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Re: [ontolog-forum] Logic, Datalog and SQL

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Fri, 09 Feb 2007 18:57:20 -0500
Message-id: <45CD0A60.2080302@xxxxxxxx>

Pat Hayes wrote:
>> On the other hand, in order to
>>satisfy the axioms, the 'model' must contain all
>>the structure that these axioms explicitly
>>describe, so in a very precise sense it cannot be
>>of lower fidelity than the axioms, but it can
>>well be of much higher fidelity.    (01)

It is entirely possible to have a Tarski model that is completely consistent 
with the axiom set but only exemplifies half the concepts in it.  After all, 
the model need only exemplify concepts that have axiomatic or provable 
existence requirements.  The axiom set, especially for would-be "real world" 
models often describes things that can, but need not, appear in the model.  So 
the model is of "higher fidelity" perhaps, but of narrower scope than the 
axiom set.    (02)

On the basis of significantly less expertise than Pat, Chris and John, I would 
have said we are comparing apples and oranges, which I took to be Pat's 
original point.    (03)

With respect to Petri's three types of models, I would not look for a unifying 
theory, either.  I would characterize a prototype as a presumed Tarski model 
that will test a set of axioms we haven't yet quite figured out.  And in most 
cases, a prototype does contain exactly the kind of "waste" that Pat (or 
Chris?, I've lost track) referred to, which makes it difficult to find the 
intended axiom set.  One of my former mentors, however, characterized 
"prototype" as the ultimate dicto simpliciter. ;-)    (04)

-Ed    (05)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (06)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (07)

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