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Re: [ontolog-forum] Ontology of Rough Sets

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sat, 22 Jan 2011 18:47:24 -0600
Message-id: <A7DE6D12-65D4-40B9-9F7A-E39E9C001EF6@xxxxxxx>

On Jan 22, 2011, at 4:50 PM, Christopher Menzel wrote:    (01)

> On Jan 21, 2011, at 10:22 PM, doug foxvog wrote:
>> On Fri, January 21, 2011 12:18, Christopher Menzel said:
>>> On Jan 21, 2011, at 9:46 AM, doug foxvog wrote:
>>>> ...
>>>> A standard distinction between a set and a class, is that membership in a 
>[set] cannot change, while membership in a class can.
>>> I think it's useful to distinguish two claims when it comes to the identity 
>conditions of classes:
>>> (1) Classes are not extensional (i.e., distinct classes can have the same 
>>> (2) Classes can change their membership.
>>> In the formal semantics of a number of KR languages, (1) is true but, 
>strictly speaking at least, (2) is not.
>> Ontology ALWAYS comes up against the problem that the same word is used with 
>different meanings. Meriam-Webster's 11th edition has 24 definitions for "set" 
>as a noun and 6 for "class" as a noun.
> Sure thing. Are we disagreeing about something? :-)
>> I just said that this was A standard distinction, not that the word "class"
>> was not used in other ways.
> I entirely agree; I probably wasn't clear enough, but my intention was only 
>to expand on your point.
>>> Notably, classes in OWL areexplicitly non-extensional: since a class is 
>stipulated only to *have* anextension in OWL's formal semantics, nothing 
>prevents distinct classesfrom having the same extension.  The same is true of 
>> Agreed.
>>> However, simply because there is no formal notion of change built into 
>OWL's semantics,there is no possibility, within a given interpretation, that a 
>classchange its membership.
>> The restriction here, "within a given interpretation", places the
>> restriction of unchangability on the class.  
> Right, that's all I was trying to point out.
>> A class can change its membership from one interpretation to another merely 
>with the addition or removal of statements.
> Sure.    (02)

i'm not sure I agree, and I wonder if Chris really does. What does this even 
mean, "a class can change its membership from one interpretation to another" ? 
A given class NAME may be interpreted differently in different interpretations, 
of course: but the classes themselves - the entities, whatever they are, which 
are denoted by the class names and which are, therefore, classes - cannot 
"change ... membership from one interpretation to another" since they ARE 
entities in a given interpretation. It does not make sense to speak of 'moving' 
a class (or anything else) 'from' one interpretation 'to' another.     (03)

And even if it did, how would this be achieved by addition or removal of 
STATEMENTS? Classes do not (usually) contain statements.     (04)

Seems to me that this whole discussion illustrates the kind of hopeless muddle 
one gets into when words like 'class' are used carelessly, guided only by a 
preformal intuition. The whole business of writing ontologies in formal 
languages is supposed to be helping us get past this kind of groping in the 
dark for mutual meaning. We might learn from our own field at this point, I 
suggest.     (05)

>>> As noted in an earlier message in this thread,without augmenting the notion 
>of an OWL interpretation somehow, change canonly be represented formally in 
>terms of something like a series ofinterpretations that are thought of as 
>temporally ordered.
>> Fine, for change that is thought of as temporal change.  For change that is 
>spatial/jurisdictional, the different interpretations need not be temporally 
> Absolutely true, I was focusing on change through time, although even if the 
>focus is on spatial or jurisdictional change, it seems to me that it will 
>nearly always be important also to know how the change in question is 
>temporally ordered; otherwise all we know is that there was change, that 
>something was in one location/state A at one time and another location/state B 
>at some other time, not that something changed *from* (say) location/state A 
>*to* location/state B.
>> Such change allows for membership in a class to change, so I don't think 
>that is an argument that membership in a class can not change.
> Just to be clear, I never argued that membership in a class cannot change. I 
>simply said that change of membership by an OWL class is not possible within a 
>given OWL interpretation.  That's it.
>>> That said, (2) does seem to be a strong *intuitive* idea in the KR, AI, and 
>database communities.
>> This is the meaning i was referring to.
> Never meant to suggest otherwise! :-)    (06)

Then allow me to suggest otherwise. As someone somewhat familiar with at least 
the KR and AI communities, I do not recall that the idea that class membership 
can change is, in fact, a strong intuitive idea there. If it were, the AI/KR 
field would have been happily using class language rather than, say, speaking 
of situations, ever since 1969. Temporal reasoners use many formal devices to 
represent time and change, but this simplistic notion of classes changing their 
membership is not one of them. If one were to try to use it in a realistic 
example, one would rapidly discover why.     (07)

Pat Hayes    (08)

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