Re: Asymmetry of Domain and Range in OWL

Never mind -- my answer from Friday evening doesn't work at all 
(nothing like a weekend to clear your mind :) While I can fix that 
expression to work correctly, indeed I guess it won't be FOL anyway 
since you have to quantify over a predicate?  And indeed, I think there 
is no way to say that without such quantification in FOL, let alone 
OWL. Sorry -- my mistake!

And it's perhaps a point worth making in a note if we go into 
explaining why the things work the way they do in OWL -- which is what 
started this discussion.

Just for the record, if you do quantify over predicates, the following, 
finally, should work (I think... but I may be wrong again..)

(forall ?A (=> (and (C x) (?A x))
                         (forall ?y (=> (?A ?y) (C ?y)))
	
Natasha

On Oct 22, 2004, at 5:34 PM, Natasha Noy wrote:

>
> Yes, you are right -- sorry. But still you can define direct-instance 
> ?x of ?C in FOL as iff
>
> (forall ?A (=> (and (?C ?x) (?A ?x))
>                         (= ?C ?A)))
>
> Is this wrong again?
> 	
> Of course this, by itself, has little to do with assymetry of domains 
> and ranges in OWL and I no longer remember how this came about :)
>
> Natasha
>
> On Oct 22, 2004, at 4:11 PM, Christopher Welty wrote:
>
>>
>> OK, in my world A subclassOf B has an FOL interpretation of (=> (A 
>> ?x) (B ?x)) and o instance-of A has an FOL interpretation of (A o). 
>>  You've invented a new logic on top of FOL, in which the elements of 
>> the language (i.e. subclass, instance-of) are FOL predicates.  I was 
>> talking about FOL.
>>
>> -Chris
>>
>> Dr. Christopher A. Welty, Knowledge Structures Group
>>  IBM Watson Research Center, 19 Skyline Dr., Hawthorne, NY  10532     
>> USA              
>>  Voice: +1 914.784.7055,  IBM T/L: 863.7055, Fax: +1 914.784.7455
>>  Email: welty@watson.ibm.com, Web: 
>> http://www.research.ibm.com/people/w/welty/
>>
>> public-swbp-wg-request@w3.org wrote on 10/22/2004 06:11:48 PM:
>>
>>  >
>>  > > Well, OKBC was intended to be an API, in my understanding, so it 
>> may
>>  > > very well have capabilities that are beyond FOL, as OO languages 
>> do.
>>  >
>>  > but there is an axiomatization for it in FOL in the specs, AFAIK
>>  >
>>  > >
>>  > > Regarding the axiomatization, why don't you try writing FOL 
>> axioms
>>  > > that capture this.  I don't understand how what you have said 
>> can be
>>  > > written in FOL.  
>>  >
>>  > (=> (direct-type ?C ?x)
>>  >         (not (exists ?Y (and (subclass-of ?Y ?C) (instance-of ?X 
>> ?Y))))
>>  >
>>  > (modulo the correct order of arguments for the predicates)
>>  >
>>  > > Then, much more to the point, try it in OWL.
>>  >
>>  > Ah, that's a whole other story :) But you were generalizing to FOL.
>>  >
>>  > Natasha
>>  >
>>  >
>
>

Received on Monday, 25 October 2004 06:55:41 UTC