The implication problem for functional and multivalued dependencies : An algebraic approach

  • V. S. Lakshmanan
  • C. E. Veni Madhavan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 206)


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 MVD-lattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVD-lattices 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.


Relational Database Lattice Theory Canonical Representation Scheme Lattice Dency Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • V. S. Lakshmanan
    • 1
  • C. E. Veni Madhavan
    • 1
  1. 1.School of AutomationIndian Institute of ScienceBangaloreIndia

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