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Independence in Database Relations

  • Conference paper
Logic, Language, Information, and Computation (WoLLIC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8071))

Abstract

We investigate the implication problem for independence atoms \(X \bot Y\) of disjoint attribute sets X and Y on database schemata. A relation satisfies \(X \bot Y\) if for every X-value and every Y-value that occurs in the relation there is some tuple in the relation in which the X-value occurs together with the Y-value. We establish an axiomatization by a finite set of Horn rules, and derive an algorithm for deciding the implication problem in low-degree polynomial time in the input. We show how to construct Armstrong relations which satisfy an arbitrarily given set of independence atoms and violate every independence atom not implied by the given set. Our results establish independence atoms as an efficient subclass of embedded multivalued data dependencies which are not axiomatizable by a finite set of Horn rules, and whose implication problem is undecidable.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Finland

    Juha Kontinen & Jouko Väänänen

  2. Department of Computer Science, The University of Auckland, New Zealand

    Sebastian Link

  3. Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands

    Jouko Väänänen

Authors
  1. Juha Kontinen
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  2. Jouko Väänänen
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Editor information

Editors and Affiliations

  1. School of Informatics, University of Edinburgh, EH8 9AB, Edinburgh, UK

    Leonid Libkin

  2. Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 64289, Darmstadt, Germany

    Ulrich Kohlenbach

  3. Centro de Informática, Universidade Federal de Pernambuco (UFPE), Av. Jornalista Anibal Fernandes, s/n, Cidade Universitária, 50.740-560, Recife, PE, Brazil

    Ruy de Queiroz

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Kontinen, J., Link, S., Väänänen, J. (2013). Independence in Database Relations. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2013. Lecture Notes in Computer Science, vol 8071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39992-3_17

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  • DOI: https://doi.org/10.1007/978-3-642-39992-3_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39991-6

  • Online ISBN: 978-3-642-39992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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