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Re: [ontology-summit] ontology as logical theory?

To: <cmenzel@xxxxxxxx>, <ontology-summit@xxxxxxxxxxxxxxxx>
From: <matthew.west@xxxxxxxxx>
Date: Mon, 29 Jan 2007 13:31:17 -0000
Message-id: <808637A57BC3454FA660801A3995FA8F04A2C6F2@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Dear Chris,    (01)

See below.    (02)

Regards    (03)

Matthew    (04)

> On Mon, Jan 29, 2007 at 10:06:19AM -0000, 
> matthew.west@xxxxxxxxx wrote:
> > Dear Chris,
> > > > Ok, but then why use the term "ontology"? If you are right, 
> > > > let's just use the term "logical theory"?
> > > 
> > > I don't think that would follow.  For one thing, I'm only 
> proposing  
> > > that "logical theory" is the only viable *definition* of "formal  
> > > ontology".  
> > 
> > MW: I think I would want to add to an ontology being a "logical
> > theory".  I think I would at least want to say that "a 
> formal ontology
> > is a logical theory with an intended interpretation".
> 
> Well, my whole point is that this adds nothing in the way of formal
> definition.  It's an informal gloss that helps to clarify what
> ontologies are for and how they should be understood, but it 
> is useless
> when it comes to things like sharing and reasoning upon information in
> any formal sense.  I can only share and reason upon axioms and other
> formal specifications.  Hence (or so sez I) notions like "intended
> interpretation" shouldn't be part of any formal definition.    (05)

MW: So how about:
T= Logical Theory
I= Intended interpretation
O= Ontology    (06)

For all x and x is an O
Then x is a T and x has an I.    (07)

Is that not formal? If not what is?
> 
> > MW: I might also want to drop "logical". I accept that most people
> > here are developing logical theories, but if I understand it
> > correctly, there is at least one enterprise to develop an ontology
> > based on Category Theory rather than logic.
> 
> Category theory can most definitely be formalized as a logical theory.    (08)

MW: The question is whether you HAVE to formalize category theory as a 
logical theory to develop an ontology (I don't pretend I know the 
answer).
> 
>  
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