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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 15:31:01 -0600
Message-id: <p06230911c1efef411d87@[]>
>  I beg to differ with you on the point you are making to John.  A model
>(any model) is necessarily some sort of abstraction of the thing (referent?
>real world? imagined ideal?) that it is representing.  In this way, it is
>an "approximation" of the thing that it is modeling.  If this were not so,
>then the model would be equal to the original, which is not the intent of
>modeling.    (01)

Chuck, I think you are being misled by the 
(technical, and unfortunate) use of the word 
"model" in "model theory". A better word (and 
technically more correct) is "interpretation".    (02)

This is in the context of a semantic theory of 
formalized languages (in fact, of 
representational schemes in general) which 
describes the relationship between sentences (in 
this forum, sentences of an ontology) and the 
worlds they could describe, by thinking of the 
latter as relational structures over a nonempty 
universe, and defining a satisfaction 
relationship between these structures and the 
sentences. Without going into technical details 
too far, the core idea is to identify the 
*minimal* amount of structure in the world being 
described which is sufficient to give any 
sentence in the language a precise truth-value; 
and the relational structure is this minimal 
structural description. Unfortunately, the term 
"model" was adopted early in the technical 
literature to refer to such a structures when it 
satisfies (makes true) an ontology, hence the 
overarching name "model theory". Let me call this 
model-1. But this usage does not refer to the 
sense of "model" usually associated with the 
terminology of "modelling", "simplified model", 
"model airplane", etc. (and, I suspect, in the 
title of your Center); let me call that model-2. 
It refers here only to a relational structure of 
a certain kind; that is, to a set with a set of 
relations defined over it. The semantic theory 
achieves its generality in large part by NOT 
specifying what these sets are sets of. In 
particular, they can be sets of real things, 
rather than simplified 'models' of real things.    (03)

BTW, the things in the semantic 
'model'/interpretations do not themselves have 
referents. They ARE the referents of the terms 
(names) in the sentences being interpreted. And 
to repeat, this is a semantic theory of how 
ontologies refer to whatever it is that they 
indeed refer to. So, for example, if an ontology 
claims to describe the reporting relationships 
among faculty in a university, a good way to 
mentally test it is to think of an *actual* 
university and its *actual* faculty, interpret 
the sentences of the ontology as referring to 
them, and seeing if they come out true or not, 
using the semantic theory. This seems 
unproblematic to me, even obvious: yet if what 
John says about model theory were true, it would 
be be a category error, and completely 
impossible. We would have to first build a model 
(your sense) of the university, think about the 
ontology with reference to the model, and then 
separately, and without using logic, worry about 
whether or not the model were accurate.    (04)

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).    (05)

Pat    (06)

>Charles Turnitsa
>Project Scientist
>Virginia Modeling, Analysis & Simulation Center
>Old Dominion University Research Foundation
>(757) 638-6315 (voice)
>              Christopher                                                  
>              Menzel                                                       
>              <cmenzel@xxxxxxxx                                          To
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>                                        Re: [ontolog-forum] Visual         
>                                        Complexity                         
>              02/07/07 01:58 PM                                            
>              Please respond to                                            
>              "[ontolog-forum]                                             
>                      "                                                    
>              <ontolog-forum@on                                            
>               tolog.cim3.net>                                             
>(Embedded image moved to file: pic07058.gif)
>John, it is your use of "approximation" to characterize ALL models
>without exception here that I object to.  Of course, depending on
>what it in the world one is trying to represent, a model *might*
>necessarily be an approximation, especially if one is modeling
>physical phenomena that are inherently vague or (in effect)
>infinitely complex and hence which simply cannot be represented with
>100% accuracy.  Consider, e.g., modeling a stochastic process or
>fluid flow by means of probability theory or differential equations.
>However, many physical situations involve, *at a desired level of
>granularity*, NO vagueness and NO intractable complexity at all, as
>in my previous example involving faculty and administrators at Texas
>A&M.  Many ontologies involve this kind of sharply delineated,
>unambiguously representable information.  Your diagram above belies
>this fact and suggests that models are always in some way false or
>inaccurate.  It just ain't so.
>Chris Menzel
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>    (07)

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