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Possibility Theory and its Applications: a Retrospective and Prospective view

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Decision Theory and Multi-Agent Planning

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 482))

Abstract

This paper provides an overview of possibility theory, emphasising its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. It has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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  1. IRIT-CNRS, Universite Paul Sabatier, 31062, Toulouse, France

    Didier Dubois & Henri Prade

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  1. Didier Dubois
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Editors and Affiliations

  1. University of Udine, Udine

    Giacomo Della Riccia

  2. University of Toulouse, Toulouse

    Didier Dubois

  3. University of Magdeburg, Magdeburg

    Rudolf Kruse

  4. Free University of Berlin, Berlin

    Hanz-Joachim Lenz

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Dubois, D., Prade, H. (2006). Possibility Theory and its Applications: a Retrospective and Prospective view. In: Della Riccia, G., Dubois, D., Kruse, R., Lenz, HJ. (eds) Decision Theory and Multi-Agent Planning. CISM International Centre for Mechanical Sciences, vol 482. Springer, Vienna. https://doi.org/10.1007/3-211-38167-8_6

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