Relation algebra

Summary

A relation algebra is a Boolean algebra with two more operations and a constant. They behave like composition and converse of binary relations and like the identity relation. Alfred Tarski gave the axioms in the 1940s, building on the calculus of relations of De Morgan, Peirce and Schröder. The main example is the algebra of all binary relations on a set. Relation algebras give an algebraic form of a fragment of first-order logic. Tarski and Givant showed that set theory can be formalized in this setting.