On the semantics of rule-based expert systems with uncertainty

  • Michael Kifer
  • Ai Li
Logic And Deductive Databases
Part of the Lecture Notes in Computer Science book series (LNCS, volume 326)

Abstract

We present a formal semantics for rule-based systems with uncertainty (this field has also become known as “quantitative logic programming”). Unlike previous works, our framework is general enough to accommodate most of the known schemes of reasoning with uncertainty found in the existing expert systems. We provide a rigorous treatment of the issue of evidential independence, and study its impact on the semantics. To the best of our knowledge, this issue has not been addressed before in the literature on quantitative logic programming. In expert systems evidential independence received only an ad hoc treatment, while the approaches found in the theory of evidential reasoning are feasible only in small scale systems. We discuss the problem of query optimization and, as a first step, present a quantitative semi-nave query evaluation algorithm — generalization of a method well-known in deductive databases. Treatment of negation and conflicting evidence based on, so called, support logic is given in the last part of the paper, where we extend the semantics of stratified programs to deal with uncertainty.

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7. References

  1. 1.
    K. R. Apt, H. Blair and A. Walker, “Towards a Theory of Declarative Knowledge”, in Foundations of Deductive Databases and Logic Programming, J. Minker, (ed.), Morgan-Kaufmann, 1988, 89–148.Google Scholar
  2. 2.
    I. Balbin and K. Ramamohanarao, “A Generalization of the Differential Approach to Recursive Query Evaluation”, J. of Logic Programming, 4, (1987), 259–262.Google Scholar
  3. 3.
    J. F. Baldwin, T. P. Martin and B. W. Pilsworth, FRIL Manual, EQUIPU-AIR, Ltd., Bristol, UK, 1987.Google Scholar
  4. 4.
    J. F. Baldwin and M. R. M. Monk, “Evidence Theory, Fuzzy Logic and Logic Programming”, ITRC Tech. Rep.# 109, University of Bristol, UK, 1987.Google Scholar
  5. 5.
    J. F. Baldwin, “Evidential Support Logic Programming”, Fuzzy Sets and Systems, 24, (1987), 1–26.Google Scholar
  6. 6.
    F. Bancilhon, “Naive Evaluation of Recursively Defined Relations”, Tech. Rep.# DB-004-85, MCC, 1985.Google Scholar
  7. 7.
    C. Beeri and R. Ramakrishnan, “On the Power of Magic”, Proc. of the ACM SIGACT-SIGMOD Symp. on Prin. of Database Systems, 1987, 269–283.Google Scholar
  8. 8.
    B. G. Buchanan and E. H. Shortliffe, (eds.), Rule-Based Expert Systems, Addison-Wesley, 1984.Google Scholar
  9. 9.
    A. K. Chandra and D. Harel, “Horn Clauses and Generalizations”, J. of Logic Programming, 1985, 1–15.Google Scholar
  10. 10.
    K. L. Clark, “Negation as Failure”, in Logic and Databases, H. Gallaire and J. Minker, (eds.), Plenum Press, New York, 1978, 293–324.Google Scholar
  11. 11.
    W. F. Clocksin and C. S. Mellish, Programming in Prolog, Springer Verlag, Berlin-Heidelberg-New York, 1981.Google Scholar
  12. 12.
    D. Dubois and H. Prade, (eds.), Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980.Google Scholar
  13. 13.
    E. A. Feigenbaum, “The Art of Artificial Intelligence: 1. Themes and Case Studies of Knowledge Engineering”, IJCAI-77, 1977, 1014–1029.Google Scholar
  14. 14.
    R. Frost, Introduction to Knowledge Base Systems, Macmillan Publishing C., 1986.Google Scholar
  15. 15.
    G. Gardarin, “Magic Functions: A Technique to Optimize Extended Datalog Recursive Programs”, Proc. of the ACM Intl. Conf. on Very Large Data Bases, 1987, 21–30.Google Scholar
  16. 16.
    M. L. Ginsberg, “Nonmonotonic Reasoning Using Dempster's Rule”, AAAI-84, Austin, TX, 1984, 126–129.Google Scholar
  17. 17.
    M. L. Ginsberg, “Multivalued Logics”, in Readings in Non-Monotonic Reasoning, M. L. Ginsgerg, (ed.), 1987, 251–255.Google Scholar
