Search
1994 Volume 9
Article Contents
RESEARCH ARTICLE   Open Access    

Non-standard theories of uncertainty in knowledge representation and reasoning(1)

More Information
  • Abstract: This paper provides a survey of the state of the art in plausible reasoning, that is exception tolerant reasoning under incomplete information. Three requirements are necessary for a formalism in order to cope with this problem: (i) making a clear distinction between factual information and generic knowledge; (ii) having a correct representation of partial ignorance; (iii) providing a nonmonotonic inference mechanism. Classical logic fails on requirements (i) and (iii), whilst the Bayesian approach does not fulfil (ii) in an unbiased way. In this perspective, various uncertainty modelling frameworks are reviewed: MYCIN-like fully compositional calculi, belief functions, upper and lower probability systems, and possibility theory. Possibility theory enables classical logic to be extended to layered sets of formulae, where layers express certainty levels. Finally, it is explained how generic knowledge can be expressed by constraints on possibility measures, and how possibilistic inferences can encode nonmonotonic reasoning in agreement with the Lehmann et al. postulates.
  • 加载中
  • Adams EW, 1975, The Logic of Conditionals. Reidel.

    Google Scholar

    Amarger S, Dubois D and Prade H, 1991, “Constraint propagation with imprecise conditional probabilities.” In: Proc. 7th Conf. on Uncertainty in AI, pp 26–34.

    Google Scholar

    Benferhat S, Cayrol C, Dubois D, Lang J and Prade H, 1993, “Inconsistency management and prioritized syntax-based entailment.” In: Proc.IJCAI'93, pp 640–645.

    Google Scholar

    Benferhat S, Dubois D and Prade H, 1992, “Representing default rules in possibilistic logic.” In: Proc. KR'92, pp 673–684.

    Google Scholar

    Benferhat S, Dubois D and Prade H, 1994, “Expressing independence in a possibilistic framework and its application to default reasoning.” In: Proc. ECAI'94, pp 150–154.

    Google Scholar

    Calabrese P, 1987, “An algebraic synthesis of the foundation of logic and probability.” Information Sciences42187–237.

    Google Scholar

    De Finetti B, 1936, “La logique de Ia probabilité.” In: Actes du Congrès Inter. de Philosophie Scientifique, Paris, 1935, pp 565–573. Hermann et Cie.

    Google Scholar

    De Finetti B, 1937, “La prévision, ses lois logiques et ses sources subjectives.” English translation in Studies in Subjective Probability, H Kyburg and HE Smokier, eds., Wiley, 1964.

    Google Scholar

    Dubois D, 1986, “Belief structures, possibility theory and decomposable confidence measures on finite sets.” Computers and Artificial Intelligence5 (5) 400–416.

    Google Scholar

    Dubois D, Godo L, López de Màntaras, R and Prade H, 1993, “Qualitative reasoning with imprecise probabilities.” J. Intelligent Information Systems, 3, pp 319–363.

    Google Scholar

    Dubois D, Lang J and Prade H, 1991, Possibilistic logic. Tech. Report IRIT/91–98-R. (In DM Gabbay et al., eds.), Handbook of Logic in Al and Logic Programming, 3. Oxford University Press, 1994, pp 439–513.

    Google Scholar

    Dubois D and Prade H, 1988a, Possibility Theory. Plenum Press.

    Google Scholar

    Dubois D and Prade H, 1988b, “An introduction to possibilistic and fuzzy logics.” In Smets P et al. (eds.), Non-Standard Logics for Automated Reasoning, pp 287–326. Academic Press.

    Google Scholar

    Dubois D and Prade H, 1991, “Epistemic entrenchment and possibilistic logic.” Artificial Intelligence50223–239.

    Google Scholar

    Dubois D and Prade H, 1993, “A glance at non-standard models and logics of uncertainty and vagueness.” In: Dubucs JP (ed.), Philosophy of Probability, pp 169–222. Kluwer Academic.

