Re: [ontolog-forum] a skill of definition - "river"

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

@ John,

I appreciate Waismann's point. I don't think what I said is in opposition to it, as far as i can tell, it embraces it. Though I like to get at his insight by thinking that once specified, any system begins to decay. Suggesting then simply that maintenance / upkeep / revision is a necessary part of any specification framework.

@ Matthew 

Oops. Thanks for clarifying, I was confusing senses of extension :P.

> or whether one particular ontic category hierarchy is appropriate for all, I think efforts would be more fruitful in explicating / generating mappings between what various peoples find useful.  I.E. take the IDEAS hierarchy and compare it to DOLCE or SUMO -- what's being reused?
> [MW] Wrong question. More important is how do you map from one to the other.

I think those questions (reuse) are part of the process of understanding and developing such mappings.

> [MW] Well the way this normally plays out is that those who take an intensional approach do not necessarily think they have something different when the membership of a set changes. So If I ask "How many cars are there". They will give a certain answer, and if I ask the same question a year later, they will give a different number, and will be quite happy that the membership of the set has changed. An extensionalist, on the other hand, will insist that these are actually two different sets: Cars-at-time-1 and Cars-at-time-2, and a 4D extensionalist will say that the set of all cars, is all the cars that have existed and will exist.

So each ontology interprets the notion of set differently, which affects the notion of a definition. 

Forgive me if what I say is obvious, but for posterity, in the above we have a statement, "set of all cars" which corresponds to three distinct sets, depending on what framework one employs.

Let's call them:

Sint - intensional

Sext - extensional 

S4Dex - 4D extensional 

which are unique. 

So in an intensional framework, depending on when a query is executed (a question is asked), Sint= Sext@Tquery.

In a 4D extensional framework, set S4Dex  = U (forall i) Sext@Ti

                 where @Tx is the unique name of each set in the extensional perspective at time x.

Seemingly, the above suggests that if we want mappings to work, while each group may choose their own framework, if they intend to interoperate, we need to know what pieces of information we need to track (though perhaps not ontologically commit to), to enable such mappings. Thus if using an intensional framework, with an eye on translating to an extensional one, we'd need to track when extensions are generated, etc.

Is this a semi-accurate catch-up to where people thinking about this issue are?

Ali

On Mon, Feb 16, 2009 at 2:19 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

Ali, Mitch, and Frank,

AH> If you've given a definition of River, and it is inadequate

 > when you encounter something as the Okavango River, ought it
 > not indicate that you only need to update your definition of
 > river? Isn't the whole point of defining something trying to
 > abstract the generalizable qualities / properties of the
 > object/entity under consideration? You can still have a

 > monotonic logic, you just need smart revision policies...

It's always possible to legislate a definition and to revise
the definition whenever you encounter an exception.  But the
point of Waismann's notion of 'open texture' is that there is
no stopping point.  If you arbitrarily choose a stopping point,
you will inevitably exclude unanticipated cases that are just
as reasonable as the ones you do include.

That is a serious problem for any legal system.  Any system
of laws has inevitable exceptions and borderline cases that
require a judge and jury to decide.

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