Simple conditions for guaranteeing higher normal forms in relational databases

The analysis of a relational database to reduce its component schemes into fourth normal form is not trivial. Decompositions into Boyce–Codd normal form is not difficult, but the concepts and analysis needed to further decompose into fourth normal form are usually difficult to comprehend and use. A diagrammatic representation of dependencies is described which provides an informal aid to the construction of relational schemes in fourth normal form.

In the conceptual design of relational databases one of the main goals is to create a conceptual scheme, which minimize redundancies and eliminate deletion and addition anomalies, i.e. to create relation schemes in some good normal form. The study of relational databases has produced a host of normal forms: 2NF, 3NF, BCNF, Elementary-Key Normal Form, 4NF, Weak 4NF, PJ/NF, DK/NF, LTKNF, (3,3)NF, etc. There are two features which characterize these normal forms. First, they consider each relation separately. We believe that a normal form (which reflects the goodness of the conceptual design) should be related to the whole conceptual scheme. Second, the usefullness of all normal forms in relational database design have been based on the assumption that a data definition language (DDL) of a database management system (DBMS) is able to enforce key dependencies. However, different DDLs have different capabilities in defining constraints. In this paper we will discuss the design of conceptual relational schemes in general. We will also define a good normal form (GNF) which requires a minimally rich DDL; this normal form is based only on a primitive concept of constraints. We will not, however, discuss the normalization process itself – how one might, if possible, convert a relation scheme that is not in some normal form into a collection of relation schemes each of which is in that normal form.

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

A new normal form, namely, object-normal form (ONF), is introduced. It is shown that the existing definitions of the fifth normal form (5NF) are unsatisfactory. The correct definition is given for the first time. The importance of the 5NF is demonstrated. For improving data representation in a database with a 5NF schema, the notion of negating relation is introduced. It serves as a basis for the new normal form, namely, the sixth normal form. Combining requirements of the ONF and other normal forms, new normal forms are defined: the fourth object-normal form, the fifth object-normal form, and the sixth object-normal form. It is shown that the standard order of steps of the normalization procedure should be changed: first, the specific requirements of the fourth normal form should be satisfied, and only then the requirements of the second normal form, and so forth.

Although relational languages do not require higher normal forms, they are nevertheless useful as tools for analysis of data and for the imposition of constraints which protect data from some update anomalies. As the first to the third normal forms have been covered before, we shall devote this chapter to the other normal forms, in particular the fourth normal form. We shall also attempt to answer questions such as “is there an ultimate normal form?” and make some comments on the practical usefulness of some of the more exotic theoretical work on normalisation.

The relational database design approach requires the process of normalization in order to minimize data redundancy and update anomalies in the relational schema. Algorithms defined in normalization theory depend upon various dependencies namely functional, multivalued, join and inclusion dependencies that should be carefully defined for a database application. Identification of these dependencies and a minimal cover is a complex and time consuming task for almost all practical problems. This work discusses how the normalization process can be eliminated from the required steps of database design. It explores various constructs of entity relationship diagram (ERD) and their transformation to relational schema. This work elaborates how un-normalized relations are created during the entity relationship (ER) model to relational schema transformation. A set of rules is presented which if followed at the stage of conceptual modeling would always generate a relational schema that satisfies normal forms up to Boyce-Codd normal form (BCNF), thus eliminating the need for normalization. The motivation behind this paper is to save the database designer's valuable time and effort otherwise required in defining dependencies, in finding a minimal cover and in normalizing a given relational schema.

This paper describes the use of cooperative group learning concepts in support of an undergraduate database management course that emphasizes the theoretical and practical aspects of database application development. The course project is divided into three main phases, involving requirements analysis and conceptual design, relational database mapping and prototyping, and database system implementation using Microsoft Access. The project deliverables are designed so that students not only develop a database implementation, but also evaluate their design in terms of functional dependencies, normal forms, the lossless join property, and the dependency preservation property, thus establishing the need for sound database design principles. Students are required to actively participate in each phase, with students assuming different roles in each phase to allow them to experience different leadership responsibilities. As part of the grading process, students evaluate their own performance as well as the performance of others in the group. This paper describes our experience with the structure and administration of cooperative groups and provides a discussion of the lessons we have learned, including initial observations of the effectiveness of the approach.

Boyce–Codd normal form and object normal forms

We propose a normal form for nested relations, called NF-NR, which removes undesirable anomalies from a nested relational database schema. Both functional dependencies and multivalued dependencies are considered. NF-NR reduces to 3NF/4NF if the nested relation considered is actually a flat relation. Especially, NF-NR removes global redundancies among a set of nested relations. Two approaches to NF-NR database design, namely the restructuring rules approach and the ER approach, are discussed. We relate NF-NR to ER-NF, a normal form of ER defined earlier, by defining a simple mapping from an ERD in ER-NF to a set of nested relations in NF-NR. This approach effectively removes ambiguitics and redundancies on a semantic level and hence gives a set of nested relations with clean semantics and yet in good normal form. A set of desirable properties for any normal form for nested relations are described and an evaluation of several existing normal forms is given based on this set of properties. The evaluation shows that NF-NR improves over previously proposed normal forms in various aspects and is a more practical normal form for nested relations.

