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A Review of Uncertainty Handling Formalisms

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Applications of Uncertainty Formalisms

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1455))

Abstract

Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.

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References

  1. S. K. Andersen, F. V. Jensen, K. G. Olesen, and F. Jensen. HUGIN—a shell for building Bayesian belief universes for expert systems. In Proceedings of the 11th International Joint Conference on Artificial Intelligence, pages 783–791, San Mateo, CA, 1989. Morgan Kaufmann.

    Google Scholar 

  2. J. A. Barnett. Computational methods for a mathematical theory of evidence. In Proceedings of the 7th International Joint Conference on Artificial Intelligence, pages 868–875, Los Altos, CA, 1981. William Kaufmann.

    Google Scholar 

  3. S. Benferhat, D. Dubois, and H. Prade. Argumentative inference in uncertain and inconsistent knowledge bases. In Proceedings of the 9th Uncertainty in Artificial Intelligence, pages 411–419. Morgan Kaufmann, 1993.

    Google Scholar 

  4. S. Benferhat and L. Garcia. A local handling of inconsistent knowledge and default bases. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  5. J. Bigham. Computing beliefs according to Dempster-Shafer and possibilistic logic. In Proceedings of the 3rd International Conference on Information Processing and Management of Uncertainty, Paris, pages 59–61, 1990.

    Google Scholar 

  6. J. Bigham. Exploiting uncertain and temporal information in correlation. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  7. P. Bosc, L. Lietard, and H. Prade. An ordinal approach to the processing of fuzzy queries with exible quantifiers. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  8. F. Brazier, J. Engelfreit, and J. Truer. Analysis of multi-interpretable ecological monitoring information. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998

    Google Scholar 

  9. T. Chard. Qualitative probability versus quantitative probability in clinical diagnosis: a study using a computer simulation. Medical Decision Making, 11:38–41, 1991.

    Google Scholar 

  10. P. Cheeseman. Probabilistic vs. fuzzy reasoning. In L. N. Kanal and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 85–102. Elsevier Science Publishers, Amsterdam, The Netherlands, 1986.

    Google Scholar 

  11. P. Cheeseman. Discussion of the paper by Lauritzen and Spiegelhalter. Journal of the Royal Statistical Society, B, 50:203, 1988.

    Google Scholar 

  12. P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4:58–142, 1988.

    Google Scholar 

  13. D. A. Clark. Numerical and symbolic approaches to uncertainty management in AI. Artificial Intelligence Review, 4:109–146, 1990.

    Google Scholar 

  14. P. R. Cohen. Heuristic Reasoning about Uncertainty: An Artificial Intelligence Approach. Pitman, London, UK, 1985.

    Google Scholar 

  15. J. de Kleer. An assumption-based TMS. Artificial Intelligence, 28:127–162, 1986.

    Google Scholar 

  16. J. de Kleer and B. C. Williams. Diagnosing multiple faults. Artificial Intelligence, 32:97–130, 1987.

    MATH  Google Scholar 

  17. A. P. Dempster. Upper and lower probabilities induced by a multi-valued mapping. Annals of Mathematical Statistics, 38:325–339, 1967.

    MathSciNet  MATH  Google Scholar 

  18. A. P. Dempster. A generalisation of Bayesian inference (with discussion). Journal of the Royal Statistical Society B, 30:205–232, 1968.

    MATH  Google Scholar 

  19. A. P. Dempster. Comments on ‘An inquiry into computer understanding’ by Peter Cheeseman. Computational Intelligence, 4:72–73, 1988.

    Google Scholar 

  20. J. Doyle. A truth maintenance system. Artificial Intelligence, 12:231–272, 1979.

    MathSciNet  Google Scholar 

  21. D. Driankov. A calculus for belief-intervals representation of uncertainty. In B. Bouchon-Meunier and R. R. Yager, editors, Uncertainty in Knowledge-Based Systems, pages 205–216. Springer-Verlag, Berlin, Germany, 1986.

