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Re: [ontolog-forum] Ontological correctness

To: Michael Gruninger <mudcat@xxxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 1 Feb 2007 11:04:28 -0600
Message-id: <p06230904c1e7cb556565@[]>
Michael Gruninger <mudcat@xxxxxxxxxxxxxxx> wrote:
>Hi Chris,
>Quoting Christopher Menzel <cmenzel@xxxxxxxx>:
>>  On 31 Jan, at 10:44 , Pat Hayes wrote:
>>  >> Hi Everyone,
>>  >>
>>  >> ... I do think, though, that some
>>  >> measure of correction of logical constructions is probably also
>>  > necessary,
>>  >
>>  > Amen to that. But it is very hard to see how this is to be done. I
>>  > REALLY wish there were a nontrivial and useful notion of how to
>>  > measure 'correctness' of an ontology. It is not enough to just say,
>>  > it is correct if it "fits the facts" in some sense, since ontologies
>>  > may be based on very different, possibly mutually contradictory,
>>  > conceptualizations, and yet both fit the facts perfectly well.
>>  Yes, exactly.  And even the idea that there are theory/ontology-
>>  independent "facts" relative to which an ontology can be deemed
>>  correct is a HIGHLY dubious notion.
>I'm a little puzzled by these comments.
>Although there may be no absolute notion of correctness, there are
>several possible relative notions of the correctness of an ontology.
>First, an ontology may be correct with respect to the intended interpretations
>of its nonlogical lexicon. The intended interpretations are specified as some
>class of structures, and the ontology is correct with respect to these
>if every one of the intended structures is a model of the axioms of the
>An ontology will be complete with respect to these intended structures if all
>of the models of the axioms are isomorphic (or 
>possibly elementarily equivalent)
>to the intended structures.    (01)

I agree this is very nice definition of 
correctness and completeness, the straight 
model-theoretic view. Unfortunately, though, it 
doesn't seem (to me) to be very useful in 
practice, for several reasons. First, this kind 
of completeness is almost never obtainable, 
because of Goedel: you can't even get it for 
arithmetic. Second, even if we abandon 
completeness, its about as hard (harder?) to 
describe the class of intended models as it is to 
state the facts using the formal language itself. 
Take an example, an OWL ontology to keep things 
simple, say the JPL 'features' ontology in the 
SWEET series. If you read it its fairly clear 
what it is supposed to be 'about' in some sense 
(atmospheric phenomena, like hurricanes and 
weather fronts). Is it correct? I'm not sure, not 
knowing enough about the topic: but checking its 
models against an weatherman's intuitions doesn't 
seem like a more productive way to answer the 
question than to ask the weatherman to learn OWL 
and then just read the damn thing. What is gained 
here by talking about 'intended structures'? 
Suppose someone else makes a weather ontology 
which treats a Sweet:phenomena class as an OWL 
property rather than a class. Which is "right"? 
The relational structrures will look very 
different (though there are of course mappings 
between them) but they can both be 'fitted' onto 
the actual weather, one presumes, but 'fitted' 
differently.    (02)

In a nutshell: reality isn't a relational 
structure. One can hallucinate a relational 
structure onto it in many different ways. Which 
of *these* is "right"? Does the question even 
make sense?    (03)

Pat    (04)

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