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Modeling Uncertainty with Propositional Assumption-Based Systems

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Applications of Uncertainty Formalisms

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

Abstract

This paper proposes assumption-based systems as an efficient and convenient way to encode uncertain information. Assumption based systems are obtained from propositional logic by including a special type of propositional symbol called assumption. Assumptions are needed to express the uncertainty of the given information. Assumption-based systems can be used to judge hypotheses qualitatively or quantitatively. This paper shows how assumption-based systems are obtained from causal networks, it describes how symbolic arguments for hypotheses can be computed efficiently, and it presents ABEL, a modeling language for assumption-based systems and an interactive tool for probabilistic assumption-based reasoning.

Research supported by grant No.2100-042927.95 of the Swiss National Foundation for Research.

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References

  • Anrig, B., Haenni, R., & Lehmann, N. 1997a. ABEL — A New Language for Assumption-Based Evidential Reasoning under Uncertainty. Tech. Rep. 97-01. University of Fribourg, Institute of Informatics.

    Google Scholar 

  • Anrig, B., Haenni, R., Kohlas, J., & Lehmann, N. 1997b. Assumption-based Modeling using ABEL. In: Gabbay, D., Kruse, R., Nonnengart, A., & Ohlbach, H.J. (eds), First International Joint Conference on Qualitative and Quantitative Practical Reasoning; ECSQARU-FAPR’97Springer, for Lecture Notes in Artif. Intell.

    Google Scholar 

  • Bertschy, R., & Monney, P.A. 1996. A Generalization of the Algorithm of Heidtmann to Non-Monotone Formulas. Journal of Computational and Applied Mathematics, 76, 55–76.

    Article  MathSciNet  Google Scholar 

  • de Kleer, J. 1986. An Assumption-based TMS. Artificial Intelligence, 28, 127–162.

    Article  Google Scholar 

  • Dempster, A. 1967. Upper and Lower Probabilities Induced by a Multivalued Mapping. Ann. Math. Stat., 38, 325–339.

    Article  MathSciNet  Google Scholar 

  • Haenni, R. 1996. Propositional Argumentation Systems and Symbolic Evidence Theory. Ph.D. thesis, Institute of Informatics, University of Fribourg.

    Google Scholar 

  • Inoue, K. 1991. An Abductive Procedure for the CMS/ATMS. Pages 34–53 of: Martins, J.P., & Reinfrank, M. (eds), Truth Maintenance Systems, Lecture Notes in A.I. Springer.

    Google Scholar 

  • Kohlas, J. 1994. Mathematical Foundations of Evidence Theory. Tech. Rep. 94-09. Institute of Informatics, University of Fribourg.

    Google Scholar 

  • Kohlas, J. 1995. Mathematical Foundations of Evidence Theory. Pages 31–64 of: Coletti, G., Dubois, D., & Scozzafava, R. (eds), Mathematical Models for Handling Partial Knowledge in Artificial Intelligence. Plenum Press.

    Google Scholar 

  • Kohlas, J., & Monney, P.A. 1993. Probabilistic Assumption-Based Reasoning. In: Heckerman, & Mamdani (eds), Proc. 9th Conf. on Uncertainty in Artificial Intelligence. Kaufmann, Morgan Publ.

    Google Scholar 

  • Kohlas, J., & Monney, P.A. 1994. Probabilistic Assumption-Based Reasoning. Tech. Rep. 94-22. Institute of Informatics, University of Fribourg.

    Google Scholar 

  • Kohlas, J., & Monney, P.A. 1995. A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer.

    Google Scholar 

  • Kohlas, J., & Moral, S. 1995. Propositional Information System. Working Paper. Institute of Informatics, University of Fribourg.

    Google Scholar 

  • Kohlas, J., Monney, P.A., Anrig, B., & Haenni, R. 1996. Model-Based Diagnostics and Probabilistic Assumption-Based Reasoning. Tech. Rep. 96-09. University of Fribourg, Institute of Informatics.

    Google Scholar 

  • Laskey, K.B., & Lehner, P.E. 1989. Assumptions, Beliefs and Probabilities. Artificial Intelligence, 41, 65–77.

    Article  MathSciNet  Google Scholar 

  • Lauritzen, S.L., & Spiegelhalter, D.J. 1988. Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems. Journal of Royal Statistical Society, 50(2), 157–224.

    MathSciNet  MATH  Google Scholar 

  • Lehmann, N. 1994. Entwurf und Implementation einer annahmenbasierten Sprache. Diplomarbeit. Institute of Informatics, University of Fribourg.

    Google Scholar 

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

    Google Scholar 

  • Provan, G.M. 1990. A Logic-Based Analysis of Dempster-Shafer Theory. International Journal of Approximate Reasoning, 4, 451–495.

    Article  MathSciNet  Google Scholar 

  • Reiter, R., & de Kleer, J. 1987. Foundations of Assumption-Based Truth Maintenance Systems. Proceedings of the American Association in AI, 183–188.

    Google Scholar 

  • Saffiotti, A., & Umkehrer, E. 1991. PULCINELLA: A General Tool for Propagating Uncertainty in Valuation Networks. Tech. Rep. IRIDIA, Université de Bruxelles.

    Google Scholar 

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

    Google Scholar 

  • Shenoy, P.P., & Shafer, G. 1990. Axioms for Probability and Belief Functions Propagation. In: Shachter, R.D., & al. (eds), Uncertainty in Artificial Intelligence 4. North Holland.

    Google Scholar 

  • Siegel, P. 1987. Représentation et Utilisation de la Connaissance en Calcul Propositionel. Ph.D. thesis, Université d’Aix-Marseille II. Luminy, France.

    Google Scholar 

  • Steele, G. L. 1990. Common Lisp — the Language. Digital Press.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Haenni, R. (1998). Modeling Uncertainty with Propositional Assumption-Based Systems. 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_21

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  • DOI: https://doi.org/10.1007/3-540-49426-X_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65312-7

  • Online ISBN: 978-3-540-49426-3

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