates logical abduction with a parameterized distribution over abducibles. We show that statistical abduction combined with tabulated search provides an efficient algorithm for probability computation, a Viterbi-like algorithm for finding the most likely explanation, and an EM learning algorithm (the graphical EM algorithm) for learning parameters associated with the distribution which achieve the same computational complexity as those specialized algorithms for HMMs (hidden Markov models), PCFGs (probabilistic context-free grammars) and sc-BNs (singly connected Bayesian networks).

This paper is based on a workshop paper presented at the UAI-2000 workshop on Fusion of Domain Knowledge with Data for Decision Support, Stanford, 2000.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bacchus, F., Using First-Order Probability Logic for the Construction of Bayesian Networks, Proc. of UAI’93, pp219–226, 1993.

    Google Scholar 

  2. Baker, J.K., Trainable Grammars for Speech Recognition, Proc. of Spring Conference of the Acoustical Society of America, pp547–550, 1979.

    Google Scholar 

  3. Breese, J.S., Construction of Belief and Decision Networks, J. of Computational Intelligence, Vol. 8 No. 4 pp624–647, 1992.

    Article  Google Scholar 

  4. Castillo, E., Gutierrez, J.M., and Hadi, A.S., Expert Systems and Probabilistic Network Models, Springer-Verlag, 1997.

    Google Scholar 

  5. Charniak, E., A neat theory of marker passing, Proc. of AAAI’86, pp584–588, 1986.

    Google Scholar 

  6. Charniak, E., Statistical Language Learning, The MIT Press, 1993.

    Google Scholar 

  7. Clark, K., Negation as failure, In Gallaire, H., and Minker, J. (eds), Logic and Databases, pp293–322, Plenum Press, 1978.

    Google Scholar 

  8. Cormen, T.H., Leiserson, C. E. and Rivest, R.L., Introduction to Algorithms, MIT Press, 1990.

    Google Scholar 

  9. Csinger, A., Booth, K.S. and Poole, D., AI Meets Authoring: User Models for Intelligent Multimedia, Artificial Intelligence Review 8, pp447–468, 1995.

    Article  Google Scholar 

  10. Cussens, J., Loglinear models for first-order probabilistic reasoning, Proc. of UAI’99, pp126–133, 1999.

    Google Scholar 

  11. Cussens, J., Parameter estimation in stochasitc logic programs, Machine Learning 44, pp245–271, 2001.

    Article  MATH  Google Scholar 

  12. Dekhtyar, A.and Subrahmanian, V.S., Hybrid Probabilistic Programs, Proc. of ICLP’97, pp391–405, 1997.

    Google Scholar 

  13. Doets, K., From Logic to Logic Programming, MIT Press, Cambridge, 1994.

    MATH  Google Scholar 

  14. Eshghi, K. Abductive Planning with Event Calculus, Proc. of ILCP’88, pp562–579, 1988.

    Google Scholar 

  15. Hobbs, J.R., Stickel, M.E., Appelt, D.E. and Martin, P., Interpretation as abduction, Artificial Intelligence 63, pp69–142, 1993.

    Article  Google Scholar 

  16. Kakas, A.C., Kowalski, R.A. and Toni, F., Abductive Logic Programming, J. Logic Computation, Vol. 2 No. 6, pp719–770, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  17. Kakas, A.C., Kowalski, R.A. and Toni, F., The role of abduction in logic programming, Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, pp235–324, 1998.

    Google Scholar 

  18. Kameya, Y. and Sato, T., Efficient EM learning with tabulation for parameterized logic programs, Proc. of CL2000, LNAI 1861, Springer-Verlag, pp269–284, 2000.

    Google Scholar 

  19. Koller, D. and Pfeffer, A., Learning probabilities for noisy first-order rules, Proc. of IJCAI’97, Nagoya, pp1316–1321, 1997.

    Google Scholar 

  20. Koller, D., McAllester, D. and Pfeffer, A., Effective Bayesian Inference for Stochastic Programs, Proc. of AAAI’97, Rhode Island, pp740–747, 1997.

