Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T18:18:29.717Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  07 July 2009

Didier Duboid  and
Henri Prade
Didier Duboid
Affiliation:
Institut de Recherche en Inforinatique de Toulouse (IRIT)—CNRS Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Henri Prade
Affiliation:
Institut de Recherche en Inforinatique de Toulouse (IRIT)—CNRS Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
The Knowledge Engineering Review , Volume 9 , Issue 4 , December 1994 , pp. 399 - 416
Copyright
Copyright © Cambridge University Press 1994

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, EW, 1975, The Logic of Conditionals. Reidel.CrossRefGoogle 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.CrossRefGoogle 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 Sciences 42 187–237.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 Intelligence 5 (5) 400–416.Google Scholar
Dubois, D, Godo, L, Lópezde Màntaras, R 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 Intelligence 50 223–239.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.CrossRefGoogle 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
Fariñasdel Cerro, L 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 Intelligence 66, 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.CrossRefGoogle 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.CrossRefGoogle 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 Intelligence 44 167–207.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. Society 50(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 Intelligence 55 1–60.CrossRefGoogle 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 Intelligence 28 71–87.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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 Control 8 338–353.Google Scholar
Zadeh, LA, 1978, “Fuzzy sets as a basis for a theory of possibility.” Fuzzy sets and Systems 1 3–28.Google Scholar
Zadeh, LA, 1985, “Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions.” IEEE Trans. SMC 15(6) 745–763.Google Scholar