Abstract functional dependency structures. (English) Zbl 0727.68028

The functional dependency (FD) is represented in a matroid like manner. It is shown that this framework covers many important particular cases, including FD-relations in a database. A Galois connection of the FD- relations with closure systems is elaborated.


68P15 Database theory
Full Text: DOI


[1] Armstrong, W. W., Dependency structures of database relationships, (Proc. Information Processing, 74 (1974), North-Holland: North-Holland Amsterdam), 580-583
[2] Beeri, C., On the membership problem for functional and multivalued dependencies in relational databases, ACM Trans. Database Systems, 3, 241-259 (1980) · Zbl 0441.68118
[3] Beeri, C.; Dowd, M.; Fagin, R.; Statman, R., On the structure of Armstrong relations for functional dependencies, J. ACM, 1, 30-46 (1984) · Zbl 0629.68096
[4] Birkhoff, G., Lattice Theory (1984), Amer. Mathematical Soc: Amer. Mathematical Soc Providence, RI: Nauka: Amer. Mathematical Soc: Amer. Mathematical Soc Providence, RI: Nauka Moscow, Russian translation · Zbl 0126.03801
[5] Cohn, P. M., Universal Algebra (1981), Reidel: Reidel Dordrecht · Zbl 0141.01002
[6] Delobel, C.; Casey, R. G., Decomposition of a database and the theory of boolean switching functions, IBM J. Res. Develop., 5, 374-386 (1973) · Zbl 0259.68016
[7] Dlab, V., General algebraic dependence structures and some applications, Coll. Math, 14, 265-273 (1966) · Zbl 0136.26302
[8] Fagin, R., Functional dependency in a relational database and propositional logic, IBM J. Res. Develop., 6, 534-544 (1977) · Zbl 0366.68022
[9] Grätzer, G., General Lattice Theory (1978), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0385.06015
[10] Malvestuto, F. M., Theory of random observables in relational data bases, Inform. Systems, 4, 281-289 (1983) · Zbl 0519.68085
[11] Marczewski, E., A general scheme of the notions of independence in mathematics, Bull. de l’Acad. Polonaise des Sciences, Série des Sci. Math., Astr. et Phys., 6, 731-736 (1958) · Zbl 0088.03001
[12] Martin, N. F.G.; England, J. W., Mathematical Theory of Entropy (1981), Addison-Wesley: Addison-Wesley London · Zbl 0187.45003
[13] Matúš, F., Independence and Radon projections on compact groups, (Ph.D. Thesis (1989), Institute of Inf. Th. and Aut: Institute of Inf. Th. and Aut Prague)
[14] Naylor, A. W., On decomposition theory: generalized dependence, IEEE Trans. Systems Man. Cybernet, 10, 699-713 (1981) · Zbl 0473.68054
[15] Geiger, D.; Pearl, J., Logical and algorithmic properties of conditional independence, (Proc. 2nd Internat. Workshop on Artificial Intelligence and Stat. (1989), Fort Lauderdale: Fort Lauderdale Florida) · Zbl 0814.62006
[16] Saxena, P. C.; Tripathi, R. C., Cancellation rule and a complete axiomatization for the set of functional dependencies, Comput. and Artificial Intelligence, 4, 347-356 (1989) · Zbl 0681.68127
[17] Saxena, P. C.; Tripathi, R. C., An algorithm to find minimal cover of a set of functional dependencies, Comput. and Artificial Intelligence, 3, 277-285 (1988) · Zbl 0647.68107
[18] Neveu, J., Bases Mathématique du Calcul des Probabilités (1964), Masson: Masson Paris · Zbl 0137.11203
[19] Ullman, J. D., Principles of Database Systems (1982), Computer Science Press: Computer Science Press Potomac, MD · Zbl 0558.68078
[20] White, N., Theory of Matroids (1986), Cambridge Univ. Press: Cambridge Univ. Press London
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