Relation algebra with binders
The language of relation algebras is expanded with variables denoting individual elements in the domain and with the down arrow binder from hybrid logic. Every elementary property of binary relations is expressible in the resulting language, something which fails for the relation algebraic language. That the new language is natural for speaking about binary relations is indicated by the fact that both Craig's Interpolation, and Beth's Definability theorems hold for its set of validities. The paper contains a number of worked examples.
relation algebras hybrid logic binary relations interpolation modal logic fork algebras beth definability