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Armstrong-like relations for functional partition dependencies. (English) Zbl 0845.68035

Summary: D. Simovici and C. Reischer [Combinatorics, graph theory, and computing, Proc. 17th Southeast. Conf., Boca Raton/Fl. 1986, Congr. Numerantium 55, 181-186 (1986; Zbl 0641.68173)] have introduced the notion of functional partition dependency (fpd) and have given a system of axioms for fpd’s, which under certain conditions is sound and complete. In the definition of fpd appears the word “partition”. Because of this, the role of domains is necessary in order to specify the domains of quantifiers and partitions. Usually, dependencies are first-order sentences in a language with a single predicate letter. A relation satisfies a set of dependencies if there exists a model for the associated set of sentences.
R. Fagin [J. Assoc. Comput. Mach. 29, 952-985 (1982; Zbl 0493.68092)] introduced implicational and embedded implicational dependencies and studied the existence of Armstrong relations for this large class of dependencies. These dependencies are domain-independent, because the underlying domains are not necessary to determine whether a given relation satisfies a dependency. The fpd’s are domain-dependent. The notion of satisfaction of an fpd will be restricted only on a unique domain.
In this paper, some results about the “Armstrong-like relations” for fpd’s are obtained.

MSC:

68P20 Information storage and retrieval of data
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