  18. 18.
    U. Guntzer and W. K. A. R. Bayer, “On Evaluation of Recursion in Deductive Database Systems by Efficient Differential Fixpoint Iteration”, 3-d Int. Conf. on Data Engineering, 1987, 120–129.Google Scholar
  19. 19.
    F. Hayes-Roth, D. Waterman and D. Lenat, (eds.), Building Expert Systems, Addison-Wesley, 1983.Google Scholar
  20. 20.
    F. Hayes-Roth, “Rule-Based Systems”, Comm. ACM, 28, 9 (Sep. 1985), 921–932.Google Scholar
  21. 21.
    D. E. Heckerman and E. J. Horovitz, “On the Expressive Power of Rule-Based Systems for Reasoning with Uncertainty”, Automated Reasoning, 1987, 121–126.Google Scholar
  22. 22.
    L. N. Kanal and J. F. Lemmer, (eds.), Uncertainty in Artificial Intelligence (Machine Intelligence and Pattern Recognition, vol. 4), North Holland, 1986.Google Scholar
  23. 23.
    M. Kifer and E. L. Lozinskii, “A Framework for an Efficient Implementation of Deductive Database Systems”, Proceedings of the 6-th Advanced Database Symposium, Tokyo, Japan, Aug. 1986.Google Scholar
  24. 24.
    R. C. T. Lee, “Fuzzy Logic and the Resolution Principle”, J. of ACM, 1972, 109–119.Google Scholar
  25. 25.
    V. Lifschitz, “On the Declarative Semantics of Logic Programs with Negation”, in Foundations of Deductive Databases and Logic Programming, J. Minker, (ed.), Morgan-Kaufmann, Los Altos, CA, 1988, 177–192.Google Scholar
  26. 26.
    J. W. Lloyd, Foundations of Logic Programming (Second Edition), Springer Verlag, 1987.Google Scholar
  27. 27.
    H. Prade, “A Synthetic View of Approximate Reasoning Techniques”, IJCAI, 1983, 130–136.Google Scholar
  28. 28.
    T. C. Przymusinski, “On the Declarative Semantics of Deductive Databases and Logic Programs”, in Foundations of Deductive Databases and Logic Programming, J. Minker, (ed.), Morgan-Kaufmann, Los Altos, CA, 1988, 193–216.Google Scholar
  29. 29.
    R. Reiter, “On Closed World Databases”, in Logic and Databases, H. Gallaire and J. Minker, (eds.), Plenum Press, New York, 1978, 55–76.Google Scholar
  30. 30.
    D. C. Rine, “Some Relationships between Logic Programming and Multiple-Valued Logic”, Symp. on Multiple-Valued Logic, 1986, 160–163.Google Scholar
  31. 31.
    E. Sandewall, “A Functional Approach to Non-Monotonic Logic”, IJCAI-85, 1985, 100–106.Google Scholar
  32. 32.
    G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, 1976.Google Scholar
  33. 33.
    E. Shapiro, “Logic Programs with Uncertainties: A Tool for Implementing Rule-Based Systems”, IJCAI-83, 1983, 529–532.Google Scholar
  34. 34.
    V. S. Subrahmanian, “On the Semantics of Quantitative Logic Programs”, IEEE Symposium on Logic Programming, 1987, 173–182.Google Scholar
  35. 35.
    J. D. Ullman, Principles of Database and Knowledge-Base Systems, Computer Science Press, Rockville, MD, 1988.Google Scholar
  36. 36.
    M. H. van Emden and R. A. Kowalski, “The Semantics of Predicate Logic as a Programming Language”, J. ACM, 23, 4 (Oct. 1976), 733–742.CrossRefGoogle Scholar
  37. 37.
    M. H. van Emden, “Quantitative Deduction and its Fixpoint Theory”, The Journal of Logic Programming, 1986, 37–53.Google Scholar
  38. 38.
    L. Vieille, “Recursive Axioms in Deductive Databases: The Query-Subquery Approach”, Proc. of the 1-st Conf. on Expert Database Systems, Charleston, SC, 1986, 179–196.Google Scholar
  39. 39.
    M. Zamankova-Leech and A. Kandel, Fuzzy Relational Databases — a Key to Expert Systems, Verlag TUV Rheinland, Koln, 1984.Google Scholar
  40. 40.
    A. Zvieli, “A Fuzzy Relational Calculus”, Proc. of the 1-st Int. Conf. of Expert Database Systems, Charlestone, SC, 1986, 225–240.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Michael Kifer
    • 1
  • Ai Li
    • 1
  1. 1.Department of Computer ScienceSUNY at Stony BrookU.S.A.

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