On the composition and decomposition of attributes and tuples
In this paper NEST (UNNEST) is decomposed into attribute composition and tuple composition (into attribute decomposition and tuple decomposition, resp.). It is shown that by the complete graph and the edge labelling associated to a relation as in  we can represent the set of multi-valued dependencies in the given relation. Therefore, by this complete graph and edge labelling, we can represent Boolean dependencies and multivalued dependencies of the relation that we obtain from the given relation through tuple compositions and attribute compositions. A concept of insistency of operators is proposed. A necessary and sufficient condition for an operator to be ℱ-insistent for a given Boolean dependency ℱ is offered.
KeywordsComplete Graph Functional Dependency Propositional Logic Edge Labelling Attribute Decomposition
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- 1.J. Berman, J. Blok: Positive boolean dependencies. Inform. Process. Letters, 27, 3 (1988), pp. 147–150.Google Scholar
- 2.J. Demetrovics, L. Rónyai, Hua nam Son: Dependency Types. Computers. Math. Applic. 21, 1 (1991), pp. 25–33.Google Scholar
- 3.J. Demetrovics, L. Rónyai, Hua nam Son: On the representation of dependencies by propositional logic. In: J. Demetrovics, B. Thalheim, H.-D. Gerhardt (eds): Proc. MFDBS 91 (Rostock, Germany). LNCS 495, Springer-Verlag 1991, pp. 230–242.Google Scholar
- 4.J. Demetrovics, L. Rónyai, Hua nam Son: Functional dependencies among BDs. (to appear).Google Scholar
- 5.R. Fagin: Functional dependencies in relational database and Propositional Logic. IBM J. Res. and Develop. 21, 6 (1977), 5, pp. 534–544.Google Scholar
- 6.P.C. Fischer, L.V. Saxion, S.J. Thomas, D.V. Gucht: Interactions between dependencies and nested relational structures. JCSS 31, 3 (1985), pp. 343–355.Google Scholar
- 7.G. Jaeschke, H.-J. Schek: Remarks on the algebra on non first normal form relations. In: Proc. ACM SIGACT-SIGMOD Symposium on Principles of database systems, 1982, pp. 124–138.Google Scholar
- 8.A. Makinouchi: A consideration on normal form of not-necessarily-normalized relations in the relational data model. In: Proc. of the Conference on Very Large Data Bases (Tokio, 1977), pp. 447–453.Google Scholar
- 9.Z.M. Ozsoyoglu, L.Y. Yuan: A new normal form for nested relations. ACM Trans on Database Systems, 12, 1 (1987), pp. 111–136.Google Scholar
- 11.Y. Sagiv, C. Delobel, D.S.JR. Parker, R. Fagin: Correction to “An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic”, JACM 34, 4 (1987), pp. 1016–1018.Google Scholar
- 12.B. Thalheim, S. Al-Fedhagi: Preserving two-tuple dependencies under projection. Acta Cybernetica 9, 4 (1990), pp. 441–458.Google Scholar