    Google Scholar 

  22. D. Dubois, J. Lang, and H. Prade. A possibilistic assumption-based truth maintenance system with uncertain justifications, and its application to belief revision. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, pages 87–106, Berlin, Germany, 1990. Springer Verlag.

    Google Scholar 

  23. D. Dubois, J. Lang, and H. Prade. Fuzzy sets in approximate reasoning, Part 2: Logical approaches. Fuzzy Sets and Systems, 40:203–244, 1991.

    MathSciNet  MATH  Google Scholar 

  24. D. Dubois and H. Prade. Necessity measures and the resolution principle. IEEE Transactions on Systems, Man and Cybernetics, 17:474–478, 1987.

    MathSciNet  MATH  Google Scholar 

  25. D. Dubois and H. Prade. Modelling uncertainty and inductive inference: a survey of recent non-additive probability systems. Acta Psychologica, 68:53–78, 1988.

    Google Scholar 

  26. D. Dubois and H. Prade. Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, NY, 1988.

    MATH  Google Scholar 

  27. D. Dubois and H. Prade. Processing of imprecision and uncertainty in expert system reasoning models. In C. Ernst, editor, Management Expert Systems, pages 67–88. Addison Wesley, 1988.

    Google Scholar 

  28. R. O. Duda, P. E. Hart, and N. J. Nilsson. Subjective Bayesian methods for a rule-based inference system. In Proceedings of the National Computer Conference, pages 1075–1082, 1976.

    Google Scholar 

  29. M. Elvang-Gøransson and A. Hunter. Argumentative logics: Reasoning from classically inconsistent information. Data and Knowledge Engineering Journal, 16:125–145, 1995.

    MATH  Google Scholar 

  30. D. W. Etherington. Reasoning with Incomplete Information. Pitman, London, UK, 1988.

    MATH  Google Scholar 

  31. K. D. Forbus and J. de Kleer. Building Problem Solvers. MIT Press, Cambridge, MA, 1993.

    MATH  Google Scholar 

  32. J. Fox. Three arguments for extending the framework of probability. In L. N. Kanal and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 447–458. Elsevier Science Publishers, Amsterdam, The Netherlands, 1986.

    Google Scholar 

  33. J. Fox and S. Parsons. Arguing about beliefs and actions. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  34. P. Gärdenfors. Knowledge in flux: Modelling the Dynamics of Epistemic States. MIT Press, Cambridge, MA, 1988.

    MATH  Google Scholar 

  35. J. Gebhardt and R. Kruse. Background to and perspectives on possibilistic graphical models. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    MATH  Google Scholar 

  36. M. Ginsberg. Non-monotonic reasoning using Dempster’s rule. In Proceedings of the 4th National Conference on Artificial Intelligence, pages 112–119, Los Altos, CA, 1984. William Kaufmann.

    Google Scholar 

  37. J. Gordon and E. H. Shortliffe. A method for managing evidential reasoning in a hierarchical hypothesis space. Artificial Intelligence, 26:323–357, 1985.

    MathSciNet  MATH  Google Scholar 

  38. R. Haenni. Modelling uncertainty in propositional assumption-based systems. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  39. D. Heckerman and M. Wellman. Bayesian networks. Communications of the ACM, 38:27–30, 1995.

    Google Scholar 

  40. D. E. Heckerman. Probability interpretation for MYCIN’s certainty factors. In L. N. Kanal and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 167–196. Elsevier Science Publishers, Amsterdam, The Netherlands, 1986.

    Google Scholar 

  41. M. Henrion, G. Provan, B. Del Favero, and G. Sanders. An experimental comparison of numerical and qualitative probabilistic reasoning. In Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence, pages 319–326, San Francisco, CA, 1994. Morgan Kaufmann.