    Google Scholar

    Dubois D and Prade H, 1994a, “Focusing versus updating in belief function theory.” In: Yager RR et al. (eds.), Advances in the Dempster–Shafer Theory of Evidence, pp 71–95. Wiley.

    Google Scholar

    Dubois D and Prade H, 1994b, “Conditional objects as nonmonotonic consequence relations.” In: Proc. KR'94.

    Google Scholar

    Dubois D, Prade H and Smets P, 1993, “Representing partial ignorance.” In: Post-UAI-93 Workshop on Higher Order Uncertainty, Washington, DC. Revised version to appear in IEEE Trans. on Systems, Man and Cybernetics.

    Google Scholar

    Elkan C, 1993, “The paradoxical success of fuzzy logic.” Proc. AAAl'93, pp 698–703.

    Google Scholar

    Fariñas del Cerro, L, Herzig A and Lang J, 1992, “From ordering-based nonmonotonic reasoning to conditional logics.” In: Proc. ECAI'92, pp 314–318. Extended version. Artificial Intelligence66, 375–393.

    Google Scholar

    Fine TL, 1973, Theories of Probability. Academic Press.

    Google Scholar

    Fonck P, 1993, Réseaux d'inférence pour le raisonnement possibiliste. Thèse de Docteur es Sciences, Université de Liège, Belgium.

    Google Scholar

    Gabbay DM, 1985, “Theoretical foundations for non-monotonic reasoning in expert systems.” In: Apt KR (ed.), Logics and Models of Concurrent Systems, pp 439–457. Springer-Verlag.

    Google Scholar

    Gärdenfors P, 1988, Knowledge in Flux. The MIT Press.

    Google Scholar

    Gärdenfors P and Makinson D, 1994, “Non-monotonic inference based on expectations.” Artificial Intelligence 65, 197–245.

    Google Scholar

    Geffner H, 1992, Default Reasoning: Causal and Conditional Theories. The MIT Press.

    Google Scholar

    Goldszmidt M, Morris P and Pearl J, 1990, “A maximum entropy approach to nonmonotonic reasoning.” In: Proc. AAAI'90, 646–652.

    Google Scholar

    Goldszmidt M and Pearl J, 1992, “Rank-based systems.” In: Proc. KR'92, pp 661–672.

    Google Scholar

    Goodman IR, Nguyen HT and Walker EA, 1991, Conditional Inference and Logic for Intelligent Systems. North-Holland.

    Google Scholar

    Kraus K, Lehmann D and Magidor M, 1990, “Nonmonotonic reasoning, preferential models and cumulative logics.” Artificial Intelligence44167–207.

    Google Scholar

    Kyburg Jr HE, 1974, The Logical Foundations of Statistical Inference. Reidel.

    Google Scholar

    Lauritzen SL and Spiegelhalter DJ, 1988, “Local computations with probabilities on graphical structures and their application to expert systems.” J. Royal Statist. Society50(2) 157–224.

    Google Scholar

    Léa Sombé, 1990, Reasoning Under Incomplete Information in Artificial Intelligence. Wiley.

    Google Scholar

    Lehmann D, 1993, Another perspective on default reasoning. Inst. Computer Science, Hebrew University, Jerusalem.

    Google Scholar

    Lehmann D and Magidor M, 1992, “What does a conditional knowledge base entail?” Artificial Intelligence551–60.

    Google Scholar

    Lewis D, 1973, Counterfactuals. Basil Blackwell.

    Google Scholar

    Makinson D and Gärdenfors P, 1991, “Relations between the logic of theory change and nonmonotonic logic.” In: Furmann A and Moreau M (eds.), The Logic of Theory Change, 185–205. Springer-Verlag.

    Google Scholar

    Nilsson N, 1986, “Probabilistic logic.” Artificial Intelligence2871–87.

    Google Scholar

    Pearl J, 1988, Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.

    Google Scholar

    Pearl J, 1990, “System Z: A natural ordering of defaults with tractable applications to default reasoning.” In: Vardi M (ed), Proc. TARK'90, pp 121–135. Morgan Kaufmann.

