# On Relational Algebra with Marked Nulls.

Witold Lipski Jr.:
On Relational Algebra with Marked Nulls.
PODS 1984: 201-203@inproceedings{DBLP:conf/pods/Lipski84,
author = {Witold Lipski Jr.},
title = {On Relational Algebra with Marked Nulls},
booktitle = {Proceedings of the Third ACM SIGACT-SIGMOD Symposium on Principles
of Database Systems, April 2-4, 1984, Waterloo, Ontario, Canada},
publisher = {ACM},
year = {1984},
isbn = {0-89791-128-8},
pages = {201-203},
ee = {http://doi.acm.org/10.1145/588011.588040, db/conf/pods/Lipski84.html},
crossref = {DBLP:conf/pods/84},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

BibTeX
## Abstract

We formulate some natural conditions which should be satisfied in an extension of the relational algebra from the usual relations to tables with null values, and we explain the motivation behind these conditions. Roughly speaking, our conditions say that the extended algebra makes it possible to correctly compute the "true tuples" in the result of applying a relational expression (query) to tables with nulls (database state), and that the computation can be carried out recursively, following the structure of the expression. We prove that these conditions are exactly equivalent to other conditions proposed earlier by the author and T. Imielinski. We give a simple proof of the correctness of the "naive" extension of the relational algebra to tables with marked nulls, where the nulls are treated as if they were regular values, and which supports the operations of projection, positive selection, union, join and renaming of attributes. We also show that the result of the naive evaluation of such an expression (query) is equal to the response to the query as defined -- in a proof-theoretic framework -- by Reiter.
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BibTeX
## Printed Edition

Proceedings of the Third ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, April 2-4, 1984, Waterloo, Ontario, Canada.
ACM 1984, ISBN 0-89791-128-8

Contents BibTeX

## References

- [IL1]
- Tomasz Imielinski, Witold Lipski Jr.:
On Representing Incomplete Information in a Relational Data Base.
VLDB 1981: 388-397 BibTeX
- [IL2]
- Tomasz Imielinski, Witold Lipski Jr.:
Incomplete Information in Relational Databases.
J. ACM 31(4): 761-791(1984) BibTeX
- [IL3]
- Tomasz Imielinski, Witold Lipski Jr.:
Incomplete Information and Dependencies in Relational Databases.
SIGMOD Conference 1983: 178-184 BibTeX
- [Lip]
- ...
- [Mai]
- David Maier:
The Theory of Relational Databases.
Computer Science Press 1983, ISBN 0-914894-42-0

Contents BibTeX
- [MUV]
- David Maier, Jeffrey D. Ullman, Moshe Y. Vardi:
On the Foundations of the Universal Relation Model.
ACM Trans. Database Syst. 9(2): 283-308(1984) BibTeX
- [Rei]
- ...
- [Ull]
- Jeffrey D. Ullman:
Principles of Database Systems, 2nd Edition.
Computer Science Press 1982, ISBN 0-914894-36-6

BibTeX

## Referenced by

- Oliver Haase, Andreas Henrich:
A Closed Approach to Vague Collections in Partly Inaccessible Distributed Databases.
ADBIS 1999: 261-274

BibTeX

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