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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ABRIAL 74: Abrial J.R. — "Data Semantics" — Data Base Management-North-Holland 1974.
BANCILHON 76: Bancilhon F.M. — "Data Structures: Specification and Realization" — Ph.D. Thesis — University of Michigan — January 1976.
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.
CODD 70: Codd. E.E. — "A Relational Model for Large Shared Data Banks" — Communications of the ACM — Volume 13 — Number 6 — June 1970.
CODD 71: Codd E.F. — "A Data Base Sublanguage Founded on the Relational Calculus" — Proceedings of ACM SIGFIDET Workshop on Data Description, Access and Control — San Diego — CA — 1971.
CODD 72: Codd E.F. — "Relational Completeness of Data Base Sublanguages", in Data Base Systems (Rustin Ed), Prentice Hall 1972.
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© 1978 Springer-Verlag Berlin Heidelberg
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Bancilhon, F. (1978). On the completeness of query languages for relational data bases. In: Winkowski, J. (eds) Mathematical Foundations of Computer Science 1978. MFCS 1978. Lecture Notes in Computer Science, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08921-7_60
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DOI: https://doi.org/10.1007/3-540-08921-7_60
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