Matúš, František Abstract functional dependency structures. (English) Zbl 0727.68028 Theor. Comput. Sci. 81, No. 1, 117-126 (1991). 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. Reviewer: M.Zimand (Bucureşti) Cited in 7 Documents MSC: 68P15 Database theory Keywords:functional dependency PDF BibTeX XML Cite \textit{F. Matúš}, Theor. Comput. Sci. 81, No. 1, 117--126 (1991; Zbl 0727.68028) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.