Relation Algebra ≠ Relational Algebra

This clarifies a persistent naming confusion: relational algebra (the database foundation introduced by Ted Codd around 1970) is not the same as relation algebra (the mathematical, axiomatic "calculus of relations" associated with Tarski). Relational algebra underpins SQL-style query languages and, by Codd's theorem, is equivalent in power to the domain-independent fragment of relational calculus (a controlled fragment of first-order logic). Relation algebra, by contrast, is an abstract algebraic structure modeling binary relations; it corresponds to first-order logic limited to three distinct variables (FOL^3) and can be extended - via a fork operator - to recover full first-order expressiveness.

The distinction matters beyond terminology because relation algebra has its own history of applications in formal methods and, increasingly, in database research. Tools like the Alloy analyzer implement "relational logic" grounded in that algebraic perspective, and a small community led by Dirk Van Gucht has adapted relation-algebra ideas to querying systems - examples include IUGQL and the newer Prela query language, claimed to be the first such language since IUGQL. To reduce ongoing confusion, renaming relation algebra as "Tarski's Algebra of Relations" (TAR) is proposed so practitioners can more easily recognize and adopt its expressive, algebraic approach.