Re: Asymmetry of Domain and Range in OWL

At 17:34 -0700 22-10-2004, 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?

Hi Natasha, this is not wrong, but it is second order, because you're 
quantifying over predicates. We can manipulate this kind of 
quantification over a finite domain (the given vocabulary of a 
theory), then moving it from proper second order to just meta-level, 
but it is not yet FOL.

>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 :)

The point is that "direct" typing of OO is not in FOL, but in its meta-theory.
Hence, in order to distinguish direct vs. inferred typing, the only 
way is through annotational properties that keep track of the 
inferred classifications.

This has not much to do with "asymmetry" of domain/range (for which 
Chris has given a satisfactory reply at the beginning ot his email).


>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.
>>Dr. Christopher A. Welty, Knowledge Structures Group
>>  IBM Watson Research Center, 19 Skyline Dr., Hawthorne, NY  10532 
>>  Voice: +1 914.784.7055,  IBM T/L: 863.7055, Fax: +1 914.784.7455
>>  Email:, Web: 
>> 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
>>  >
>>  >


Aldo Gangemi
Research Scientist
Laboratory for Applied Ontology
Institute for Cognitive Sciences and Technology
National Research Council (ISTC-CNR)
Via Nomentana 56, 00161, Roma, Italy
Tel: +390644161535
Fax: +390644161513

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Received on Monday, 25 October 2004 10:34:03 UTC