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Marginal problem in different calculi of AI

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Advances in Intelligent Computing — IPMU '94 (IPMU 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 945))

Abstract

By the marginal problem we understand the problem of the existence of a global (full-dimensional) knowledge representation which has prescribed lessdimensional representations as marginals. The paper deals with this problem in several calculi of AI: probabilistic reasoning, theory of relational databases, possibility theory, Dempster-Shafer's theory of belief functions, Spohn's theory of ordinal conditional functions. The following result, already known in probabilistic framework and in the framework of relational databases, is shown also for the other calculi: the running intersection property is the necessary and sufficient condition for pairwise compatibility of prescribed less-dimensional knowledge representations being equivalent to the existence of a global representation. Moreover, a simple method of solving the marginal problem in the possibilistic framework and its subframeworks is given.

Supported by the grant n. 201/94/0471 “Marginal problem and its application” of the Grant Agency of Czech Republic.

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Authors and Affiliations

  1. Inst. of Inform. Theory and Autom, Academy of Sciences of Czech Republic, Pod vodárenskou věží 4, 18208, Prague 8, Czech Republic

    Milan Studený

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  1. Milan Studený
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Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1995 Springer-Verlag Berlin Heidelberg

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Studený, M. (1995). Marginal problem in different calculi of AI. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035968

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  • DOI: https://doi.org/10.1007/BFb0035968

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  • Online ISBN: 978-3-540-49443-0

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