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Re: [ontolog-forum] Visual Complexity

To: Charles D Turnitsa <CTurnits@xxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 7 Feb 2007 16:26:56 -0600
Message-id: <p06230916c1f000090c5c@[]>
>There is a common usage of "model" in which what
>I am here calling the ontology is itself thought
>of as a model of reality, in which many aspects
>are left out, which is simplified and perhaps
>inaccurate, but useful for some purpose, enabling
>inferences to be made that can then be
>interpreted as applying (perhaps with some
>necessary care) to reality. The word "model" used
>in this way is then almost an exact inverse of
>its sense in the Tarskian semantic theory:
>model-2 refers to the descriptive entity (the
>ontology or pragmatic formal description) whose
>application to reality is captured by a semantic
>theory which refers to the world described by the
>model-2, and calls this world, which it models
>(-2), it's model (-1).    (01)

Hmm, re-reading the above, I can't understand it myself. Let me try again.    (02)

Take the example of an ontology describing faculty relationships, and 
take TAMU (Chris Menzels' home institution) as the reality being 
described. Now, obviously there is more to TAMU than just faculty and 
their relationships: there are students, and buildings, and history 
and football and many other things. So one might reasonably say that 
this ontology, applied to TAMU, is a simplified 'model' of the 
reality, in the model-2 sense. Now, is that model accurate (as far as 
it goes: we all agree it is incomplete)? Since this model-2 consists 
of formal sentences, we can pose this question more precisely using a 
semantic theory: it is accurate when all the sentences are true of 
the reality being described. Tarskian "model theory" makes this 
intuition mathematically precise, by identifying the needed 
structures in the reality being described that are just enough to 
determine the truth or otherwise of the sentences. Suppose indeed we 
apply this theory to this example; then the model-2 is accurate just 
when the actual TAMU has a structure which makes it into a model-1 of 
the ontology, i.e. of the model-2. So which is the model of the 
other? In your sense, accuracy is described by saying that the 
ontology is indeed a 'model' of TAMU, using sense 2. In Tarskian 
terminology, the very same condition is described by saying that TAMU 
is a 'model' of the ontology, using sense 1.    (03)

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