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Re: LC reply drafted

From: Sebastian Rudolph <rudolph@aifb.uni-karlsruhe.de>
Date: Wed, 13 May 2009 12:07:04 +0200
To: Bijan Parsia <bparsia@cs.manchester.ac.uk>
Message-Id: <0F1A53C5-110E-4377-9C81-670CE01046FA@aifb.uni-karlsruhe.de>
Cc: W3C OWL Working Group <public-owl-wg@w3.org>
Bijan,

if I understood you correctly, your main concern was the use of the  
term "extension" (for several reasons). Not being a native speake, I  
was not aware that the term is more a technical and less an  
intuitively understandable one. I've come up with a new version of the  
respective sentence which avoids the term and paraphrases it. I've  
updated the response draft accordingly.

On the other issue, I think saying that "classes essentially represent  
sets of individuals" is nothing severely wrong, but rather a  
simplification which is appropriate for the Primer. When being  
confronted with the documents on semantics, the interested reader will  
soon realise that the concrete set a class represents varies with the  
choice of the interpretation. Honestly, I see no way of nicely and  
primer-adequately expressing this without potentially confusing  
newcomers.

Best,
  Sebastian

Am 12.05.2009 um 23:45 schrieb Bijan Parsia:

> On 12 May 2009, at 22:24, Sebastian Rudolph wrote:
>
>>
>> Am 12.05.2009 um 21:54 schrieb Bijan Parsia:
>>
>>> On 12 May 2009, at 20:41, Sebastian Rudolph wrote:
>>>
>>>> Dear all,
>>>>
>>>> if I interpreted the intention of the below LC comment correctly,  
>>>> Richard would like to see an explicit statement that classes just  
>>>> represent sets of individuals
>>>
>>> But that would be to say something false. OWL Classes most  
>>> obviously do not "just" represent sets of individuals (as they can  
>>> be mapped to distinct sets in different interpretations). If  
>>> anything, OWL Classes are first order logic formulae with one free  
>>> variable (and thus, when atomic, correspond to monadic predicates).
>>>
>>
>> I don't see a problem with the current wording.
>
> An extension is a set. OWL classes do not denote sets (simplicter),  
> but only sets given an interpretation.
>
>
>> Given a "state of affairs" (as we informally try to describe the  
>> notion of "interpretation" in Section 3), a class represents a set  
>> of individuals. Given another "state of affairs", the set might be  
>> different.
>
> Exactly.
>
>> I'm all in favour of being logically precise but letting "monadic  
>> predicates of first-order logic" enter the Primer-scene would IMHO  
>> not be particularly appropriate for the character of the document.
>
> I didn't say we should put it in there. But we shouldn't put in  
> something that is equally technical (extension) and actually wrong.
>
>
>>>> and that the notion of a "concept" is something related but  
>>>> different.
>>>> I tried to address this by adding two sentences to the Primer  
>>>> document, see the diff at
>>>>
>>>> http://www.w3.org/2007/OWL/wiki/index.php?title=Primer&diff=23464&oldid=23440
>>>
>>> ""In modeling, classes are often used to denote the extension sets  
>>> of concepts of human thinking, like ''person'' or ''woman''."""
>>>
>>> But this is precisely wrong:
>>> 	http://en.wikipedia.org/wiki/Definition#Intension_and_extension
>>>
>>> (reductio ad wikipedia :)). So please don't use the word  
>>> "extension".
>>
>> Forgive me, but I don't find the contradiction that you may have  
>> spotted
>
> Ok.
>
>> (besides being a bit sceptic about using wikipedia for an  
>> authoritative argument).
>
> Sigh. I'm just using it for convenience. That bit isn't wrong and it  
> was easier than inlining.
>
>> In my understanding - which I believe is the common one - the  
>> extension (set) of a concept is the set of objects belonging to  
>> that concept,
>
> Yes.
>
>> the extension of the concept "human" is the set of all humans etc.  
>> So what's wrong with that?
>
> Well, first, if you object to the technicality of  "first order  
> formulae with one free variable", I don't know why "extension" is  
> any better.
>
> Second, an OWL class expression does not have a single extension. It  
> has an extension per interpretation. When, in common philosophical  
> parlance, one says that "the extension of the concept 'human' is the  
> set of all humans" one is implicitly referring to a distinguished  
> interpretation, to wit, the actual world. Hence, the common  
> discussion of "creature with a heart" and "creature with a kidney"  
> being extensionally equivalent but intensionally distinct (since in  
> the distinguished interpretation, the actual world, we (hypothesize)  
> that all (actual) creatures with hearts also have kidneys;  
> obviously, there could be a world where there was a creature with a  
> heart but no kidneys, hence the non-(intensional) equivalence of the  
> two concepts since their extensions *can* diverge).
>
> In point of fact, "Concept" is probably a historically better name  
> than "class", but "class" is perfectly harmless in this context and  
> has a lot of weight behind it.
>
> But if we are going to clarify with technical notions, we should  
> clarify correctly. If we are going to speak loosely, that's ok, but  
> lets do so with an eye to the broadest pedagogic benefit. For me,  
> that means not tuning it to satisfy the someone who seems rather  
> idiosyncratic in their understanding.
>
> Cheers,
> Bijan.
>

_________________________________________________
Dr. Sebastian Rudolph
Institute AIFB, University of Karlsruhe, D-76128 Karlsruhe
rudolph@aifb.uni-karlsruhe.de    phone +49 (0)721 608 7362
www.sebastian-rudolph.de                 fax +49 (0)721 608 5998
Received on Wednesday, 13 May 2009 10:08:20 UTC

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