@MISC{Studeny_marginalproblem, author = {Milan Studeny}, title = {Marginal Problem in Different Calculi of AI}, year = {} }

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Abstract

. By the marginal problem we understand the problem of the existence of a global (full-dimensional) knowledge representation which has prescribed less-dimensional 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. 1 Introduction Dealing with integration of knowledge in probabilistic expert systems ...