Some results about normal forms for functional dependency in the relational datamodel

Non-deterministic ideal operators: An adequate tool for formalization in Data Bases

“…Since K ↑ is upper closed, Proposition 6.11 ensures that A = K ↑ ∪(K ↑)↓ * and, from the definition of K −1 , we have that (K ↑)↓ * = K −1 ↓. (2) is the definition of antikey in antichain proposed in [17]. Now, as an immediate consequence of the above proposition and Lemma 6.3, we have the following corollary.…”

“…Example 6 (Demetrovics and Vu [17]). Let us consider U = {a, b, c, d}, s = (2 U , F) and s = (2 U , F ) where F and F are given by…”

“…In this section we give a formal definition of the normal forms for FDs more frequently used in the bibliography [17]: the second normal form (2FN), the third normal form (3FN) and Boyce-Codd's normal form. (FNBC).…”

“…Several authors [8,14,16,17,20] propose formal approaches using lattice theory for the study of functional dependencies, closing operators and the characterization of key concepts of the relational model. Our work follows that path, and it is based on the introduction of the concept of non-deterministic ideal operator in the framework of lattice theory.…”

Some combinatorial algorithms connecting hypergraphs

“…Let us give some necessary definitions that are used in the next sections. The concepts give in this section can be found in [1,2,3,4,7,9,10,15,16,17,18].…”