Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T19:23:01.164Z Has data issue: false hasContentIssue false
  • English
  • Français

An AI view of the treatment of uncertainty

Published online by Cambridge University Press:  07 July 2009

Alessandro Saffiotti
Alessandro Saffiotti
Affiliation:
Dipartimento di Scienze dell'Informazione, Universitá di Pisa, c.so Italia 40, 56100 PISA, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reviews many of the very varied concepts of uncertainty used in AI. Because of their great popularity and generality “parallel certainty inference” techniques, so-called, are prominently in the foreground. We illustrate and comment in detail on three of these techniques; Bayes' theory (section 2); Dempster-Shafer theory (section 3); Cohen's model of endorsements (section 4), and give an account of the debate that has arisen around each of them. Techniques of a different kind (such as Zadeh's fuzzy-sets, fuzzy-logic theory, and the use of non-standard logics and methods that manage uncertainty without explicitly dealing with it) may be seen in the background (section 5).

The discussion of technicalities is accompanied by a historical and philosophical excursion on the nature and the use of uncertainty (section 1), and by a brief discussion of the problem of choosing an adequate AI approach to the treatment of uncertainty (section 6). The aim of the paper is to highlight the complex nature of uncertainty and to argue for an open-minded attitude towards its representation and use. In this spirit the pros and cons of uncertainty treatment techniques are presented in order to reflect the various uncertainty types. A guide to the literature in the field, and an extensive bibliography are appended.

