M. Studeny: Marginal problem in different calculi of AI. In Advances in Intelligent Computing - IPMU'94 (B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh eds.), Lecture Notes in Computer Science 945, Springer-Verlag, Berlin - Heidelberg 1995, pp. 348-359.

By the marginal problem is understood the problem of the existence of a global (full-dimensional) knowledge representation which has prescribed less-dimensional representations as marginals. It arises in several calculi of artificial intelligence: 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 a necessary and sufficient condition for pairwise compatibility of prescribed less-dimensional knowledge representations being equivalent to the existence of a global representation having them as marginals. Moreover, a simple method of solving the marginal problem in the possibilistic framework and its subframeworks is described.

AMS classification 68T30, 94D05, 68P15

marginal problem
database relation
natural conditional function
possibility theory
Dempster-Shafer's theory
running intersection property

A pdf copy (converted postscript version) (219kB) is available.

The paper builds on the following works: