[DL] correct understanding of DL semantics

Jigneshkumar Viradia s0007111 at mail.inf.tu-dresden.de
Thu Oct 4 12:40:50 CEST 2007

Hi Chuming,

> 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,

Here you assumed empty A-Box and T-Box, now obviously your
interpretation is 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.

Before interpretation modification you had;

Lawyer^I := {John}
Doctor^I := {Mary}
hasChild^I:= {(John, Mary)}

After modification of interpretation you have:

Lawyer^I := {Mary, John}
Doctor^I := {Mary}
hasChild^I:= {(John, Mary)}

> 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?

In this case, the interpretation of role name "hasChild" will not change.
Mary (element of domain of Interpretation) is always the same Mary , if
you do not delete it from domain of interpretation.

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

In Description Logic, you interpret concepts, roles and individuals
according to current interpretation. You do not go into past.

Best regards,
Jignesh Viradia

> Thank you for any comments!
> Chuming Chen
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