WoLLIC 2011: Logic, Language, Information and Computation pp 110-122 | Cite as
The Boyce-Codd-Heath Normal Form for SQL
Abstract
In the relational model of data the Boyce-Codd-Heath normal form, commonly just known as Boyce-Codd normal form, guarantees the elimination of data redundancy in terms of functional dependencies. For efficient means of data processing the industry standard SQL permits partial data and duplicate rows of data to occur in database systems. Consequently, the combined class of uniqueness constraints and functional dependencies is more expressive than the class of functional dependencies itself. Hence, the Boyce-Codd-Heath normal form is not suitable for SQL databases. We characterize the associated implication problem of the combined class in the presence of NOT NULL constraints axiomatically, algorithmically and logically. Based on these results we are able to establish a suitable normal form for SQL.
Keywords
Normal Form Functional Dependency Inference Rule Uniqueness Constraint Relation SchemaPreview
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References
- 1.Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)MATHGoogle Scholar
- 2.Arenas, M., Libkin, L.: A normal form for XML documents. ACM Trans. Database Syst. 29(1), 195–232 (2004)CrossRefGoogle Scholar
- 3.Arenas, M., Libkin, L.: An information-theoretic approach to normal forms for relational and XML data. J. ACM 52(2), 246–283 (2005)MathSciNetCrossRefMATHGoogle Scholar
- 4.Armstrong, W.W.: Dependency structures of database relationships. Information Processing 74, 580–583 (1974)Google Scholar
- 5.Atzeni, P., Morfuni, N.: Functional dependencies and constraints on null values in database relations. Information and Control 70(1), 1–31 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 6.Biskup, J., Dayal, U., Bernstein, P.: Synthesizing independent database schemas. In: SIGMOD Conference, pp. 143–151 (1979)Google Scholar
- 7.Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)CrossRefMATHGoogle Scholar
- 8.Codd, E.F.: Recent investigations in relational data base systems. In: IFIP Congress, pp. 1017–1021 (1974)Google Scholar
- 9.Date, C., Darwen, H.: A guide to the SQL standard. Addison-Wesley Professional, Reading (1997)Google Scholar
- 10.Diederich, J., Milton, J.: New methods and fast algorithms for database normalization. ACM Trans. Database Syst. 13(3), 339–365 (1988)MathSciNetCrossRefGoogle Scholar
- 11.Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Database Syst. 34(2) (2009)Google Scholar
- 12.Hartmann, S., Link, S.: Numerical constraints on XML data. Inf. Comput. 208(5), 521–544 (2010)MathSciNetCrossRefMATHGoogle Scholar
- 13.Hartmann, S., Link, S.: When data dependencies over SQL tables meet the Logics of Paradox and S-3. In: PODS Conference (2010)Google Scholar
- 14.Heath, I.J.: Unacceptable file operations in a relational data base. In: SIGFIDET Workshop, pp. 19–33 (1971)Google Scholar
- 15.Imielinski, T., Lipski Jr., W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)MathSciNetCrossRefMATHGoogle Scholar
- 16.Köhler, H.: Finding faithful Boyce-Codd normal form decompositions. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 102–113. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 17.Köhler, H., Link, S.: Armstrong axioms and Boyce-Codd-Heath normal form under bag semantics. Inf. Process. Lett. 110(16), 717–724 (2010)MathSciNetCrossRefMATHGoogle Scholar
- 18.Lien, E.: On the equivalence of database models. J. ACM 29(2), 333–362 (1982)CrossRefMATHGoogle Scholar
- 19.Makowsky, J.A., Ravve, E.V.: Dependency preserving refinements and the fundamental problem of database design. Data Knowl. Eng. 24(3), 277–312 (1998)CrossRefMATHGoogle Scholar
- 20.Sagiv, Y., Delobel, C., Parker Jr., D.S., Fagin, R.: An equivalence between relational database dependencies and a fragment of propositional logic. J. ACM 28(3), 435–453 (1981)MathSciNetCrossRefMATHGoogle Scholar
- 21.Schaerf, M., Cadoli, M.: Tractable reasoning via approximation. Artif. Intell. 74, 249–310 (1995)MathSciNetCrossRefMATHGoogle Scholar
- 22.Vincent, M.: Semantic foundation of 4NF in relational database design. Acta Inf. 36, 1–41 (1999)MathSciNetCrossRefGoogle Scholar
- 23.Vincent, M., Liu, J., Liu, C.: Strong FDs and their application to normal forms in XML. ACM Trans. Database Syst. 29(3), 445–462 (2004)CrossRefGoogle Scholar
- 24.Zaniolo, C.: Database relations with null values. J. Comput. Syst. Sci. 28(1), 142–166 (1984)MathSciNetCrossRefMATHGoogle Scholar