    Google Scholar 

  42. E. J. Horvitz, D. E. Heckerman, and C. P. Langlotz. A framework for comparing alternative formalisms for plausible reasoning. In Proceedings of the 5th National Conference on Artificial Intelligence, pages 210–214, Los Altos, CA, 1986. Morgan Kaufmann.

    Google Scholar 

  43. A. Hunter. Uncertainty in Information Systems. McGraw-Hill, London, UK, 1996.

    Google Scholar 

  44. D. J. Israel. Some remarks on the place of logic in knowledge representation. In N. Cercone and G. McCalla, editors, The Knowledge Frontier: Essays in the Representation of Knowledge, pages 80–91. Springer Verlag, New York, NY, 1987.

    Google Scholar 

  45. G. J. Klir. Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like? Fuzzy Sets and Systems, 24:141–160, 1987.

    MathSciNet  MATH  Google Scholar 

  46. P. Krause, S. Ambler, M. Elvang-Gøransson, and J. Fox. A logic of argumentation for reasoning under uncertainty. Computational Intelligence, 11:113–131, 1995.

    MathSciNet  Google Scholar 

  47. P. Krause, J. Fox, P. Judson, and M. Patel. Qualitative risk assessment fulfills a need. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  48. P. J. Krause and D. A. Clark. Representing Uncertain Knowledge: An Artificial Intelligence Approach. Intellect, Oxford, UK, 1993.

    Google Scholar 

  49. P. J. Krause and J. Fox. Combining symbolic and numerical methods for reasoning under uncertainty. In D. J. Hand, editor, AI and Computer Power; The Impact on Statistics, pages 99–114. Chapman and Hall, London, UK, 1994.

    Google Scholar 

  50. M. Lalmas. Modelling information retrieval with Dempster-Shafer’s theory of evidence. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  51. K. B. Laskey and P. E. Lehner. Assumptions, beliefs and probabilities. Artificial Intelligence, 32:65–77, 1990.

    MathSciNet  Google Scholar 

  52. S. L. Lauritzen and D. J. Spiegelhalter. Local computations on graphical structures, and their application to expert systems. Journal of the Royal Statistical Society, B, 50:157–224, 1988.

    MathSciNet  MATH  Google Scholar 

  53. D. V. Lindley. Making Decisions. John Wiley & Sons, Chichester, UK, 1975.

    Google Scholar 

  54. W. Łukaszewicz. Two results on default logic. In Proceedings of the 9th International Joint Conference on Arti_cial Intelligence, pages 459–461, Los Altos, CA, 1985. Morgan Kaufmann.

    Google Scholar 

  55. W. Łukaszewicz. Considerations on default logic: an alternative approach. Computational Intelligence, 4:1–16, 1988.

    Google Scholar 

  56. P. Magni, R. Bellazi, and F. Locatelli. Using uncertainty management techniques in medical therapy planning: a decision theoretic approach. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  57. P. Magrez and Ph. Smets. Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems. International Journal of Intelligent Systems, 4:181–200, 1975.

    MATH  Google Scholar 

  58. J. Martins and S. Shapiro. A model of belief revision. Artificial Intelligence, 35:25–79, 1988.

    MathSciNet  MATH  Google Scholar 

  59. D. A. McAllester. An outlook on truth maintenance. AI Memo 551, AI Laboratory, MIT, 1980.

    Google Scholar 

  60. J. McCarthy. Circumscription—a form of non-monotonic reasoning. Artificial Intelligence, 13:27–39, 1980.

    MathSciNet  MATH  Google Scholar 

  61. S. Moral and N. Wilson. Importance sampling Monte-Carlo algorithms for the calculation of Dempster-Shafer belief. In Proceedings of the 6th International Conference on Information Processing and the Management of Uncertainty, pages 1337–1344, 1996.

    Google Scholar 

  62. P. Nicolas and T. Schaub. The XRay system: an implementation platform for local query-answering in default logics. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  63. N. J. Nilsson. Probabilistic logic. Artificial Intelligence, 28:71–87, 1986.

