Re: LC reply drafted

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.

Received on Tuesday, 12 May 2009 21:46:16 UTC