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On the completeness of query languages for relational data bases

  • François Bancilhon
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 64)

Abstract

In this paper, we have studied the problem of completeness of relational query languages. We have etablished a criterion for completeness. A query language was proved to be complete. Since this language is the one used as a standard for completeness this results gives strong theoretical basis to Codd's definition of completeness.

There are however some limitations to this notion of completeness : for instance there is no first order formula describing the transitive closure r* of a binary relation r ! While this seems at first to be in contradiction with theorem 2, one should recall that the notion of completeness we have introduced is static. Therefore, for any configuration τ consisting of a binary relation r there exists a formula rτ of the first order calculus describing the transitive closure of r, but this formula depends on τ and there is no formula describing the mapping which associates with a binary relation its transitive closure.

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References

  1. ABRIAL 74: Abrial J.R. — "Data Semantics" — Data Base Management-North-Holland 1974.Google Scholar
  2. BANCILHON 76: Bancilhon F.M. — "Data Structures: Specification and Realization" — Ph.D. Thesis — University of Michigan — January 1976.Google Scholar
  3. BRACCHI 76: Bracchi G., Paolini P., Pelagatti G. — "Mappings in Data Base Systems" — Rapporto Interno n o 76-11 — Istituto di Elettrotecnica ed Elettronica del Politecnico di Milano — November 1976.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • François Bancilhon
    • 1
  1. 1.Iria — LaboriaLe ChesnayFrance

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