On Wed, May 31, 2006 at 07:05:17PM -0400, John Sowa wrote:
> Chris,
>
> Although I'm sure that we agree on how people use ordinary
> language, I have been trying to emphasize that there is a
> continuum between the informal and the formal.
>
> CM> Well, as far as actual ontology construction goes, by my
> > lights model theory is actually *prior* in the sense that
> > it should have been worked out as part of the KR system
> > one is using.
>
> Yes, but all that does it to demonstrate the the KR system
> is consistent. (01)
Actually it doesn't ;-) -- or needn't, anyway. Granted, the model
theory for FOL and related systems almost trivially guarantees
consistency, as all you need to show is that every logical axiom is true
in any nonempty domain and that the rules of inference are sound. But
when the model theory for a language requires structures that can be
quite complex -- e.g., the model theory for OWL Full -- one might not be
able to tell just by looking at it that there *are* any such structures;
proof of consistency in these cases might be highly nontrivial.
(Indeed, I'm not sure anyone has demonstrated that OWL Full actually has
any models, its rigorous model theory notwithstanding.) (02)
> That's good to know, but it doesn't ensure that what people say so
> consistently has any relationship to what they intended to say. (03)
Well, of course. I hope you didn't hear me suggesting anything to the
contrary. (04)
> CM> An actual ontologist will then use the KR language
> > directly and generally having nothing whatever to do with
> > its model theory in practice, any more than an engineer
> > will have anything to do with the mathematical underpinnings
> > of her calculator.
>
> This gets into the question of how and whether the mental
> models or the engineering models are related to the Tarski-
> style models. (05)
Interesting, for sure, but not really relevant to the points *I* was
making (which is not to say: not relevant überhaupt ;-) . (06)
-chris (07)
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