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

In this paper, we propose the application of formal methods to Software Engineering  . The most used data model is the relational model and we present, within the general framework of lattice theory, this analysis of functional dependencies. For this reason, we characterize the concept of ff-family by means of a new concept which we call non-deterministic ideal operator (nd.ideal-o). The study of nd.ideal-o.s allows us to obtain results about functional dependencies as trivial particularizations, to clarify the semantics of the functional dependencies and to progress in their efficient use, and to extend the concept of schema. Moreover, the algebraic characterization of the concept of Key of a schema allows us to propose new formal definitions in the lattice framework for classical normal forms in relation schemata. We give a formal definition of the normal forms for functional dependencies more frequently used in the bibliography: the second normal form (2FN), the third normal form(3FN) and Boyce–Codd's normal form (FNBC).