[DL] correct understanding of DL semantics

[Enrico Franconi]

Hi,
in the standard semantic setting for DL you are referring to,  
everything is to be considered static, i.e., the interpretation of  
concepts, roles, and individual is to be considered just as the  
description of a single state and it is fixed in time, and so it does  
not change.
Your example should be modelled either as an ABox update, and the  
semantics of your updated knowledge base is exactly the one that  
holds at the end of the update, regardless of what was true before  
the update - i.e., it does not depend on previous states.
If you want to characterise some sort of dependencies between states  
due to the cahnges, then you have to adopt a more sophisticated (non- 
standard) (description) logic formalising these aspects.
cheers
--e.

On 21 Sep 2007, at 01:36, Chuming Chen wrote:

> 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
>
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