Relational Lattices

  • Tadeusz Litak
  • Szabolcs Mikulás
  • Jan Hidders
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

relational lattices relational algebra database theory algebraic logic lattice theory cylindric algebras Formal Concept Analysis standard context incidence relation arrow relations 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tadeusz Litak
    • 1
  • Szabolcs Mikulás
    • 2
  • Jan Hidders
    • 3
  1. 1.Informatik 8Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.School of Computer Science and Information SystemsBirkbeck, University of LondonLondonUK
  3. 3.Elektrotechn., Wisk. and InformDelft University of TechnologyDelftThe Netherlands

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