Hi Chris, (01)
Quoting Chris Menzel <cmenzel@xxxxxxxx>: (02)
> 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. (03)
As I mentioned in another thread, I agree with you -- a formal ontology
should be a set of sentences in a language with a model theory.
Anything beyond the set of sentences is extralogical notation
that may or may not be needed to correctly and completely interpret
the terms in the ontology's vocabulary.
A "formal specification" is something that is
typically written in mathematical english (e.g. a specification of the
class of mathematical structures that are isomorphic to models of the axioms).
If an ontology is not complete with respect to this specification, then the
formal specification becomes an extralogical mechanism that is required
to communicate the intended interpretation of the terms.
In such a case, is the ontology still formal? (04)
>
> > 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. (05)
This is a good point -- if we define a formal ontology to be a set of sentences
in a language with a model theory, then an ontology based on Category Theory
needs to use some language with a specific syntax, otherwise Category Theory
is an elaborate form of documentation and the ontology is effectively informal
(not that there's anything wrong with that). (06)
- michael (07)
_________________________________________________________________
Msg Archives: http://ontolog.cim3.net/forum/ontology-summit/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontology-summit/
Unsubscribe: mailto:ontology-summit-leave@xxxxxxxxxxxxxxxx
Community Files: http://ontolog.cim3.net/file/work/OntologySummit2007/
Community Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2007
Community Portal: http://ontolog.cim3.net/ (08)
|