Re: Defining properties between classes

Hello,
First of all, many thanks to both for your suggestions.

To Michael:

> Hm, sounds to me as if P should be a super property of the Cartesian
product
> of C and D?

Yes, that's it. Also, your solution seems the most reasonable way to
directly model this in SROIQ (although, as you pointed out, not very
intuitive).
Moreover, I found that the same idea has been presented last year at DL08 in
[1].


To Bijan:

> I've having trouble understanding why one would want this to the point of
having trouble thinking
> of solutions! Could you describe your representational problem?
Sure: in our orthodontics ontology the problem has emerged in defining
features of some classes of diseases. For example, every element in the
class of tooth size discrepancies (TSD, i.e. anomalies in the size of teeth)
should have a relation isAnomalyOf to every element of the class Tooth (that
models kinds of teeth, i.e. molar, canine etc). This wants to be a way to
model that "tooth size discrepancies are anomalies of teeth".
The same issue appears similarly in other parts of the ontology, possibly
because some of the classes should be considered as "collective individuals"
in some cases (as in the one above).

However, as pointed out in [1], this problem and the issue of representing
properties as cartesian product of classes seems to be of general interest,
e.g. to represent "All elephants are bigger than all mice" or
"Antihistamines alleviate allergies".

> Oh, this seems different. This seems to be the "may" problem. See:
>      http://www.webont.org/owled/2008/papers/owled2008eu_submission_14.pdf

Thanks for the interesting reference: the "may" representation can be a way
to see my problem, but in fact I'm just interested in the "coarser"
semantics described above.

> You mean, something like,
>       D = oneOf (:x, :y, ;z).
>       x != y != z.
>       C = P min 3 D.
>
> (So, every C has to have a P relation to x, y, and z.)
>
> But where you don't want to put in a set of values for D and don't want to
have to know its
> cardinality in advance?

This solution indeed works, but, as you suggest, I must specify the elements
and cardinality of the class D. The problems arise whenever I should modify
the instances of D: I should rememeber to modify also the cardinality
restriction in C.
But the main problem is that this is not very intuitive: what does it mean
that "TSD is an anomaly of 4 kinds of tooth" without knowing the fact that
Tooth has exactly 4 elements?
By the way, if we want to stay in OWL-DL and SHOIN, this can be only
represented as:

C = P min 3.
P hasRange D.

But what if D is not the only class in the range of P?


Thanks again for all your advices as they helped me to better define my
problem.
Kind regards,
Loris Bozzato

--
[1]
http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-353/RudolphKraetzschHitzler.pdf

-- 
Loris Bozzato - PhD student
Dipartimento di Informatica e Comunicazione
Università degli Studi dell'Insubria, Varese, Italy

Tel: (+39) 0332 218949 - Fax: (+39) 0332 218919
Mail: loris.bozzato@uninsubria.it
Web: http://www.dicom.uninsubria.it/~loris.bozzato/<http://www.dicom.uninsubria.it/%7Eloris.bozzato/>