Decomposing Relations into Orderings

  • Michael Winter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)

Abstract

In various applications one is interested in decomposing a given relation in a suitable manner. In this paper we want to study several decompositions of a binary relation R of the form R=F;E;G, i.e., into a composition of a partial function F, an ordering E and the converse of a partial function G.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chin, L.H., Tarski, A.: Distributive and modular laws in the arithmetic of relation algebras. University of California Press, Berkley (1951)Google Scholar
  2. 2.
    Codd, E.F.: A relational model of data for large shared data banks. Comm. ACM 13(6), 377–387 (1970)MATHCrossRefGoogle Scholar
  3. 3.
    Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland, Amsterdam (1990)MATHGoogle Scholar
  4. 4.
    Ganter, B., Wille, R.: Formal Concept Analysis - Mathematical Foundations. Springer, Heidelberg (1999)MATHGoogle Scholar
  5. 5.
    Jaoua, A., Belkhiter, N., Ounalli, H., Moukam, T.: Databases. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, Advances in Computer Science, pp. 196–210. Springer, Vienna (1997)Google Scholar
  6. 6.
    Olivier, J.P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C.R. Acad. Sci. Paris 290, 939–941 (1980)MATHMathSciNetGoogle Scholar
  7. 7.
    Olivier, J.P., Serrato, D.: Squares and Rectangles in Relational Categories - Three Cases: Semilattice, Distributive lattice and Boolean Non-unitary. Fuzzy sets and systems 72, 167–178 (1995)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Riguet, J.: Quelques propriétés des relations difonctionelles. C. R. Acad. Sci. Paris 230, 1999–2000 (1950)MATHMathSciNetGoogle Scholar
  9. 9.
    Riguet, J.: Les relations de Ferrers. C. R. Acad. Sci. Paris 232, 1729–1730 (1951)MATHMathSciNetGoogle Scholar
  10. 10.
    Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989); English version: Relations and Graphs. Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoret. Comput. Sci., Springer, Heidelberg (1993).Google Scholar
  11. 11.
    Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous Relation Algebras. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, Advances in Computer Science, pp. 40–54. Springer, Vienna (1997)Google Scholar
  12. 12.
    Winter, M.: Strukturtheorie heterogener Relationenalgebren mit Anwendung auf Nichtdetermismus in Programmiersprachen. Dissertationsverlag NG Kopierladen GmbH, München (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael Winter
    • 1
  1. 1.Department of Computer ScienceSt. CatharinesCanada

Personalised recommendations