    Google Scholar

    Poole DL, 1985, “On the comparison of theories: Preferring the most specific explanation.” In: Proc. IJCAI'85, pp 144–147.

    Google Scholar

    Rescher N, 1969, Many-Valued Logic. McGraw-Hill.

    Google Scholar

    Shafer G, 1976, A Mathematical Theory of Evidence. Princeton University Press.

    Google Scholar

    Shenoy PP and Shafer G, 1990, “Axioms for probability and belief-function propagation.” In: Shachter RD et al. (eds), Uncertainty in Artificial Intelligence 4, pp 169–198. North-Holland.

    Google Scholar

    Shoham Y, 1988, Reasoning About Change. The MIT Press.

    Google Scholar

    Smets P, 1988, “Belief functions.” In: Smets P et al. (eds), Non-Standard Logics for Approximate Reasoning, pp 253–286. Academic Press.

    Google Scholar

    Spohn W, 1988, “Ordinal conditional functions: A dynamic theory of epistemic states.” In: Harper WL and Skyrms B (eds.), Causation in Decision, Belief Change, and Statistics, pp 105–134. Kluwer Academic.

    Google Scholar

    Thöne H, Güntzer U and Kieβling , 1992, “Towards precision of probabilistic bounds propagation.” In: Proc. 8th Conf. on Uncertainty in Al, pp 315–322.

    Google Scholar

    Zadeh LA, 1965, “Fuzzy sets.” Information and Control8338–353.

    Google Scholar

    Zadeh LA, 1978, “Fuzzy sets as a basis for a theory of possibility.” Fuzzy sets and Systems13–28.

    Google Scholar

    Zadeh LA, 1985, “Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions.” IEEE Trans. SMC15(6) 745–763.

    Google Scholar

  • Cite this article

    Didier Duboid, Henri Prade. 1994. Non-standard theories of uncertainty in knowledge representation and reasoning(1). The Knowledge Engineering Review. 9:7128 doi: 10.1017/S0269888900007128
    Didier Duboid, Henri Prade. 1994. Non-standard theories of uncertainty in knowledge representation and reasoning(1). The Knowledge Engineering Review. 9:7128 doi: 10.1017/S0269888900007128

Article Metrics

Article views(14) PDF downloads(216)

Other Articles By Authors

RESEARCH ARTICLE   Open Access    

Non-standard theories of uncertainty in knowledge representation and reasoning(1)

The Knowledge Engineering Review  9 Article number: 10.1017/S0269888900007128  (1994)  |  Cite this article

Abstract: Abstract: This paper provides a survey of the state of the art in plausible reasoning, that is exception tolerant reasoning under incomplete information. Three requirements are necessary for a formalism in order to cope with this problem: (i) making a clear distinction between factual information and generic knowledge; (ii) having a correct representation of partial ignorance; (iii) providing a nonmonotonic inference mechanism. Classical logic fails on requirements (i) and (iii), whilst the Bayesian approach does not fulfil (ii) in an unbiased way. In this perspective, various uncertainty modelling frameworks are reviewed: MYCIN-like fully compositional calculi, belief functions, upper and lower probability systems, and possibility theory. Possibility theory enables classical logic to be extended to layered sets of formulae, where layers express certainty levels. Finally, it is explained how generic knowledge can be expressed by constraints on possibility measures, and how possibilistic inferences can encode nonmonotonic reasoning in agreement with the Lehmann et al. postulates.

    • Copyright © Cambridge University Press 19941994Cambridge University Press
References (51)
  • About this article
    Cite this article
    Didier Duboid, Henri Prade. 1994. Non-standard theories of uncertainty in knowledge representation and reasoning(1). The Knowledge Engineering Review. 9:7128 doi: 10.1017/S0269888900007128
    Didier Duboid, Henri Prade. 1994. Non-standard theories of uncertainty in knowledge representation and reasoning(1). The Knowledge Engineering Review. 9:7128 doi: 10.1017/S0269888900007128
  • Catalog

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return