(2015) Bui, Dmitriy; Puzikova, Anna; Буй, Дмитро Борисович; Пузікова, Анна Валентинівна
(en) Axiomatics for multivalued dependencies in table databases and axiomatics for functional and multivalued dependencies are reviewed; the completeness of these axiomatics is established in terms of coincidence of syntactic and semantic consequence relations; the completeness criteria for these axiomatic systems are formulated in terms of cardinalities (1) of the universal domain D , which is considering in interpretations, and (2) the scheme R, which is a parameter of all constructions, because only the tables which attributes belong to this scheme R are considering. The results obtained in this paper and developed mathematical technique can be used for algorithmic support of normalization in table databases.
(Institut of Mathematics and Computer Science, 2015) Bui, Dmitriy; Puzikova, Anna; Пузікова, Анна Валентинівна; Буй, Дмитро Борисович
(en) Axiomatics for multivalued dependencies in table databases and axiomatics for functional and multivalued dependencies are reviewed. For each axiomatic relations of syntactic and semantic succession are considered. A rigorous and convincing proof of correctness and completeness of these axiomatics (within the paradigm of mathematical logic) is established. In particular, the properties of closures of sets of specified dependencies are investigated. The properties of set-theoretic function restriction have been used as mathematical framework.