Context. The complexity of understanding the concept of multivalued dependencies (when setting out their theoretical foundations, an axiomatic approach is used) in relational (table) databases leads to problems of their modeling, which in turn can cause a violation of data integrity. A partial solution to these issues is facilitated by the search for equivalent axiomatic systems of multivalued dependencies that are minimal in terms of the number and power of their components. This, in turn, requires establishing the equivalence of these axiomatic systems and proving the independence of their elements. The object of the study is the axiomatisations of multivalued dependencies.The purpose of the work is to establish the equivalence of two axiomatic systems of multivalued dependencies, one of which is minimal in terms of the number and power of components, and to prove the independence of specified axiomatics. Method. Set-theoretic and logical-algebraic methods are used in the construction of proofs. The equivalence of two axiomatic systems of multivalued dependencies is established classically: the relation of syntactic inference is considered and sequences of multivalued dependencies are constructed that are proofs of the rules of each axiomatics from the components of the other. To build proof of independence of the axiomatic system, models of relational schemes are proposed, such that for an axiom or rule whose independence is being proved, it is impossible to construct proof from set of other axioms or rules.Results. Equivalence of the axiomatisation of multivalued dependencies proposed by a group of scientists Beeri, Fagin and Howard and the Biskup’s axiomatisation of multivalued dependencies has been established. The independence of the Biskup’s axiomatic system is proved in the sense that without loss of completeness it is impossible to remove neither the only axiom nor none of the inference rules.Conclusions. The independence of the Biskup’s axiomatisation of multivalued dependencies, which has no more in number and power of components than other axiomatic systems of multivalued dependencies, is proved. Using such axiomatic system has advantages in the development of CASE-tools (Computer-Aided Software Engineering Tools), which include the implementation of reducing the relational database schema to the fourth normal form, and also, when manually designing a logical model of a relational database.

Why is the snowflake schema a good data warehouse design?

The normalization of relational database schema is the most important trade-off between database performance and data redundancy. This is also one of the major hurdles among database beginners. This critical topic is not only challenging instructors on how to convey the knowledge correctly, but also challenging students on how to acquire the knowledge efficiently. With this concern in mind, this intelligent tutoring system is created as an additional assistance to both instructors and students. This system can be adopted as an in-class course ware or out-class tutoring system. In this paper, I presented the design and implementation philosophy of the user interface module that is empowering the intended tutoring system to push through learn-by-doing while guiding a student to normalize a relational schema from first normal form into third normal form. The synergistic effect between a tutoring system and a student is also discussed.

Relational model is the most essential database model for decades and is examined in various ways. A very important concept in the relational modeling is the concept of dependencies. Particularly a set of functional dependencies and its equivalent minimal cover are discussed here for synthesizing third normal form relations. A traditional synthesis algorithm have been used to reduce the set of functional dependencies, F, into an equivalent minimal cover. This cover is then used to develop a relational schema; however, a given set of functional dependencies may have more than one minimal covers. In turn, different minimal covers may give rise to different relational schema. Database designers had already been agreed upon the use of popular inference rules of Armstrong to obtain minimal covers from the set F of functional dependencies. Despite the frequent use of the traditional synthesis algorithm, there is still a lack of formality and simplicity support in that algorithm to produce a minimum cover, especially; the step(s) of the algorithm in which the set of functional dependencies of F are used to make left-irreducible remain informal. In this paper, an extension is proposed to the synthesis algorithm that aids in to produce an optimal minimal cover more systematically from the given set of functional dependencies. The optimal minimal cover obtained by this extension would be appropriate for synthesizing third normal form relational schema from the universal relation scheme.

This paper is about designing a complete interactive tool, named JMathNorm, for relational database (RDB) normalization using Mathematica. It is an extension of the prototype developed by the same authors [1] with the inclusion of Second Normal Form (2NF), and Boyce-Codd Normal Form (BCNF) in addition to the existing Third normal Form (3NF) module. The tool developed in this study is complete and can be used for real-time database design as well as an aid in teaching fundamental concepts of DB normalization to students with limited mathematical background. JMathNorm also supports interactive use of modules for experimenting the fundamental set operations such as closure, and full closure together with modules to obtain the minimal cover of the functional dependency set and testing an attribute for a candidate key. JMathNorm's GUI interface is written in Java and utilizes Mathematica's JLink facility to drive the Mathematica kernel.

The traditional relational database model may be extended into a fuzzy database model based on the mathematical framework of fuzzy set theory to process imprecise or uncertain information. While designing such a fuzzy relational database model that does not suffer from data redundancy and anomalies, the present authors have defined several fuzzy normal forms in ref [1]. However, as one decomposes an unnormalized relation into a desired normal form, it should also satisfy the essential properties of dependency preservation and lossless join of relation schemes which take a significant role in the design theory of a relational database. We have concentrated on these two important issues in this paper and have designed algorithms that confirm dependency preservation and lossless join decomposition of an unnormalized relation into the fuzzy third normal form or fuzzy Boyce Codd normal form. The algorithms have been tested and validated with examples.