Abductive Inference with Probabilistic Networks

  • Christian Borgelt
  • Rudolf Kruse
Chapter
Part of the Handbook of Defeasible Reasoning and Uncertainty Management Systems book series (HAND, volume 4)

Abstract

Abduction is a form of non-deductive logical inference. Examples given by [Peirce, 1958], who is said to have coined the term “abduction”, include the following:

I once landed at a seaport in a Turkish province; and as I was walking up to the house which I was to visit, I met a man upon horseback, surrounded by four horsemen holding a canopy over his head. As the governour of the province was the only personage I could think of who would be so greatly honoured, I inferred that this was he. This was a hypothesis.

Fossils are found; say remains like those of fishes, but far in the interior of the country. To explain the phenomenon, we suppose the sea once washed over this land. This is another hypothesis.

Numberless documents and monuments refer to a conqueror called Napoleon Bonaparte. Though we have not seen him, what we have seen, namely all those documents and monuments, cannot be explained without supposing that he really existed. Hypothesis again.

Keywords

Bayesian Network Directed Acyclic Graph Conditional Independence Argument Scheme Probabilistic Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. [Andersen et al., 1989]
    S. K. Andersen, K. G. Olesen, E. V. Jensen and F. Jensen. HUGIN — a shell for building Bayesian belief universes for expert systems. Proceedings of the 11th International Joint Conference on Artificial Intelligence (IJCAI’89, Detroit, MI), 1080–1085. Morgan Kaufman, San Mateo, CA, 1989.Google Scholar
  2. [Baldwin et al., 1995]
    J. F. Baldwin, T. P. Martin and B.W. Pilsworth. FRIL—Fuzzy and Evidential Reasoning in Artificial Intelligence. Research Studies Press/J. Wiley & Sons, Taunton/Chichester, 1995.Google Scholar
  3. [Bochenski, 1954]
    I. M. Bochenski. Die zeitgenössischen Denkmethoden. Franke-Verlag, Tübingen, 1954.Google Scholar
  4. [Borgelt, 1992]
    C. Borgelt. Konzeptioneller Vergleich verschiedener numerischer und logischer Ansätze abduktiver Inferenz. Diplomarbeit, TU Braunschweig, 1992.Google Scholar
  5. [Borgelt and Kruse, 1997]
    C. Borgelt and R. Kruse. Evaluation measures for learning probabilistic and possibilistic networks. Proceedings of the 6th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’97, Barcelona), Vol. 2:1034–1038 IEEE Press, Piscataway, NJ, 1997.Google Scholar
  6. [Borgelt and Kruse, 1999]
    C. Borgelt and R. Kruse. A Critique of Inductive Causation. Proc. 5 th European Conf. on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’99, London), LNAI 1638, 68–79. Springer, Heidelberg, 1999.Google Scholar
  7. [Buntine, 1994]
    W. Buntine. Operations for learning with graphical models. Journal of Artificial Intelligence Research 2: 159–225, 1994.Google Scholar
  8. [Bylander et al., 1991]
    T. Bylander, D. Allemang, M. C. Tanner and J. R. Josephson. The computational complexity of abduction. Artificial Intelligence 49: 25–60. North-Holland, Amsterdam, 1991.Google Scholar
  9. [Castillo et al., 1997]
    E. Castillo, J. M. Gutierrez and A. S. Hadi. Expert Systems and Probabilistic Network Models. Springer, New York, NY, 1997.CrossRefGoogle Scholar
  10. [Charniak and McDermott, 1985]
    E. Chamiak and D. McDermott. Introduction to Artificial Intelligence. Addison-Wesley, Reading, MA, 1985.Google Scholar
  11. [Chow and Liu, 1968]
    C. K. Chow and C. N. Liu. Approximating discrete probability distributions with dependence trees. IEEE Trans. on Information Theory 14 (3): 462–467. IEEE Press, Piscataway, NJ, 1968.Google Scholar
  12. [Cooper and Herskovits, 1992]
    G. F. Cooper and E. Herskovits. A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9:309–347. Kluwer, Dordrecht, 1992.Google Scholar
  13. [Dawid, 1979]
    A. Dawid. Conditional independence in statistical theory. SIAM Journal on Computing 41: 1–31, 1979.Google Scholar
  14. [Dechter, 1996]
    R. Dechter. Bucket elimination: a unifying framework for probabilistic inference. Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (UAI’96, Portland, OR), 211–219. Morgan Kaufman, San Mateo, CA, 1996.Google Scholar
  15. [Dubois and Prade, 1988]
    D. Dubois and H. Prade. Possibility Theory. Plenum Press, New York, NY, 1988.CrossRefGoogle Scholar
  16. [Hempel, 1966]
    C. G. Hempel. Philosophy of Natural Science. Prentice-Hall, Englewood Cliffs, NJ, 1966.Google Scholar
  17. [Hojsgaard and Thiesson, 1994]
    S. Hojsgaard and B. Thiesson. BIFROST — block recursive models induced from relevant knowledge, observations, and statistical techniques. Computational Statistics and Data Analysis, 1994.Google Scholar
  18. [Josephson and Josephson, 1996]
    J. R. Josephson and S. G. Josephson. Abductive Inference — Computation, Philosophy, Technology. Cambridge University Press, Cambridge, MA, 1996.Google Scholar
  19. [Kruse et al., 1991]
    R. Kruse, E. Schwecke, and J. Heinsohn. Uncertainty and Vagueness in Knowledge-based Systems: Numerical Methods (Series: Artificial Intelligence). Springer, Berlin, Germany 1991Google Scholar