Type
Research Article
Information
The Knowledge Engineering Review , Volume 2 , Issue 2 , June 1987 , pp. 75 - 97
Copyright
Copyright © Cambridge University Press 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, J.B. (1976). “Probabilistic Reasoning and Certainty Factors.” Mathematical Biosciences 32. Also in (Buchanan-Shortlifle, 1984), ch. 12.Google Scholar
Barbuti, R. and Salibra, A. (1986). “Logic Negation in Logic Programming and its Three-Valued Semantics.” Internal Report, Computer Science Department, University of Pisa.Google Scholar
Barnett, J.A. (1981). “Computational Methods for a Mathematical Theory of Evidence.” Proc. of the 7th IJCAI, Vancouver, British Columbia, Canada.Google Scholar
Bezdek, J.C. (1976). “Feature Selection for Binary Data–Medical Diagnosis with Fuzzy-Sets.” AFIPS Proc. 45, 1057–1068.CrossRefGoogle Scholar
Buchanan, B.G. and Shortliffe, E.H. (1975). “A Model of Inexact Reasoning in Medicine.” Mathematical Biosciences 23, 351–379. Also in (Buchanan-Shortliffe, 1981), ch. 11.Google Scholar
Buchanan, B.G. and Shortliffe, E.H. (Ed.) (1984). Rule Based Export Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, Addison-Wesley.Google Scholar
Carnap, R. (1950). Logical Foundations of Probability. Univ. of Chicago Press, Chicago.Google Scholar
McCarthy, J. and Hayes, P.J. (1969). “Some Philosophical Problems from the Standpoint of Artifical Intelligence,” in Meltzer, and Michie, (Eds), Machine Intelligence 4, Edinburgh, 163–502.Google Scholar
Cheeseman, P. (1984). “Learning of Expert Systems from Data.” IEEE Proc. of Workshop on Principles of Knowledge-Based Systems, Denver, Colorado, 115–112.Google Scholar
Cohen, P.R. (1984). “Progress Report on the Theory of Endorsements: A Heuristic Approach to Reasoning About Uncertainty.” IEEE Proc. of Workshop on Principles of Knowledge-Based Systems, Denver, Colorado.Google Scholar
Cohen, P.R. (1985). Heuristic Reasoning about Uncertainty: An Artificial intelligence Approach. Pitnam, Boston.Google Scholar
Cohen, P.R. and Sullivan, M. (1985). “An Endorsement-Based Plan Recognition Program.” Proc. of the 9th IJCAI, Los Angeles, California.Google Scholar
Davis, R. (1979). “Panel on Dealing With Uncertainty,” in Proc. of 6th IJCAI, Tokyo, Japan.Google Scholar
de Finetti, B. (1937). “La prévision- seis logiques, seis sources subjectives,” Annales de r Institut H. Poincare 7, 1–68.Google Scholar
Dempster, A.P. (1968). “A Generalization of Bayesian Inference.” Journal of Royal Statistical Society Ser. B 30, 205–247.Google Scholar
Domotor, Z. (1985). “Probability Kinematics, Conditionals, and Entropy Principles.” Synthese 63, 75–114.CrossRefGoogle Scholar
Dubois, D. and Prade, H. (1985). “Combination and Propagation of Certainty With Belief Functions–a reexaminaron,” in Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Dubois, D. and Prade, H. (1986). “A Tentative Comparison of Numerical Approximate Reasoning Methodologies”, Workshop on IDSS for Plant Operation, CCE, Ispra, 1986.Google Scholar
Duda, R.O., Hart, P.E. and Nilsson, N.J. (1976). “Subjective Bayesian Methods for Rule-Based Inference Systems.” AFIPS Proc. 45, New York, 1075–1082.CrossRefGoogle Scholar
Erman, L.D., Hayes-Roth, F., Lesser, V.R. and Reddy, D.R. (1980). “The HEARSAY-II Speech-Understanding System: Integrating Knowledge to Resolve Uncertainty.” Computing Surveys 12(2), 213–253.CrossRefGoogle Scholar
Le Faivre, R.A. (1976). “Procedural Representation in a Fuzzy Problem-Solving System.” AFIPS Proc. 45, 1069–1074.CrossRefGoogle Scholar
Ferrante, R.D. (1985). “The Characteristic Error Approach to Conflict Resolution,” in Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Fox, J. (1986). “Three Arguments for Extending the Framework of Probability,” in Kanal-Lemmer, 447–458.CrossRefGoogle Scholar
Fox, J. (1987). “Making decisions under the influence of Knowledge,” in Morris, P. (ed.), Modelling Cognition. John Wiley & Sons Ltd, 199–212.Google Scholar
Friedman, L. (1981). “Extended Plausible Inference.” Proc. of the 7th IJCAI, Vancouver, British Columbia, Canada.Google Scholar
Gaines, B.R. and Kohout, L.J. (1977). “The Fuzzy Decade: a Bibliography of Fuzzy Systems and Closely Related Topics.” International Journal of Man-Machine Studies 9, 1–68.CrossRefGoogle Scholar
Garbolino, P. (1986). “A Comparison of some Rules for Probabilistic Reasoning.” Workshop on I.D.S.S. for Plant Operation, J.R.C., Ispra.Google Scholar
Garvey, T.D., Lowrance, J.D. and Fischler, M.A. (1981). “An Inference Technique for Integrating Knowledge from Disparate Sources.” Proc. of the 7th IJCAI, Vancouver, British Columbia, Canada.Google Scholar
Ginsberg, M.L. (1984). “Non-Monotonic Reasoning Using Dempster's Rule.” Proc. of 1st National Conf. on Art. Int., AAAI, Austin, Texas.Google Scholar
Glicksman, J. (1983). “Using Multiple Information Sources in a Computational Vision System.” Proc. of 8th IJCAI, Karlsruhe, West Germany, 1078–1080.Google Scholar
Gordon, J. and Shortliffe, E.H. (1984). “The Dempster-Shafer Theory of Evidence,” in Buchanan-Shortliffe, ch. 13.Google Scholar
Hacking, I. (1975). The Emergence of Probability. Cambridge University Press.Google Scholar
Halpern, J.Y. and McAllester, D.A. (1984). “Likelihood, Probability and Knowledge,” in Proc. of 1st National Conf. on Art. Int., AAAI, Austin, Texas.Google Scholar
Halpern, J.Y. and Rabin, M.O. (1983). “A Logic to Reason About Likelihood.” Proc. of the 15th Annual Symposium on the Theory of Computing, 310–319.CrossRefGoogle Scholar
Halpern, J.Y. and Rabin, M.O. (1987). “A Logic to Reason about Likelihood.” Artificial intelligence 32, 379–405.CrossRefGoogle Scholar
Huges, G.E. and Cressell, M.J. (1968). An Introduction to Modal Logic, Methuen, London.Google Scholar
