Puzikova A. Theory of normalization in table databases

The purpose of the candidate's thesis is the axiomatics for functional and multivalued dependencies in table databases and a fragment of mathematical normalization theory for 2-4 normal forms. In the work it is represented a review of the existing literature on the theory of normalization in relational (table) databases. On the basis of analysis of the sources and own results logical connections between the definitions of classical and basic non-classical normal forms are established. It is shown that two definitions of Fagin's Projection-Join Normal Form (PJ/NF) are not equivalent. The mathematical proofs of correctness of the axiomatics for functional dependencies and axiomatics for functional and multivalued dependencies are constructed. Known in the literature proofs of the completeness of these axiomatics are reconstructed and complemented (in terms of coincidence of syntactic and semantic consequence relations). Proofs of completeness of these axiomatics are constructed under the assumption, that universal domain contains at least two elements, а scheme - at least two attributes. To correct it the completeness criteria for each of axiomatic systems in terms of cardinalities of the universal domain and scheme are established.