Restructuring and dependencies in databases
Let ϕ: ℜ→L be a mapping between databases over (different) schemes R and S. This paper considers the following question. What can we say about dependencies in ϕ(r) if we know dependencies in r ∈ ℜ. It is shown that under some conditions the existence of a sound and complete inference system for ℜ implies the existence of a sound and complete inference system for the triple (ℜ, ϕ, L). In the case of functional dependencies some necessary and sufficient conditions for the existence of a sound and complete inference system for the triple (ℜ, ϕ, L) is obtained. However, these conditions are rather strong. But these conditions could be eliminated if we extend the language for dependencies' description. The so called (untyped) mixed functional dependencies that generalize the functional ones are introduced. For these dependencies a sound and complete inference system D is constructed. Moreover, from the system D and the mapping ϕ a sound and complete inference system for the triple (ℜ, ϕ, L) is obtained.
KeywordsFunctional dependencies Mixed functional dependencies Induced dependencies Complete inference systems
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- [ABU]Aho A.V., Beeri C., Ullman J.D. The theory of joins in relational databases. ACM Trans. Database Syst., 4(1979), N3, 297–314.Google Scholar
- [A]Armstrong W.W. Dependency structures of data base relations-hips. 1974 IFIP Congr., 580–583.Google Scholar
- [CM]Chan E.P.F., Mendelzon A.O. Independent and separable database schemes. In Procceedings of the 2nd ACM Symposium on Principles of Database Systems. ACM, New York, 1983, 288–296.Google Scholar
- [GMV]Graham M.C., Mendelzon A.O., Vardi M.Y. Notions on dependency satisfaction. J. ACM, 1986, v. 33, N1, 105–129.Google Scholar
- [GY]Graham M.C., Yannakakis M. Independent database schemas. J. Comput. Syst. Sci., 1984, v. 28, N1, 121–141.Google Scholar
- [GJ]Grant J., Jacobs B.E. On the family of generalized dependency constraints. J. ACM, 1982, v.29, N4, 986–997.Google Scholar
- [H]Honeyman P. Testing satisfaction of functional dependencies. J. ACM, 1982, v. 29, N3, 668–677.Google Scholar
- [IS]Imelinski T., Spyratos N. On lossless transformation of database schemes not necessarily satisfying universal instance assumption. Proc. 3d ACM Symp. Princip. Database Syst., 1984, 258–265.Google Scholar
- [M]Maier D. The Theory of Relational Databases. Comput. Sci. Press, 1983.Google Scholar
- [MMSU]Maier D., Mendelzon A.O., Sadri F., Ullman J.D. Adequacy of decompositions of relational databases. J. Comp. Syst. Sci., 21(1980), N3, 368–379.Google Scholar