  20. [Lauritzen and Spiegelhalter, 1988]
    S. L. Lauritzen and D. J. Spiegelhalter. Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, Series B, 2 (50): 157–224. Blackwell, Oxford, 1988.Google Scholar
  21. [Lauritzen et al., 1993]
    S. L. Lauritzen, B. Thiesson and D. Spiegelhalter. Diagnostic systems created by model selection methods — a case study. Proceedings of the 4th International Workshop on Artificial Intelligence and Statistics (Fort Lauderdale, FL), pp. 93–105, 1993.Google Scholar
  22. [Losee, 1993]
    J. Losee. A Historical Introduction to the Philosophy of Science (3rd edition). Oxford University Press, Oxford, 1993.Google Scholar
  23. [Patil et al., 1982]
    R. S. Patil, P. Szolovits and W. B. Schwartz. Modeling knowledge of the patient in acid-base and electrolyte disorders. In: P. Szolovits, ed. Artifical Intelligence in Medicine, pp. 191–226. Westview Press, Boulder, CO, 1982.Google Scholar
  24. [Pearl, 1986]
    J. Pearl. Fusion, Propagation, and Structuring in Belief Networks. Artificial Intelligence 29: 241–288, 1986.CrossRefGoogle Scholar
  25. [Pearl, 1992]
    J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (2nd edition). Morgan Kaufman, San Mateo, CA, 1992.Google Scholar
  26. [Pearl and Paz, 1987]
    J. Pearl and A. Paz. Graphoids: A Graph Based Logic for Reasoning about Relevance Relations. In: B. D. Boulay et al., eds. Advances in Artificial Intelligence 2, pp. 357–363. North Holland, Amsterdam, 1987.Google Scholar
  27. [Pearl and Wermuth, 1993]
    J. Pearl and N. Wermuth. When can association graphs admit a causal interpretation? Proceedings of the 4th International Workshop on Artificial Intelligence and Statistics (Fort Lauderdale, FL), pp. 141–150, 1993.Google Scholar
  28. [Peirce, 1958]
    C. S. Peirce. (C. Hartshome, P. Weiss and A. Burks, eds.) Collected Papers of Charles Sanders Peirce. Havard University Press, Cambridge, MA, 1958.Google Scholar
  29. [Peng and Reggia, 1989]
    Y. Peng and J. A. Reggia. Abductive Inference Models for Diagnostic Problem Solving. Springer, New York, NY, 1989.Google Scholar
  30. [Popper, 1934]
    K. R. Popper. Logik der Forschung. 1st edition: Julius Springer, Vienna, 1934. 9th edition: J. C. B. Mohr, Tübingen, 1989. English edition: The Logic of Scientific Discovery, Hutchinson, London, 1959.Google Scholar
  31. [Rasmussen, 1992]
    L. K. Rasmussen. Blood Group Determination of Danish Jersey Cattle in the F-blood Group System (Dina Research Report 8). Dina Foulum, Tjele, 1992.Google Scholar
  32. [Salmon, 1973]
    W. C. Salmon. Logic (2nd edition). Prentice-Hall, Englewood Cliffs, NJ, 1973.Google Scholar
  33. [Savage, 1954]
    L. J. Savage. The Foundations of Statistics. J. Wiley & Sons, New York, NY, 1954Google Scholar
  34. [Singh and Valtorta, 1993]
    M. Singh and M. Valtorta. An algorithm for the construction of Bayesian network structures from data. Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI’93), pp. 259–265. Morgan Kaufman, San Mateo, CA, 1993.Google Scholar
  35. [Smith, 1989]
    J. Q. Smith. Influence Diagrams for Statistical Modeling. Annals of Statistics 17 (2): 654–672, 1989.CrossRefGoogle Scholar
  36. [Spiegelhalter et al., 1993]
    D. Spiegelhalter, A. Dawid, S. Lauritzen and R. Cowell. Bayesian Analysis in Expert Systems. Statistical Science 8 (3): 219–283, 1993.CrossRefGoogle Scholar
  37. [Spirtes et al., 1993]
    P. Spirtes, C. Glymour and R. Schemes. Causation, Prediction, and Search (Lecture Notes in Statistics 81). Springer, New York, NY, 1993.Google Scholar
  38. [Spohn, 1980]
    W. Spohn. Stochastic independence, causal independence, and shieldability. Journal of Philosophical Logic 9: 73–99, 1980.CrossRefGoogle Scholar
  39. [Thiele, 1997]
    W. Thiele. Wasservögel und Strandvögel: Arten der Küsten und Feuchtgebiete. BLV Naturführer, Munich, 1997.Google Scholar
  40. [Verma and Pearl, 1990]
    T. S. Verma and J. Pearl. Causal networks: semantics and expressiveness. In: R. D. Shachter, T. S. Levitt L.N. Kanal, and J.F. Lemmer, eds. Uncertainty in Artificial Intelligence 4, pp. 69–76. North Holland, Amsterdam, 1990.Google Scholar
  41. [Verma and Pearl, 1992]
    T. S. Verma and J. Pearl 1992. An algorithm for deciding if a set of observed independencies has a causal explanation. Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence (UAI’92, Stanford, CA), pp. 323–330. Morgan Kaufman, San Mateo, CA, 1992.Google Scholar
  42. [Whittaker, 1990]
    J. Whittaker. Graphical Models in Applied Multivariate Statistics. J. Wiley & Sons, Chichester, 1990.Google Scholar
  43. [Zhang and Poole, 1996]
    N. L. Zhang and D. Poole. Exploiting causal independence in Bayesian network inference. Journal of Artificial Intelligence Research 5: 301–328, 1996.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Christian Borgelt
    • 1
  • Rudolf Kruse
    • 1
  1. 1.Department of Knowledge Processing and Language EngineeringOtto-von-Guericke-University of MagdeburgGermany

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