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Relational Lattices

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Relational and Algebraic Methods in Computer Science (RAMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8428))

Abstract

Relational lattices are obtained by interpreting lattice connectives as natural join and inner union between database relations. Our study of their equational theory reveals that the variety generated by relational lattices has not been discussed in the existing literature. Furthermore, we show that addition of just the header constant to the lattice signature leads to undecidability of the quasiequational theory. Nevertheless, we also demonstrate that relational lattices are not as intangible as one may fear: for example, they do form a pseudoelementary class. We also apply the tools of Formal Concept Analysis and investigate the structure of relational lattices via their standard contexts.

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Author information

Authors and Affiliations

  1. Informatik 8, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstraße 3, 91058, Erlangen, Germany

    Tadeusz Litak

  2. School of Computer Science and Information Systems, Birkbeck, University of London, WC1E 7HX, London, UK

    Szabolcs Mikulás

  3. Elektrotechn., Wisk. and Inform, Delft University of Technology, Mekelweg 4, 2628CD, Delft, The Netherlands

    Jan Hidders

Authors
  1. Tadeusz Litak
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  2. Szabolcs Mikulás
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  3. Jan Hidders
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Editor information

Editors and Affiliations

  1. NICTA and UNSW, Anzac Parade 223, 2033, Kensington, NSW, Australia

    Peter Höfner

  2. School of Computational Sciences, Chapman University, One University Drive, 92866, Orange, CA, USA

    Peter Jipsen

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  4. Department of Computer Science, University of Augsburg, Universitätsstraße 6a, 86159, Augsburg, Germany

    Martin Eric Müller

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© 2014 Springer International Publishing Switzerland

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Litak, T., Mikulás, S., Hidders, J. (2014). Relational Lattices. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_20

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

  • Online ISBN: 978-3-319-06251-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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