Normal Forms

Normal forms are a hierarchy of conditions on relational schemas — defined in terms of functional and multivalued dependencies — each of which rules out a particular class of redundancy and the anomalies it causes.

Definition

A normal form is a property of a relation schema, stated in terms of its functional or multivalued dependencies, whose satisfaction guarantees the absence of a specific kind of redundancy and associated update, insertion, and deletion anomalies.

Scope

This topic covers the normal forms and the redundancy each removes: first normal form (atomic attribute values), second and third normal form (eliminating partial and transitive dependencies on candidate keys), Boyce-Codd normal form (every nontrivial functional dependency has a superkey on its left), and fourth normal form (eliminating nontrivial multivalued dependencies). It explains how to test membership in each form using dependencies. It excludes the mechanics of decomposing a schema to reach a normal form, treated under schema refinement.

Core questions

• What condition does each normal form impose, and what redundancy does it eliminate?
• How are partial and transitive dependencies related to second and third normal form?
• When is a schema in Boyce-Codd normal form but not lower forms, or vice versa?
• How do multivalued dependencies motivate fourth normal form?
• How is a relation tested for membership in a given normal form?

Key concepts

• first normal form (atomicity)
• second normal form (no partial dependencies)
• third normal form (no transitive dependencies)
• Boyce-Codd normal form
• prime and non-prime attributes
• multivalued dependencies
• fourth normal form
• anomaly elimination

Key theories

First through third normal form

1NF requires atomic attribute values; 2NF removes dependencies of non-prime attributes on part of a candidate key; 3NF additionally removes transitive dependencies, so non-prime attributes depend only on candidate keys.

Boyce-Codd normal form

A schema is in BCNF if for every nontrivial functional dependency X → Y, X is a superkey; BCNF removes all redundancy due to functional dependencies but a BCNF decomposition may fail to preserve all dependencies.

Fourth normal form and multivalued dependencies

Fagin's fourth normal form generalizes BCNF to multivalued dependencies, requiring that every nontrivial multivalued dependency have a superkey on its left, eliminating redundancy that functional dependencies cannot describe.

Clinical relevance

Normal forms give database designers a concrete checklist for producing schemas free of redundancy-driven anomalies; in practice most operational databases target third normal form or BCNF, while designers knowingly relax these forms for performance in analytic and reporting workloads.

History

Codd defined 1NF, 2NF, and 3NF in the early 1970s; the stronger BCNF was developed by Boyce and Codd shortly after. Ronald Fagin introduced 4NF (1977) for multivalued dependencies and later 5NF for join dependencies, completing the classical hierarchy used in teaching and practice.

Key figures

• Edgar F. Codd
• Raymond F. Boyce
• Ronald Fagin

Seminal works

• codd1972
• fagin1977
• silberschatz2019

Frequently asked questions

Which normal form should I aim for?

Most transactional designs target third normal form or Boyce-Codd normal form, which remove the redundancy caused by functional dependencies. Fourth and fifth normal forms address rarer multivalued and join dependencies. Higher is not always better in practice: designers sometimes stop at 3NF or denormalize for read performance.

Can a schema be in a higher normal form but not a lower one?

The classical forms 1NF through BCNF are nested, so being in BCNF implies being in 3NF, 2NF, and 1NF. However a schema can satisfy 3NF while failing BCNF, which is the usual case where designers must choose between BCNF and preserving all functional dependencies.