Is 2NF a Stable Normal Form?

TL;DR

This paper investigates the stability of the 2NF normal form in relational databases, revealing that in some cases, normalization must proceed directly from 1NF to 3NF due to the structure of functional dependencies.

Contribution

It demonstrates that 2NF is not always a stable normal form and provides conditions under which normalization must skip directly to 3NF.

Findings

In some cases, 2NF cannot be achieved without moving to 3NF.

Normalization depends on the specific set of functional dependencies.

A minimal setup with a single composite key illustrates the phenomenon.

Abstract

Traditionally, it was accepted that a relational database can be normalized step-by-step, from a set of un-normalized tables to tables in $1NF$, then to $2NF$, then to $3NF$, then (possibly) to $BCNF$. The rule applied to a table in $1NF$ in order to transform it to a set of tables in $2NF$ seems to be too straightforward to pose any difficulty. However, we show that, depending on the set of functional dependencies, it is impossible to reach $2NF$ and stop there; one must, in these cases, perform the normalization from $1NF$ to $3NF$ as an indecomposable move. The minimal setup to exhibit the phenomena requires a single composite key, and two partially overlapping chains of transitive dependencies.