    Google Scholar 

  21. Lakshmanan, L.V.S. and Sadri, F., Probabilistic Deductive Databases, Proc. of ILPS’94 pp254–268, 1994.

    Google Scholar 

  22. Manning, C. D. and Schütze, H., Foundations of Statistical Natural Language Processing, The MIT Press, 1999.

    Google Scholar 

  23. McLachlan, G. J. and Krishnan, T., The EM Algorithm and Extensions, Wiley Interscience, 1997.

    Google Scholar 

  24. Muggleton, S., Stochastic Logic Programs, in Advances in Inductive Logic Programming (Raedt, L. De ed.) OSP Press, pp254–264, 1996.

    Google Scholar 

  25. Ng, R. and Subrahmanian, V.S., Probabilistic Logic Programming, Information and Computation 101, pp150–201, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  26. Ngo, L. and Haddawy, P., Answering Queries from Context-Sensitive Probabilistic Knowledge Bases, Theoretical Computer Science 171, pp147–177, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  27. Nilsson, N.J., Probabilistic Logic, Artificial Intelligence 28, pp71–87, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  28. Pearl, J., Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, 1988.

    Google Scholar 

  29. Pfeffer, A., IBAL:A Probabilistic Programming Language, Proc. of IJCAI’01, pp733–740, 2001.

    Google Scholar 

  30. Poole, D., Goebel, R. and Aleliunas, R., Theorist: a logical reasoning system for default and diagnosis, In Cercone, N., and McCalla., eds., The Knowledge Frontier, Springer, pp331–352, 1987.

    Google Scholar 

  31. Poole, D., Probabilistic Horn abduction and Bayesian networks, Artificial Intelligence 64, pp81–129, 1993.

    Article  MATH  Google Scholar 

  32. Rabiner, L. and Juang, B. Foundations of Speech Recognition, Prentice-Hall, 1993.

    Google Scholar 

  33. Sato, T., A Statistical Learning Method for Logic Programs with Distribution Semantics, Proc. of ICLP’95, pp715–729, 1995.

    Google Scholar 

  34. Sato, T. and Kameya, Y., PRISM:A Language for Symbolic-Statistical Modeling, Proc. of IJCAI’97, pp1330–1335, 1997.

    Google Scholar 

  35. Sato, T., Modeling Scientific Theories as PRISM Programs, ECAI Workshop on Machine Discovery, pp37–45, 1998.

    Google Scholar 

  36. Sato, T., Parameterized Logic Programs where Computing Meets Learning, Proc. of FLOPS2001, LNCS 2024, 2001, pp40–60.

    Google Scholar 

  37. Sato, T., Kameya, Y., Abe, S. and Shirai, K., Fast EM learning of a Family of PCFGs, Titech Technical Report (Dept. of CS) TR01-0006, Tokyo Institute of Technology, 2001.

    Google Scholar 

  38. Sato, T. and Kameya, Y., Parameter Learning of Logic Programs for Symbolic-statistical Modeling, submitted for publication.

    Google Scholar 

  39. Sato, T., Abe, S., Kameya, Y. and Shirai, K., A Separate-and-Learn Approach to EM Learning of PCFGs, Proc. of NLPRS2001, Tokyo, 2001.

    Google Scholar 

  40. Sakama, T. and Inoue, K., Representing Priorities in Logic Programs, Proc. of JIC-SLP’96, MIT Press, pp82–96, 1996.

    Google Scholar 

  41. Shanahan, M., Prediction is Deduction but Explanation is Abduction, Proc. of IJCAI’89, pp1055–1060, 1989.

    Google Scholar 

  42. Tamaki, H. and Sato, T., OLD resolution with tabulation, Proc. of ICLP’86, LNCS 225, pp84–98, 1986.

    Google Scholar 

  43. Wetherell, C.S., Probabilistic Languages: A Review and Some Open Questions, Computing Surveys, Vol. 12, No. 4, pp361–379, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  44. White, H.C., An Anatomy of Kinship, Prentice-Hall INC., 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama Meguro-ku, Tokyo, Japan, 152-8552

    Taisuke Sato & Yoshitaka Kameya

Authors
  1. Taisuke Sato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoshitaka Kameya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos St., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  2. Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, London, SW7 2BZ, UK

    Fariba Sadri

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sato, T., Kameya, Y. (2002). Statistical Abduction with Tabulation. In: Kakas, A.C., Sadri, F. (eds) Computational Logic: Logic Programming and Beyond. Lecture Notes in Computer Science(), vol 2408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45632-5_22

Download citation

  • DOI: https://doi.org/10.1007/3-540-45632-5_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43960-8

  • Online ISBN: 978-3-540-45632-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation