The implication problem for functional and multivalued dependencies : An algebraic approach
 V. S. Lakshmanan,
 C. E. Veni Madhavan
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Abstract
Computation of the dependency basis is the fundamental step in solving the implication problem for MVDs in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of an MVDlattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVDlattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a) computing the inference basis of a given set M of MVDs; (b) computing the dependency basis of a given attribute set w.r.t. M; and (c) solving the implication problem for MVDs. Finally, we show that our results naturally extend to incorporate FDs also in a way that enables the solution of the implication problem for both FDs and MVDs put together.
 Title
 The implication problem for functional and multivalued dependencies : An algebraic approach
 Book Title
 Foundations of Software Technology and Theoretical Computer Science
 Book Subtitle
 Fifth Conference, New Delhi, India December 16–18, 1985 Proceedings
 Pages
 pp 303328
 Copyright
 1985
 DOI
 10.1007/3540160426_17
 Print ISBN
 9783540160427
 Online ISBN
 9783540397229
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 206
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 V. S. Lakshmanan ^{(1)}
 C. E. Veni Madhavan ^{(1)}
 Author Affiliations

 1. School of Automation, Indian Institute of Science, 560 012, Bangalore, India
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