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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abadi, M., and J.Y. Halpern: Decidability and Expressiveness for First-Order Logics of Probability. IBM Research Report RJ 7220, 1989.
Apt, K.F.: Introduction to Logic Programming. Centre for Mathematics and Computer Science Report CSR 8741, 1987.
Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. University of Alberta, 1988.
Bacchus, F.: “Lp, a Logic for Representing and Reasoning with Statistical Knowledge,” in: Computational Intelligence 6 (1990a) 209–231.
Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. MIT Press, 1990b.
Bundy, A.: “Incidence Calculus: a Mechanism for Probabilistic Reasoning,” in: Journal of Automated Reasoning 1 (1985) 263–284.
Corrêa da Silva, F.S.: Automated Reasoning with Uncertainties. University of Edinburgh, Department of Artificial Intelligence, 1992.
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.
Corrêa da Silva, F.S., and A. Bundy: A Rational Reconstruction of Incidence Calculus. University of Edinburgh, Department of Artificial: Intelligence Report 517, 1991.
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.
Dubois, D., and H. Prade: “Fuzzy Sets, Probability and Measurement,” in: European Journal of Operational Research 40 (1989) 135–154.
Dudley, R.M.: Real Analysis and Probability. Wadsworth & Brooks/Cole, 1989.
Fagin, R., and J.Y. Halpern: Uncertainty, Belief, and Probability. IBM Research Report RJ 6191, 1989a.
Fagin, R., and J.Y. Halpern: A New Approach to Updating Beliefs. IBM Research Report RJ 7222, 1989.
Fitting, M.: “Logic Programming on a Topological Bilattice,” in: Fundamenta Informaticae XI (1988) 209–218.
Fitting, M.: “Bilattices in Logic Programming,” in: Proceedings of the 20th International Symposium on Multiple-valued Logic, 1990.
Halpern, J.Y.: “An Analysis of First-Order Logics of Probability,” in: Artificial Intelligence 46 (1990) 311–350.
Halpern, J.Y., and R. Fagin: Two Views of Belief: Belief as Generalised Probability and Belief as Evidence. IBM Research Report RJ 7221, 1989.
Hinde, C.J.: “Fuzzy Prolog,” in: International Journal of Man-Machine Studies 24 (1986) 569–595.
Ishizuka, M., and K. Kanai: “Prolog-ELF Incorporating Fuzzy Logic.” in: IJCAI'85 — Proceedings of the 9th International Joint Conference on Artificial Intelligence, 1985.
Kifer, M., and V.S. Subrahmanian: “Theory of Generalized Annotated Logic Programs and Its Applications,” in: Journal of Logic Programming 12, 1991.
Klement, E.P.: “Construction of Fuzzy σ-algebras Using Triangular Norms,” in: Journal of Mathematical Analysis and Applications 85 (1982) 543–565.
Kunen, K.: “Signed Data Dependencies in Logic Programs,” in: Journal of Logic Programming 7 (1989) 231–245.
Lee, R.C.T.: “Fuzzy Logic and the Resolution Principle,” in: Journal of the ACM 19 (1972) 109–119.
Mendelson, E.: Introduction to Mathematical Logic (3rd. ed). Wadsworth & Brooks/Cole, 1987.
Nilsson, N.J.: “Probabilistic Logic,” in: Artificial Intelligence 28 (1986) 71–87.
Ng, R., and V.S. Subrahmanian: “Probabilistic Logic Programming,” in: Information and Computation 101, 1992.
Orci, I.P.: “Programming in Possibilistic Logic,” in: International Journal of Expert Systems 2 (1989) 79–96.
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.
Ruspini, E.H.: “On the Semantics of Fuzzy Logic,” in: SRI International 475, 1989.
Saffiotti, A.: “An AI View of the Treatment of Uncertainty,” in: The Knowledge Engineering Review 2 (1987) 75–97.
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, 1976.
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.
Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, 1967.
Smets, P.: “Probability of a Fuzzy Event: An Axiomatic Approach,” in: Fuzzy Sets and Systems 7 (1982) 153–164.
Turi, D.: Logic Programs with Negation: Classes, Models, Interpreters. Centre for Mathematics and Computer Science Report CSR 8943, 1989.
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.
Van Emden, M.H.: “Quantitative Deduction and its Fixpoint Theory,” in: Journal of Logic Programming 1 (1986) 37–53.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corrêa da Silva, F.S., Robertson, D.S., Hesketh, J. (1994). Automated reasoning with uncertainties. In: Masuch, M., Pólos, L. (eds) Knowledge Representation and Reasoning Under Uncertainty. Logic at Work 1992. Lecture Notes in Computer Science, vol 808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58095-6_5
Download citation
DOI: https://doi.org/10.1007/3-540-58095-6_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58095-9
Online ISBN: 978-3-540-48451-6
eBook Packages: Springer Book Archive