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Re: [ontolog-forum] Conceptual Schema, ISO TR9007 (1987) and Ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 5 Jan 2011 14:13:48 -0600
Message-id: <AF6E4769-5A28-4D45-9A70-106389181740@xxxxxxxx>
On Jan 5, 2011, at 12:02 PM, Edward Barkmeyer wrote:
> I think we have an important difference in terminology.
> Sjir wrote this definition (from TR9007):
>> *Conceptual schema*
>> *A consistent collection of sentences expressing the necessary propositions *
>> *that hold for a universe of discourse.
>> *
> Given that definition, I would write:
> Ontology:  A consistent collection of sentences expressing propositions that 
>hold for a universe of discourse in a language supported by automated 
>reasoning tools.
> The distinction between 'necessary proposition that holds' and 'proposition 
>that holds' is an alethic or non-monotonic logic concern....    (01)

I'm not sure I entirely understand Ed's point here, but I agree that adding the 
qualifier "necessary" is asking for trouble.  I *think* the force in Sjir's 
definition is simply that the sentences in the ontology are required to hold in 
the domain in question. In that case, I think it is better simply to say that 
they are *axiomatic* for the domain, that is, they are taken as given; or, 
semantically put, that there are no models of the domain in which they are 
false.    (02)

One other concern here is the qualifier "consistent" in both Sjir's and Ed's 
definitions. Consistency per se is undecidable in first-order logic.  Hence, if 
you insist that a collection of sentences must be consistent in order to count 
as an ontology, it follows that it will in general be undecidable whether or 
not a purported ontology actually *is* an ontology.  My recommendation would be 
simply to eliminate the qualifier. I don't see any reason why an inconsistent 
set of sentences should not count as an ontology; it just might not be a very 
good or useful one.  And, by the same token, if the inconsistency is "buried" 
deeply enough, the ontology might still prove to be very useful indeed.    (03)

Chris Menzel    (04)

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