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

To: Charles D Turnitsa <CTurnits@xxxxxxx>, Chris Menzel <chris.menzel@xxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 9 Feb 2007 13:59:15 -0600
Message-id: <p06230908c1f2811341d7@[]>
>I am going to break my own plea to drop the subject by asking Chris if both
>of these senses - the Model of an airplane, as well as a Tarskian Model,
>exhibit some "lossy"-ness?
>Model, now matter how it is used, seems to be some sort of extended
>implementation from an original (whether it is an abstraction, like a
>mathematical, computer, or physical model - or some instantiation of a
>series of axioms).  In doing this extension, something is lost from the
>original (in the case of the model plane, it is reduced in size,
>functionality, and fidelity - in the case of a Tarskian model it is reduced
>from an ideal state explained in axioms to something that can change and
>lose some of its adherence to those axioms).
>But it might be better to not make this observation . . .    (01)

:-)    (02)

In fact, in the case of the relationship between 
a Tarskian 'model' (ie satisfying interpretation; 
I will use scare quotes for this sense from now 
on, when I am obliged to use it) and the axioms 
it 'models', this is indeed backwards. The 
'model' can be vastly more complicated than the 
structure defined by the axioms themselves: it 
can contain arbitrary amounts of irrelevant 
'waste' structure which does not affect the truth 
of the axioms. So for example the axioms might 
require only a finite universe, but have 'models' 
in which the universe is uncountably infinite. 
Any possibility not actually ruled out by the 
axioms explicitly is allowed to be present in 
such a 'model'. 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.    (03)

Pat    (04)

>ontolog-forum-bounces@xxxxxxxxxxxxxxxx wrote on 02/09/2007 02:01:57 PM:
>>  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?
>>  -chris
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