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A precise definition of basic relational notions and of the relational algebra

Author:

Alain PirotteAuthors Info & Claims

ACM SIGMOD Record, Volume 13, Issue 1

Pages 30 - 45

https://doi.org/10.1145/984514.984516

Published: 01 September 1982 Publication History

Abstract

This paper presents a precise definition of basic relational notions as well as a precise and general definition of the relational algebra. The paper also illustrates a method for developing semi-formal definitions of data models. A nearly formal definition of relations with unordered attributes is given, and algebraic operations are described as operating on and producing relations thus defined. The definition of algebric operations contains, as a special case, the "classical" definition of the algebra (see e.g. [CODD72]). But, in addition, several operations are generalized. The closure of the algebra is characterized precisely, with the help of an operation for renaming relation attributes.

References

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{BERN81} Benstein, P. A., D. W. Chiu, "Using Semi-Joins to Solve Relational Queries", J. ACM, Vol.28 No 1, January 1981.

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{BJOR80} Bjorner, D., "Formalization of Data Base Models", IN: Abstract Software Specifications, Bjorner Ed., Springer Lecture Notes in Computer Science 86, 1980.

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{CODD72} Codd, E. F., "Relational Completeness of Data-base Sublanguages", In: Database Systems, Courant Computer Science Symposium 6, Prentice-Hall (1972).

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{CODD79} Codd, E. F., "Extending the Database Relational Model to Capture More Meaning", ACM Trans. on Database Systems, Vol. 4 No 4, December 1979.

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{DEMO82} Demolombe, R., "Generralized Division for Relational Algebraic Language", to appear in Information Processing Letters.

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{HALL75} Hall, P. A. V., P. Hitchcock, and S. J. P. Todd, "An Algebra of Relations for Machine Computation", Proc. 2nd ACM Symposium on Principles of Programming Languages, Palo Alto (1975).

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{HARD81} Hardgrave, T. W., "Positional Set Notation", to appear in Advances in Database Management, Vol. 2, Heyden and Son, 1981.

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{LACR76}Lacroix, M., and A. Pirotte, "Generalized Joins", ACM Sigmod Record, Vol.8 No 3, September 1976.

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{LACR81} Lacroix, M., and A. Pirotte, "Associating Types with Domains of Relational Databases", Proc. ACM-NBS Workshop on Data Abstraction, Databases, and Conceptual Modeling, Sigmod Record Vol. 11 No 2, January 1981.

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{LAME80} Lamersdorf, W., and J. W. Schmidt, "Semantic Definition of PASCAL/R", Berichte Nr. 73 and 74, University of Hamburg, 1980.

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{LOUI82} Louis, G., and A. Pirotte, "A Denotational Definition of the Semantics of DRC, the Domain Relational Calculus", Proc. VLDB Conference, Mexico, 1982.

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{MERR78} Merrett, T. H., "The Extended Relational Algebra, a Basis for Query Languages", In Databases: Improving Usability and Responsiveness, Shneiderman Ed., Academic Press, 1978.

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{PECH75} Pecherer, R. M., "Efficient Evaluation of Expressions in a Relational Algebra", Proc. ACM Pacific Regional Conference, April 1975.

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{RTG82} ANSI/X3/SPARC DBSSG Relational Task Group, Final Report, M. Brodie and J. Schmidt Eds., to appear in ACM SIGMOD Record.

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{SAND81} Sandberg, G., "A Primer on Relational Database Concepts", IBM Systems Journal, Vol.20 No 1, 1981.

Digital Library

Cited By

Majkić Z(2013)Conservative intensional extension of Tarski's semanticsAdvances in Artificial Intelligence10.1155/2013/9201572013(3-3)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1155/2013/920157
Niemi TJärvelin K(1991)Prolog-Based Meta-rules for Relational Database Representation and ManipulationIEEE Transactions on Software Engineering10.1109/32.8391317:8(762-788)Online publication date: 1-Aug-1991
https://dl.acm.org/doi/10.1109/32.83913
Subieta K(1987)Denotational semantics of query languagesInformation Systems10.1016/0306-4379(87)90019-612:1(69-82)Online publication date: Jan-1987
https://doi.org/10.1016/0306-4379(87)90019-6
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A precise definition of basic relational notions and of the relational algebra
1. Information systems
  1. Data management systems
    1. Query languages

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cover image ACM SIGMOD Record

ACM SIGMOD Record Volume 13, Issue 1

September 1982

81 pages

ISSN:0163-5808

DOI:10.1145/984514

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Copyright © 1982 Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 1982

Published in SIGMOD Volume 13, Issue 1

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Cited By

Majkić Z(2013)Conservative intensional extension of Tarski's semanticsAdvances in Artificial Intelligence10.1155/2013/9201572013(3-3)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1155/2013/920157
Niemi TJärvelin K(1991)Prolog-Based Meta-rules for Relational Database Representation and ManipulationIEEE Transactions on Software Engineering10.1109/32.8391317:8(762-788)Online publication date: 1-Aug-1991
https://dl.acm.org/doi/10.1109/32.83913
Subieta K(1987)Denotational semantics of query languagesInformation Systems10.1016/0306-4379(87)90019-612:1(69-82)Online publication date: Jan-1987
https://doi.org/10.1016/0306-4379(87)90019-6
Niemi TJärvelin K(1985)A straightforward formalization of the relational modelInformation Systems10.1016/0306-4379(85)90010-910:1(65-76)Online publication date: 2-Jan-1985
https://dl.acm.org/doi/10.1016/0306-4379%2885%2990010-9
Lamersdorf WLamersdorf W(1985)LiteraturverzeichnisSemantische Repräsentation komplexer Objektstrukturen10.1007/978-3-642-70289-1_9(174-187)Online publication date: 1985
https://doi.org/10.1007/978-3-642-70289-1_9
Markowitz VRaz Y(1984)An entity-relationship algebra and its semantic description capabilitiesJournal of Systems and Software10.1016/0164-1212(84)90005-04:2-3(147-162)Online publication date: 13-Jul-1984
https://dl.acm.org/doi/10.1016/0164-1212%2884%2990005-0
Niemi T(1984)Specification of a query language by the attribute methodBIT10.1007/BF0193748424:2(171-186)Online publication date: Jun-1984
https://doi.org/10.1007/BF01937484
Niemi TJärvelin K(1983)A straightforward formalization of the relational modelACM SIGMOD Record10.1145/984540.98454214:1(15-38)Online publication date: 1-Sep-1983
https://dl.acm.org/doi/10.1145/984540.984542
Lamersdorf W(1983)Comparison of four relational data model specificationsACM SIGMOD Record10.1145/984532.98453413:3(18-31)Online publication date: 1-Apr-1983
https://dl.acm.org/doi/10.1145/984532.984534
Dayal UFagin RBernstein P(1983)Processing queries with quantifiers a horticultural approachProceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems10.1145/588058.588075(125-136)Online publication date: 21-Mar-1983
https://dl.acm.org/doi/10.1145/588058.588075
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