[DL] Metaclasses and DL

[Enrico Franconi]

On January 8, [IDM] Olivier Dameron writes:
> Dear list members,
>    In the papers on description logics that I have read so far, the fact that 
> the domain and the range of the interpretation function "I" are disjoint 
> seems supposed.
>    However, what hapens if they are not ? Let's call D the domain and R the 
> range.
> 1. D\R would be the "top level" metaclasses
> 2. D inter R would be intermediate level metaclasses (since they are elements 
> of D, they are classes; since they are also elements of R, they are instances 
> of class(es)).
> 3. R\D would be the set of "terminal" or "real" individuals
> 
>    Does this makes sense to you ?
>    If so, don't we risk to fall into a recursive loop ?

Taken from a pure semantic point of view having a domain including
both individuals and (meta)classes makes sense. In general, you may
want to have a well foundedness condition which rules out what you
call the recursive loop, but it is not strictly required (like in rdf,
for example).
cheers
-- e.

Enrico Franconi                     - franconi at inf.unibz.it
Free University of Bozen-Bolzano    - http://www.inf.unibz.it/~franconi/
Faculty of Computer Science         - Phone: (+39) 0471-315-642
I-39100 Bozen-Bolzano BZ, Italy     - Fax:   (+39) 0471-315-649