DOMAIN-OF is the inverse of the DOMAIN relation; i.e., (domain-of D R) means that D is a domain restriction of R. A DOMAIN-OF a binary relation is a class to which the binary relation can be meaningfully applied; i.e., it is possible, but not assured, that there are instances d of D for which R(d,v) holds. Of course, every instance i for which R(i,v) does hold is an instance of D.
One interpretation of the assertion (DOMAIN-OF my-class my-relation) is `the slot my-relation may apply to some of the instances of my-class.' A less precise but common paraphrase is `my-class has the slot my-relation'. User interfaces to frame and object systems often have some symbol-level heuristic for showing slots that `have' or `make sense for' the class. Keep in mind that DOMAIN-OF is a constraint on the logically consistent use of the relation, not a relevance assertion. There are many classes that are DOMAINs-OF a given relation; namely, all superclasses of the exact-domain. (THING, for example, is a DOMAIN-OF all relations.) Therefore, it is quite possible that most of the instances of a domain-of a relation do not `make sense' for that relation.
Whereever one uses (domain-of D R) it is equivalent to adding D to the list of domain restrictions on the definition of R. In other words if R was defined as (define-relation R (?x ?y) :def (and (A ?x) (B ?y))) then the statement (DOMAIN-OF D R) has the same meaning as changing the definition to (define-relation R (?x ?y) :def (and (A ?x) (D ?x) (B ?y))). For modularity reasons DOMAIN-OF is preferred only when R is not given its own definition in an ontology.