Weakening relation algebras as residuated Heyting algebras

Nick Galatos

(Joint work with Peter Jipsen)

Relation algebras admit a very nice description of their congruences and form a discriminator variety. We present a generalization, weakening relation algebras, that enjoys the same properties but could be considered as an intuitionistic version of relation algebras. We explain how these have two residuated operations, one of which is a Heyting algebra, and therefore are residuated Heyting algebras (also known as GBI-algebras) and we characterize the congruences of such algebras in two different ways.