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Re: Possible semantic bugs concerning domain and range

From: Christopher Welty <welty@us.ibm.com>
Date: Sun, 29 Sep 2002 21:04:31 -0400
To: pat hayes <phayes@ai.uwf.edu>
Cc: Ian Horrocks <horrocks@cs.man.ac.uk>, www-webont-wg@w3.org, www-webont-wg-request@w3.org
Message-ID: <OFC56765EA.48C35BE6-ON85256C44.00012D4F@pok.ibm.com>

Pat,

OK, I (at least) get it.  So if this is the semantics of ranges in rdfs 
(is it?), then probably we should not use rdfs ranges for OWL.  OWL is 
supposed to be based on description logics, which are a decidable fragment 
of FOL (not the only one, btw).   You can say all you want about the 
expressive limitations of DLs, and you can point out an infinite number of 
things they can't do.  I've thrown them away a bunch of times when I 
absolutely needed more. But if you can say what you want to say within 
their expressive limits, they you can be assured you're going to get 
answers.  Take one step over that line and ba-da-bing! - you're gone.

As an ontology designer, I would absolutely love to be unfettered in my 
expressive ability.  In fact, I usually go ahead and use nth order logic 
with modal quantifiers and all manner of cool stuff.  I love variadic 
predicates, too.    But as a system builder, I also want to know what the 
most is I can say and still be guaranteed a result.

So, anyway, seems to me this group is already committed to producing a 
standard based on a language that is sound, complete, and decidable.  So 
we will have to lose the wild-west syntax and stick with what the DL guys 
know how to implement.  All the entailments apparently help speed things 
up.

-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: +1 914.784.6078, Email: welty@us.ibm.com




pat hayes <phayes@ai.uwf.edu>
Sent by: www-webont-wg-request@w3.org
09/27/2002 11:37 PM

 
        To:     Ian Horrocks <horrocks@cs.man.ac.uk>
        cc:     www-webont-wg@w3.org
        Subject:        Re: Possible semantic bugs concerning domain and range

 


>Pat,
>
>Now we seem to have a come to a better understanding about the
>correspondence between FOL and OWL, could you re-answer the following
>question.
>
>Thanks,
>
>Ian
>
>>Pat,
>>
>>DAML+OIL, and I hope OWL, can be viewed a fragment of FOL, with atomic
>>classes and properties corresponding to unary and binary predicates
>>respectively. According to this correspondence, subClassOf axioms
>>become implications, e.g., A subClassOf B corresponds to:
>>
>>forall x . A(x) -> B(x)
>>
>>Similarly, a property range axiom P range A corresponds to:
>>
>>forall x,y P(x,y) -> A(y).
>>
>>What could be simpler and clearer than that?
>>
>>The combination of these two sentences entails
>>forall x,y P(x,y) -> B(y).
>>
>>What could be simpler and clearer than that?
>  >
>  >If you want some alternative semantics, could you please explain in
>  >similar terms what it is?

Sure. I agree this is clear and simple, and I think everyone agrees 
that something very close to this is what we all want. The issue has 
always been only whether those conditions are necessary, or necessary 
and sufficient. We all want the following to be true:

Range(P, A) -> (forall x,y P(x,y) -> A(y) )

You want

Range(P,A) <-> (forall x,y P(x,y) -> A(y) )

They are about equally clear and intuitive; but the latter rules out 
some possibilities which the former permits. I believe that all the 
'intuitive' entailments that people want in fact hold in both these 
cases; and that the former is therefore to be preferred.

The potential utility of the former is that it allows ranges to have 
properties.  Suppose we wanted to say something about ranges (perhaps 
ranges from a particular class of ranges), expressed by a predicate 
Q:  Range(P, x) -> Q(x), say. (It is SUCH a relief to be able to 
write logic!) With the second, stronger condition, this would entail 
that Q was preserved under implication, ie
(forall x (P(x) -> R(x)) -> (Q(P) -> Q(R))
which is a very strong condition for Q to have to satisfy for no good 
reason; in fact, it is so strong that it would make this practically 
useless, since hardly any useful properties satisfy this kind of 
condition (it is restricted to properties like having more than a 
certain number of instances, things like that.)

I hope this helps to make the point clearer.

Pat

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Received on Sunday, 29 September 2002 21:05:51 GMT

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