[DL] correct understanding of DL semantics

[Chuming Chen]

Dear All,

I am new to Description Logics. I am trying to understand the correct semantics
of Description Logics. especially, the changes in semantics.

I know DL Semantics is defined by interpretations.  An interpretation I
= (Delta^I, .^I), where  Delta^I is the domain of interpretation (a non-empty set) and
.^I is an interpretation function that maps:
Concept (class) name A to subset of Delta^I, Role (property) name R to
a binary relation R over Delta^I, Individual name i to an element of
Delta^I.

Now let's see an example, if I have concepts "Lawyer" and "Doctor", and
role "hasChild",  John is a "Lawyer" and Mary is "Doctor", John
"hasChild" Mary. But later on in my model, Mary gets another degree and
becomes "Lawyer" also. Now Mary is both "Lawyer" and "Doctor".  Do the
semantics of "Laywer", "Doctor", even "hasChild" change in this case?
Because if we treat concept as a subset of domain, adding Mary to
"Lawyer" certainly change the set for that concept. If role is a subset
of pair of elements in the domain, would that be changed too? Can we 
still think Mary is the same Mary? What are the correct understanding of semantics here?

I might be missing something obvious here. But mathematically speaking , the set
has been changed. Would the semantics be changed also?

Thank you for any comments!

Chuming Chen