An equivalent definition of the intercategorial entailment (i.e. an entailment between expressions of different but functionally related categories) is given and some other formal properties are established. These show that the atomicity of denotational algebras plays an essential role in the phenomenon of intercategorial entailment. Various possible applications to the semantics of non-declaratives are indicated. They suggest that intercategorial entailment, although formally different from generalized entailment and from presupposition is a generalisation of both of these notions.
