DOMAIN is short for ``domain restriction''. A domain restriction of a binary relation is a constraint on the exact-domain of the relation. A domain restriction is superclass of the exact-domain; that is, all instances of the exact-domain of the relation are also instances of the DOMAIN restriction. Thus, the DOMAIN of a relation is not unique.
In an ontology, specifying a domain restriction of a binary relation is a way to specify partial information about the objects to which the relation applies. For example, one can state that favorite-beer is a relation from beer drinkers to beers as (domain favorite-beer person). This says that all people who have
a favorite-beer are instances of person, even though there may be some instances of person who do not have a favorite beer.
Representation systems can use these specifications to classify terms and check integrity constraints.
(<=> (Domain ?Relation ?Restriction) (And (Binary-Relation ?Relation) (Class ?Restriction) (Subclass-Of (Exact-Domain ?Relation) ?Restriction)))