Ishizuka, M., Fu, K.S. and Yao, J.T.P. (1981). “Inexact Inference for Rule-Based damage Assessment of Existing Structures.” Proc. of the 7th IJCAI, Vancouver, British Columbia, Canada.Google Scholar
Kanal, L.N. and Lemmer, J.F. (Eds) (1986). Uncertainty in Artificial Intelligence. North Holland, 1986.Google Scholar
Khan, N.A. and Jain, R. (1985). “Uncertainty Management in a Distributed Knowledge Based System,” in Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Levesque, H.J. (1984). “A Logic of Implicit and Explicit Belief.” National Conf. on Art. Int., AAAI, Austin, Texas, 198–202.Google Scholar
Lindley, D.V. (1971). Making Decisions. Wiley Interscience, London.Google Scholar
Lindley, D.V. (1987). “The Probability Approach to the Treatment of Uncertainty in Artificial Intelligence and Expert Systems.” Statistical Science 2, 17–24.CrossRefGoogle Scholar
Lukasiewicz, H. (1920). “O Logice Trojwartosciowcj.” Ruch Filozoficzny 5, 169–170; also in: S. McCall, Polish Logic 1920–1939, Oxford University Press, Oxford, 1967.Google Scholar
Lukasiewicz, J. (1930). “Many-Valued Systems for Prepositional Logic,” in McCall, S.: Polish Logic 1920–1939. Oxford University Press, Oxford, 1967.Google Scholar
Lu, S.Y. and Stephanou, H.E. (1984). “A Set-Theoretic Framework for the Processing of Uncertain Knowledge.” Proc. of National Conf. on Art. Int., AAAI, Austin, Texas, 216–221.Google Scholar
Nilsson, N.J. (1986). “Probabilistic Logic.” Artificial intelligence 28, 71–87.CrossRefGoogle Scholar
Pearl, J. (1986). “On Evidential Reasoning in a Hierarchy of Hypotheses.” Artificial Intelligence 28, 9–15.CrossRefGoogle Scholar
Pednault, E.P.D., Zucker, S.W. and Muresan, L.V. (1981). “On the Independence Assumption Underlying Subjective Bayesian Updating.” Artificial Intelligence 16, 213–222.CrossRefGoogle Scholar
Polya, G. (1954). Patterns of Plausible Inference. Princeton University Press, Princeton, New Jersey.Google Scholar
Prade, H. (1983). “A Synthetic View of Approximate Reasoning Techniques.” Proc. of 8th IJCAI, Karlsruhe, West Germany, 130–136.Google Scholar
Rescher, N. (1968). Topics in Philosophical Logic. Reidel, Dordrecht.CrossRefGoogle Scholar
Rollinger, C.R. (1983). “How to Represent Evidence–Aspects of Uncertain Reasoning.” Proc. of 8th IJCAI, Karlsruhe, West Germany.Google Scholar
Saffiotti, A. (1987). “Un sistema di inferenze non-monotone su basi di conoscenza con incertezze”, doctoral dissertation, Computer Science Department, University of Pisa (in preparation).Google Scholar
Schefe, P. (1980). “On Foundations of Reasoning With Uncertain Facts and Vague Concepts.” Int. Journal of Man-Machine Studies 12, 35–62.CrossRefGoogle Scholar
Shapiro, E. Y. (1983). “Logic Programs With Uncertainties: A Tool for Implementing Rule-Based Systems.” Proc. of 8th IJCAI, Karlsruhe, West Germany.Google Scholar
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey.CrossRefGoogle Scholar
Shafer, G. (1987). “Probability Judgment in Artificial Intelligence and Expert Systems”, Statistical Science 2, 3–16.CrossRefGoogle Scholar
Shastri, L. and Feldman, J.A. (1985). “Evidential Reasoning in Semantic Networks: A Formal Theory”, in Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Shimony, A. (1985). “The Status of the Principle of Maximum Entropy.” Synthese 63, 35–53.CrossRefGoogle Scholar
Strat, T.M. (1984). “Continuous Belief Functions for Evidential Reasoning.” Proc. of 1st National Conf. on Art. Int., AAAI, Austin, Texas, 308–313.Google Scholar
Thompson, T.R. (1985). “Parallel Formulation of Evidential Reasoning Theories.” Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Tong, R.M., Shapiro, D.G., Jeffrey, S.D. and McCune, B.P. (1983). “A Comparison of Uncertain Calculi in an Expert System for Information Retrieval.” Proc. of 8th IJCAI, Karlsruhe, West Germany, 194–197.Google Scholar
Turner, R. (1984). Logics for Artificial Intelligence. Ellis Horwood Ltd., Chichester.Google Scholar
Tversky, A. and Kahneman, D. (1974). “Judgment under Uncertainty: Heuristics and Biases.” Science 185, 1124–1131.CrossRefGoogle ScholarPubMed
Umano, M., Mizumoto, M. and Tanaka, K. (1978). “FSTDS System: A Fuzzy-Set Manipulation System.” Information Science 14, 115–149.CrossRefGoogle Scholar
Umano, M., Mizumoto, M. and Tanaka, K. (1979). “A System for Fuzzy Reasoning.” Proc. of 6th IJCAI, Tokyo, Japan, 917–919.Google Scholar
van Melle, W. (1980). “A Domain-independent System that Aids in Constructing Knowledge-based Consultation Programs.” Ph.D. dissertation, report STAN-CS-80–820 c HPP-80–22, Computer Science Department, Stanford University.Google Scholar
Weiss, S.M. and Kulikowski, C.A. (1979). “EXPERT: A System for Developing Consultation Models.” Proc. of 6th IJCAI, Tokyo, Japan, 942–947.Google Scholar
White, A.P. (1985). “PREDICTOR: An Alternative Approach to Uncertain Inference in Expert Systems”, in Proc. of 9th IJCAI, Los Angeles, California.Google Scholar
Yeh, A. (1985). “Flexible Data Fusion (& Fission)”, in Proc. of 9th IJCAI, Los Angeles, California, 420–422.Google Scholar
Zadeh, L.A. (1965). “Fuzzy sets.” Information & Control 8, 338–353.CrossRefGoogle Scholar
Zadeh, L.A. (1975). “Fuzzy Logic and Approximate Reasoning.” Synthese 30, 407–428.CrossRefGoogle Scholar
Zadeh, L.A. (1981). “PRUF: A Meaning Representation Language for Natural Languages,” in: Mamdani, E. & Gaines, B. (Eds), Fuzzy Reasoning and its Applications. Academic Press.Google Scholar
Zadeh, L.A. (1983). “Common-sense Knowledge Representation Based on Fuzzy Logic.” IEEE Computer, 10 1983, 61–65.CrossRefGoogle Scholar
Zadeh, L.A. (1985). “Syllogistic Reasoning as a Basis for Combining Evidence in Expert Systems.” Proc. of the 9th IJCAI, Los Angeles, California.Google Scholar