    MathSciNet  MATH  Google Scholar 

  64. S. Parsons. Qualitative approaches to reasoning under uncertainty. MIT Press, Cambridge, MA, 1998.

    Google Scholar 

  65. S. Parsons and J. Fox. Argumentation and decision making: a position paper. In Formal and Applied Practical Reasoning, pages 705–709, Berlin, Germany, 1996. Springer Verlag.

    Google Scholar 

  66. J. Pearl. How to do with probabilities what people say you can’t. Technical Report CSD-850031, Cognitive Systems Laboratory, Computer Science Department UCLA, 1985.

    Google Scholar 

  67. J. Pearl. Fusion, propagation and structuring belief networks. Artificial Intelligence, 29:241–288, 1986.

    MathSciNet  MATH  Google Scholar 

  68. J. Pearl. Bayesian decision methods. In Encyclopedia of Artificial Intelligence, pages 48–56. John Wiley, 1987.

    Google Scholar 

  69. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA, 1988.

    MATH  Google Scholar 

  70. G. Pinkas and R. Loui. Reasoning from inconsistency: A taxonomy of principles for resolving conict. In Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference. Morgan Kaufmann, 1992.

    Google Scholar 

  71. M. Pradhan, M. Henrion, G. Provan, B. Del Favero, and K. Huang. The sensitivity of belief networks to imprecise probabilities: an experiemntal investigation. Artificial Intelligence, 85:363–397, 1996.

    Google Scholar 

  72. H. Prakken. An argumentation framework for default reasoning. Annals of Mathematics and Artificial Intelligence, 9, 1993.

    Google Scholar 

  73. G. M. Provan. Solving diagnostic problems using extended assumption-based truth maintenance systems: foundations. Technical Report 88-10, Department of Computer Science, University of British Columbia, 1988.

    Google Scholar 

  74. J. R. Quinlan. INFERNO: a cautious approach to uncertain inference. Computer Journal, 26:255–269, 1983.

    Google Scholar 

  75. M. Ramalho. Uncertainty measures associated with fuzzy rules for connection admission control in ATM networks. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  76. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    MathSciNet  MATH  Google Scholar 

  77. E. Rich. Default reasoning as likelihood reasoning. In Proceedings of the 3rd National Conference on Artificial Intelligence, pages 348–351, Los Altos, CA, 1983. William Kaufmann.

    Google Scholar 

  78. A. Saffiotti. An AI view of the treatment of uncertainty. The Knowledge Engineering Review, 2:75–97, 1987.

    Google Scholar 

  79. A. Saffiotti. Handling uncertainty in control of autonomous robots. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  80. B. Schweitzer and A. Sklar. Associative functions and abstract semigroups. Publicationes Mathematicae Debrecen, 10:69–81, 1963.

    MathSciNet  Google Scholar 

  81. G. L. S. Shackle. Decision, order and time in human affairs. Cambridge University Press, Cambridge, UK, 1961.

    Google Scholar 

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

    MATH  Google Scholar 

  83. G. Shafer. Comments on ‘An inquiry into computer understanding’ by Peter Cheeseman. Computational Intelligence, 4:121–124, 1988.

    Google Scholar 

  84. G. Shafer and R. Logan. Implementing Dempster’s rule for hierarchical evidence. Artificial Intelligence, 33:271–298, 1987.

    MathSciNet  MATH  Google Scholar 

  85. P. P. Shenoy and G. Shafer. Axioms for probability and belief function propagation. In R. D. Shachter, T. S. Levitt, L. N. Kanal, and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence 4, pages 169–198. North-Holland, Amsterdam, The Netherlands, 1990.

