Languages and families of binary relations are standard interpretations of Kleene algebras. It is known that the equational theories of these interpretations coincide and that the free Kleene algebra is representable both as a relational and as a language algebra. We investigate the identities valid in these interpretations when we expand the signature of Kleene algebras with the meet operation. In both cases meet is interpreted as intersection. We prove that in this case there are more… CONTINUE READING