A generalisation of entity and referential integrity in relational databases
Levene, Mark ; Loizou, George
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001), p. 113-127 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Entity and referential integrity are the most fundamental constraints that any relational database should satisfy. We re-examine these fundamental constraints in the context of incomplete relations, which may have null values of the types “value exists but is unknown” and “value does not exist”. We argue that in practice the restrictions that these constraints impose on the occurrences of null values in relations are too strict. We justify a generalisation of the said constraints wherein we use key families, which are collections of attribute sets of a relation schema, rather than keys, and foreign key families which are collections of pairs of attribute sets of two relation schemas, rather than foreign keys. Intuitively, a key family is satisfied in an incomplete relation if each one of its tuples is uniquely identifiable on the union of the attribute sets of the key family, in all possible worlds of the incomplete relation, and, in addition, is distinguishable from all the other tuples in the incomplete relation by its nonnull values on some element in the key family. Our proposal can be viewed as an extension of Thalheim’s key set, which only deals with null values of type “value exists but is unknown”. The intuition behind the satisfaction of a foreign key family in an incomplete database is that each pair (F i ,K i ) of attribute sets in the foreign key family takes the foreign key attribute values over F i of a tuple in one incomplete relation referencing the key attribute values over K i of a tuple in another incomplete relation. Such referencing is defined only in the case when the foreign key attribute values do not have any null values of the type “value does not exist”; we insist that the referencing be defined for at least one such pair. We also investigate some combinatorial properties of key families, and show that they are comparable to the standard combinatorial properties of keys.

Publié le : 2001-01-01
Classification:  68P15 
@article{ITA_2001__35_2_113_0,
     author = {Levene, Mark and Loizou, George},
     title = {A generalisation of entity and referential integrity in relational databases},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {35},
     year = {2001},
     pages = {113-127},
     mrnumber = {1862458},
     zbl = {0992.68048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2001__35_2_113_0}
}

Levene, Mark; Loizou, George. A generalisation of entity and referential integrity in relational databases. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) pp. 113-127. http://gdmltest.u-ga.fr/item/ITA_2001__35_2_113_0/

[1] S. Abiteboul, R. Hull and V. Vianu, Foundations of Databases. Addison-Wesley, Reading, MA (1995). | Zbl 0848.68031

[2] ANSI/X3/SPARC, Study group on database management systems, interim report. Bull. ACM SIGFIDET 7 (1975).

[3] E.F. Codd, Extending the database relational model to capture more meaning. ACM Trans. Database Systems 4 (1979) 397-434.

[4] E.F. Codd, The Relational Model for Database Management: Version 2. Addison-Wesley, Reading, MA (1990). | Zbl 0809.68056

[5] C.J. Date, Referential integrity, in Relational Database: Selected Writings. Addison-Wesley, Reading, MA (1986) 41-63. | Zbl 0625.68071

[6] C.J. Date, Composite keys, in Relational Database Writings 1989-1991. Addison-Wesley, Reading, MA (1992) 467-474.

[7] J. Demetrovics and V.D. Thi, Relations and minimal keys. Acta Cybernet. 8 (1988) 279-285. | MR 942742 | Zbl 0662.68110

[8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979). | MR 519066 | Zbl 0411.68039

[9] T. Härder and J. Reinert, Access path support for referential integrity in SQL2. VLDB J. 5 (1996) 196-214.

[10] N. Lerat and W. Lipski Jr., Nonapplicable nulls. Theoret. Comput. Sci. 46 (1986) 67-82. | MR 868264 | Zbl 0618.68079

[11] M. Levene and G. Loizou, Null inclusion dependencies in relational databases. Inform. and Comput. 136 (1997) 67-108. | MR 1459842 | Zbl 0889.68052

[12] M. Levene and G. Loizou, A Guided Tour of Relational Databases and Beyond. Springer-Verlag, London (1999). | Zbl 0943.68047

[13] C.L. Lucchesi and S.L. Osborn, Candidate keys for relations. J. Comput. System Sci. 17 (1978) 270-279. | MR 514276 | Zbl 0395.68025

[14] D. Maier, The Theory of Relational Databases. Computer Science Press, Rockville, MD (1983). | MR 691493 | Zbl 0519.68082

[15] B. Thalheim, On semantic issues connected with keys in relational databases permitting null values. J. Inform. Process. Cybernet. 25 (1989) 11-20. | MR 989030 | Zbl 0651.68119