Re: Defining properties between classes

On 6 Feb 2009, at 01:25, Loris Bozzato wrote:
[snip]
> 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".

Yep.

> > 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.

Fair enough.

> > 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.

I would do it in a preprocessing stage, myself, as a kind of macro.

> 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?

If the semantics are correct, then surface syntax can be adjusted :)  
Not so great for publishing, I agree.

> 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?

? Range has intersection semantics.

I'd definitely use OWL 2 for this.

> Thanks again for all your advices as they helped me to better define  
> my problem

Thanks for the interesting problem. I hope you write it up for, e.g.,  
the next OWLED.

Cheers,
Bijan.

Received on Friday, 6 February 2009 08:07:30 UTC