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

To: Christopher Menzel <cmenzel@xxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 9 Feb 2007 14:31:05 -0600
Message-id: <p06230909c1f2883bef5a@[]>
>  >> On Feb 9, 2007, at 12:26 PM, Pat Hayes wrote:
>>>>   ...I think (as I said in
>>>>   an email response a few days ago) that the usages
>>>>   of "model" in "model theory" and "modelling"
>>>>   (respectively realization and prototype) are at
>>>>   best unrelated, and at worst almost directly
>>>>   opposite in meaning.
>>>  I guess I don't see that, Pat.  Don't, say, a physical model of a
>>>  Boeing 777 and my Tarskian model of the faculty and administration at
>>>  Texas A&M both represent (hence, in some sense, "model") relevant
>>>  structural features of complex real-world things?
>>  Well, you can put it that way, as John prefers, but I think its 
>>  misleading. Why isn't your Tarskian model actually part of the 
>>  (real) faculty and administration at TAMU? Or perhaps better, why 
>>  could it not be?
>Well, it *is* a set, and (extentions of) the properties of and 
>relations among the elements of the domain are just sets of n-
>tuples.  I don't see how those are in any robust sense *part* of 
>TAMU.    (01)

The relational extensions might not be 'part' of 
TAMU in any mereological sense, no. But the 
relational extensions aren't in the universe of 
discourse, right?    (02)

>  Furthermore, I might choose to represent faculty members by, 
>say, their University ID numbers in my model; even still, the model 
>is a representation of the indended structure.    (03)

Yes to the latter point, of course: one CAN make 
Tarskian models out of anything. But then it also 
follows that elements of the Tarski universe can 
be parts of TAMU, seems to me. There is no reason 
why we have to say that a relational structure 
must be made up of Platonic relation-stuff as 
opposed to real stuff.    (04)

If I am looking at an axiom like    (05)

(subClassOf Dean Faculty)    (06)

and 'testing' it by asking myself mental 
questions such as, "can I think of a TAMU Dean 
who isn't a member of the TAMU Faculty?" , then 
what I'm thinking about are the actual pieces of 
TAMU, not pieces of a model of TAMU.    (07)

Pat    (08)

>>  The oppositeness happens when we speak not of a physical model of 
>>  the plane, but a symbolic model in a computer, which amounts to a 
>>  large complicated description of the plane. Which way does the 
>>  modelling relationship go now? This is a simulation-model of the 
>>  real physical plane because it *describes* that plane accurately, 
>>  i.e. because the real physical plane is a Tarski-realization-model 
>>  of it. The 'model of' arrows in this picture are now pointing in 
>>  opposite directions; in fact, they are at opposite ends of the very 
>>  same arc.
>Point taken.
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