Relation algebra is not relational algebra

Many individuals mistakenly mix up relation algebra with relational algebra, including notable sources like Wikipedia and database expert Jamie Brandon. The confusion likely stems from the names' similarity, and it's unlikely that the creator of relational algebra, Ted Codd, knew about relation algebra, or he might have named his concept differently.

Relational algebra, introduced by Codd in his 1970 paper, serves as the foundation for relational databases. Codd later formalized his theorem (now known as Codd's theorem) which establishes the equivalence between relational algebra and domain independent relational calculus, a subset of first-order logic queries.

Relation algebra, however, remains less known outside of logic and pure mathematics. Within these fields, it's defined as an algebraic structure through a set of axioms, and the name originates from its application to binary relations. An interesting parallel to Codd's theorem is that relation algebra is equivalent to FOL^3, which limits first-order logic to use only three different variables (with nested quantifiers possible).

This equivalence can be expanded to match the expressive power of FOL with the addition of a fork operator.

Interestingly, despite its mathematical roots, relation algebra has found applications in computer science. One prominent example is the Alloy analyzer, which was originally developed as "relational logic" but was incorrectly directed to the page for relational algebra. Alloy traces its lineage to the Z notation by the late Jean-Raymond Abrial.

Recent developments suggest that relation algebra is gaining traction in database theory and systems. Dirk Van Gucht and a small group of dedicated individuals have been applying relation algebra concepts to database theory and systems, as highlighted in the authors' recent paper on the Prela query language. Prela appears to be the first query language since Van Gucht's IUGQL that is based on relation algebra.

The author suggests that relation algebra deserves more recognition and proposes a new name - "Tarski's Algebra of Relations" (TAR) - to avoid confusion with the already established relational algebra.