    Google Scholar 

  86. E. H. Shortliffe. Computer-Based Medical Consultations: MYCIN. Elsevier, New York, NY, 1976.

    Google Scholar 

  87. Ph. Smets. Belief functions. In Ph. Smets, E. H. Mamdani, D. Dubois, and H. Prade, editors, Non-Standard Logics for Automated Reasoning, pages 253–275. Academic Press, London, UK, 1988.

    Google Scholar 

  88. Ph. Smets. Belief functions versus probability functions. In B Bouchon-Meunier, L. Saitta, and R. R. Yager, editors, Uncertainty and Intelligent Systems, pages 17–24. Springer Verlag, Berlin, Germany, 1988.

    Google Scholar 

  89. Ph. Smets and Y-T. Hsia. Default reasoning and the transferable belief model. In P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence 6, pages 495–504. Elsevier Science Publishers, Amsterdam, The Netherlands, 1991.

    Google Scholar 

  90. Ph. Smets and R. Kennes. The transferable belief model. Artificial Intelligence, 66:191–234, 1994.

    MathSciNet  MATH  Google Scholar 

  91. M. Smithson. Ignorance and Uncertainty: Emerging Paradigms. Springer Verlag, New York, NY, 1989.

    Google Scholar 

  92. L. E. Sucar, D. F. Gillies, and D. A. Gillies. Objective probabilities in expert systems. Artificial Intelligence, 61:187–208, 1993.

    MathSciNet  Google Scholar 

  93. A. Tawfik and E. Neufeld. Model-based diagnosis: a probabilistic extension. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  94. S. Toulmin. The uses of argument. Cambridge University Press, Cambridge, UK., 1957.

    MATH  Google Scholar 

  95. A. Tversky and D. Kahneman. Judgement under uncertainty: Heuristics and biases. Science, 185:1124–1131, 1974.

    Google Scholar 

  96. K. van Dam. Using uncertainty techniques in radio communication systems. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  97. G. Vreeswijk. Abstract argumentation systems. In M de Glas and D Gabbay, editors, Proceedings of the First World Conference on Fundamentals of Artificial Intelligence. Angkor, 1991.

    Google Scholar 

  98. D. Wilson, A. Greig, John Gilby, and Robert Smith. Some problems in trying to implement uncertainty techniques in automated inspection. In A. Hunter and S. Parsons, editors, Applications of Uncertainty Formalisms (this volume). Springer Verlag, Berlin, 1998.

    Google Scholar 

  99. N. Wilson. Rules, belief functions, and default logic. In Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence, pages 443–449, Mountain View, CA, 1990. Association for Uncertainty in AI.

    Google Scholar 

  100. N. Wilson. Some theoretical aspects of the Dempster-Shafer theory. PhD thesis, Oxford Polytechnic, 1992.

    Google Scholar 

  101. N. Wilson and S. Moral. Fast Markov chain algorithms for calculating Dempster-Shafer belief. In Proceedings of the 12th European Conference on Artificial Intelligence, pages 672–676, Chichester, UK, 1996. John Wiley & Sons.

    Google Scholar 

  102. L. A. Zadeh. Fuzzy sets. Information and Control, 8:338–353, 1965.

    MathSciNet  MATH  Google Scholar 

  103. L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1:1–28, 1978.

    MathSciNet  MATH  Google Scholar 

  104. L. A. Zadeh. A theory of approximate reasoning. In J. Hayes, D. Michie, and L. Mikulich, editors, Machine Intelligence 9, pages 149–194. Ellis Horwood, 1979.

    Google Scholar 

  105. L. A. Zadeh. Is probability theory sufficient for dealing with uncertainty in AI? a negative view. In L. N. Kanal and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 103–116. Elsevier Science Publishers, Amsterdam, The Netherlands, 1986.

    Google Scholar 

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Parsons, S., Hunter, A. (1998). A Review of Uncertainty Handling Formalisms. In: Hunter, A., Parsons, S. (eds) Applications of Uncertainty Formalisms. Lecture Notes in Computer Science(), vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49426-X_2

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