[DL] Metaclasses and DL

[Christel Kemke]

Hi,

I followed the last e-mails on the question of whether the domain (T-Box 
concepts) and range (individual elements of the universe, structure, 
domain) of an interpretation of a T-Box can be the same - and how and why.
 
 From my understanding, the only thing we save, is to deal with 
additional names or symbols used in the universe/structure/domain. From 
my point of view, to use the same names in both domain and range of the 
I-function would make sense only when we want to deal with individuals 
again as concepts (or predicates) which means they would be used to 
denote meta-classes, so that we can have an individual (which is the 
interpretation of a concept) again as a concept. But Baader mentions, 
that this would not be necessarily the case.
Secondly, since there is no distinction between concepts and 
individuals, and if I allow I(C)=C, where C is the name of a concept as 
well as of an individual, this also should allow I(I(C)) and so forth, 
i.e. (unlimited, infinite) recursion. In response to Baader's comment: I 
don't see how the interpretation function (if one and the same function 
is used) could figure out whether a C is supposed to be treated as a 
concept or as an individual - no matter whether I have I(C)=C or 
I(A)={A,B}. From Franconi's e-mail, I understand or guess that a 
solution could be to base this recursion on a fixed-point semantics of 
the interpretation function but I don't really see this for the 
described case of concept definitions and interpretations (what is the 
fix-point if there is no groundedness?). It probably works if we simply 
state that one level (or another fixed amount) of applications of the 
I-function is enough but then: what do we gain?

Finally, I am asking (myself / the list) again: Does this really make 
sense or does it only create (unnecessary) confusion?

Regards,
Christel Kemke

-- 
Christel Kemke
Dr.rer.nat., Dipl.-Inform., B.Sc. (Honours), Dip.Psych. (Open University)
Assistant Professor
Department of Computer Science
Machray Hall, Room 562
University of Manitoba
Winnipeg, MB, R3T 2N2
Canada

Phone: +1 (204) 474-8674
Fax: +1 (204) 474-7609