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Automated reasoning with uncertainties

  • Flávio S. Corrêa da Silva
  • Dave S. Robertson
  • Jane Hesketh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 808)

Abstract

In this work we assume that uncertainty is a multifaceted concept and present a system for automated reasoning with multiple representations of uncertainty.

We present a case study on developing a computational language for reasoning with uncertainty, starting with a semantically sound and computationally tractable language and gradually extending it with specialised syntactic constructs to represent measures of uncertainty, while preserving its unambiguous semantic characterization and computability properties. Our initial language is the language of normal clauses with SLDNF as the inference rule, and we select three specific facets of uncertainty for our study: vagueness, statistics and degrees of belief.

The resulting language is semantically sound and computationally tracable. It also admits relatively efficient implementations employing α-β pruning and caching.

Keywords

Logic Program Free Variable Automate Reasoning Unit Clause Vague Predicate 
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. Abadi, M., and J.Y. Halpern: Decidability and Expressiveness for First-Order Logics of Probability. IBM Research Report RJ 7220, 1989.Google Scholar
  2. Apt, K.F.: Introduction to Logic Programming. Centre for Mathematics and Computer Science Report CSR 8741, 1987.Google Scholar
  3. Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. University of Alberta, 1988.Google Scholar
  4. Bacchus, F.: “Lp, a Logic for Representing and Reasoning with Statistical Knowledge,” in: Computational Intelligence 6 (1990a) 209–231.Google Scholar
  5. Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. MIT Press, 1990b.Google Scholar
  6. Bundy, A.: “Incidence Calculus: a Mechanism for Probabilistic Reasoning,” in: Journal of Automated Reasoning 1 (1985) 263–284.Google Scholar
  7. Corrêa da Silva, F.S.: Automated Reasoning with Uncertainties. University of Edinburgh, Department of Artificial Intelligence, 1992.Google Scholar
  8. Corrêa da Silva, F.S., and A. Bundy: On Some Equivalence Relations Between Incidence Calculus and Dempster-Shafer Theory of Evidence. 6th Conference on Uncertainty in Artificial Intelligence, 1990.Google Scholar
  9. Corrêa da Silva, F.S., and A. Bundy: A Rational Reconstruction of Incidence Calculus. University of Edinburgh, Department of Artificial: Intelligence Report 517, 1991.Google Scholar
  10. Dubois, D., and H. Prade: “An Introduction to Possibilistic and Fuzzy Logics,” in: P. Smets et al. (eds.), Non-standard Logics for Automated Reasoning Academic Press, 1988.Google Scholar
  11. Dubois, D., and H. Prade: “Fuzzy Sets, Probability and Measurement,” in: European Journal of Operational Research 40 (1989) 135–154.Google Scholar
  12. Dudley, R.M.: Real Analysis and Probability. Wadsworth & Brooks/Cole, 1989.Google Scholar
  13. Fagin, R., and J.Y. Halpern: Uncertainty, Belief, and Probability. IBM Research Report RJ 6191, 1989a.Google Scholar
  14. Fagin, R., and J.Y. Halpern: A New Approach to Updating Beliefs. IBM Research Report RJ 7222, 1989.Google Scholar
  15. Fitting, M.: “Logic Programming on a Topological Bilattice,” in: Fundamenta Informaticae XI (1988) 209–218.Google Scholar
  16. Fitting, M.: “Bilattices in Logic Programming,” in: Proceedings of the 20th International Symposium on Multiple-valued Logic, 1990.Google Scholar
  17. Halpern, J.Y.: “An Analysis of First-Order Logics of Probability,” in: Artificial Intelligence 46 (1990) 311–350.Google Scholar
  18. Halpern, J.Y., and R. Fagin: Two Views of Belief: Belief as Generalised Probability and Belief as Evidence. IBM Research Report RJ 7221, 1989.Google Scholar
  19. Hinde, C.J.: “Fuzzy Prolog,” in: International Journal of Man-Machine Studies 24 (1986) 569–595.Google Scholar
  20. Ishizuka, M., and K. Kanai: “Prolog-ELF Incorporating Fuzzy Logic.” in: IJCAI'85 — Proceedings of the 9th International Joint Conference on Artificial Intelligence, 1985.Google Scholar
  21. Kifer, M., and V.S. Subrahmanian: “Theory of Generalized Annotated Logic Programs and Its Applications,” in: Journal of Logic Programming 12, 1991.Google Scholar
  22. Klement, E.P.: “Construction of Fuzzy σ-algebras Using Triangular Norms,” in: Journal of Mathematical Analysis and Applications 85 (1982) 543–565.Google Scholar
  23. Kunen, K.: “Signed Data Dependencies in Logic Programs,” in: Journal of Logic Programming 7 (1989) 231–245.Google Scholar
  24. Lee, R.C.T.: “Fuzzy Logic and the Resolution Principle,” in: Journal of the ACM 19 (1972) 109–119.Google Scholar
  25. Mendelson, E.: Introduction to Mathematical Logic (3rd. ed). Wadsworth & Brooks/Cole, 1987.Google Scholar
  26. Nilsson, N.J.: “Probabilistic Logic,” in: Artificial Intelligence 28 (1986) 71–87.Google Scholar
  27. Ng, R., and V.S. Subrahmanian: “Probabilistic Logic Programming,” in: Information and Computation 101, 1992.Google Scholar
  28. Orci, I.P.: “Programming in Possibilistic Logic,” in: International Journal of Expert Systems 2 (1989) 79–96.Google Scholar
  29. Piasecki, K.: “Fuzzy p-Measures and their Application in Decision Making,” in: J. Kacprzyk and M. Fedrizzi (eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Berlin heidelberg: Springer Verlag, 1988.Google Scholar
  30. Ruspini, E.H.: “On the Semantics of Fuzzy Logic,” in: SRI International 475, 1989.Google Scholar
  31. Saffiotti, A.: “An AI View of the Treatment of Uncertainty,” in: The Knowledge Engineering Review 2 (1987) 75–97.Google Scholar
  32. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, 1976.Google Scholar
  33. Shapiro, E.Y.: “Logic Programming with Uncertainties — a Tool for Implementing Rule-based Systems,” in: IJCAI'83 — Proceedings of the 8th International Joint Conference on Artificial Intelligence, 1983.Google Scholar
  34. Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, 1967.Google Scholar
  35. Smets, P.: “Probability of a Fuzzy Event: An Axiomatic Approach,” in: Fuzzy Sets and Systems 7 (1982) 153–164.Google Scholar
  36. Turi, D.: Logic Programs with Negation: Classes, Models, Interpreters. Centre for Mathematics and Computer Science Report CSR 8943, 1989.Google Scholar
  37. Turksen, I.B.: “Stochastic Fuzzy Sets: a Survey,” in: J. Kacprzyk and M. Fedrizzi (eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Berlin, Heidelberg: Springer Verlag, 1988.Google Scholar
  38. Van Emden, M.H.: “Quantitative Deduction and its Fixpoint Theory,” in: Journal of Logic Programming 1 (1986) 37–53.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Flávio S. Corrêa da Silva
    • 1
  • Dave S. Robertson
    • 2
  • Jane Hesketh
    • 2
  1. 1.Instituto de Matemática e EstatísticaCid. Universitária “ASO”São Paulo SPBrazil
  2. 2.Dept. of Artificial IntelligenceUniv. of EdinburghEdinburghScotland

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