[DL] correct understanding of DL semantics

[Jigneshkumar Viradia]

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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