>Chris,
>
> 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)
>
>Chuck
>
>
>Charles Turnitsa
>Project Scientist
>Virginia Modeling, Analysis & Simulation Center
>Old Dominion University Research Foundation
>(757) 638-6315 (voice)
>cturnits@xxxxxxx
>
>
>
>
> Christopher
> Menzel
> <cmenzel@xxxxxxxx To
> > "[ontolog-forum] "
> Sent by: <ontolog-forum@xxxxxxxxxxxxxxxx>
> ontolog-forum-bou cc
> nces@xxxxxxxxxxxx
> .net Subject
> 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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