# Re: [ontolog-forum] Current Semantic Web Layer Cake

From: Kathryn Blackmond Laskey <klaskey@gmu.edu>
Date: Wed, 01 Aug 2007 12:26:40 -0400
To: "[ontolog-forum] " <ontolog-forum@ontolog.cim3.net>
Cc: SW-forum <semantic-web@w3.org>
Message-id: <p06110405c2d65f54795e@[129.174.89.24]>
```Chris,

Your remark hearkens back to our discussion of what an ontology is
really about.

Model theoretic semantics says there is a domain D, which is a set,
and the objects, attributes and relationships defined in the ontology
refer to elements of, functions defined on, and subsets of this set D.

Many people feel this is way too abstract.  "But my ontology of horse
racing is about horses!!!  And jockeys and racetracks and betting
odds!  It emphatically is not about sets!"

We have had many heated discussions in this forum about whether
sentences in a biology textbook are about cells in the world or about
cells in a biological model of cells.  Jon suggested maybe they are
about both. That they can be about both is why engineering works!
It's why you can get up in the morning expecting your car to start,
the traffic lights to work, and the bridge not to collapse.

Engineers build a computer model of the bridge because there is a
great deal less loss of life and a much greater return on the dollar
from building computer simulations of cars driving across the bridge
and testing out various designs before setting the cement mixers and
beam layers to work.  We have learned in the school of hard knocks
that it is not a good idea to try out a bridge design by building it
and seeing whether it collapses under the load we put on it.

The equations the engineer programs into the simulation are about the
bridge model.  The engineer uses this fact to debug her simulation
and to test out various bridge designs by changing aspects of the
computer model. Because the equations are about the model, she can be
confident that changes in parameters of the model will result in
changes to the simulation output that accurately reflect her
intentions.  The equations are also about the actual bridge that is
going to be built.  Well, to be precise, the equations for the
discarded designs are about bridges she is considering building, and
the ones in the final design are about the bridge she plans to build,
but they will probably be modified somewhat by the time concrete is
poured.  In any case, because the equations are about both the bridge
model and the bridge, she can be confident (if it's a good model)
that predictions she makes on the basis of the simulation (such as
how much load the bridge can bear) will be true of the actual bridge
when it is built.  Thus, the fact that the assertions are true both
of the bridge model and the real bridge is the reason that engineers
can design bridges that can carry the traffic they are designed to
carry.  Our lives depend on this vital characteristic of models.

Some of the very same equations could, under different circumstances,
be used to model airplanes or electrical circuits or pollution in the
Chesapeake Bay.  That is the beauty of mathematics.  There are common
mathematical structures that are generally useful across a wide
variety of problem domains.  It is also the bane of students who are
interested in nursing or robotics or baseball, but have to sit
through a generic mathematics course that either uses almost no
examples or requires them to do problems about applications about
which they don't care a hoot.  This gives rise to frequent turf wars
between the math department, which is sure the psychology department
or the nursing school is incapable of teaching math the way it ought
to be taught, and the nursing school or psychology department, which
complains that the mathematicians lose the students by teaching
abstractions divorced from applications that would hold the students'
interest.  Probably, both are right -- that's part of the price we
pay for mass-producing education.  But that's a different soap-box.

Kathy

At 10:31 AM -0500 8/1/07, Christopher Menzel wrote:
>  > The scopes and subject matters of Ontology and Logic shouldn't be
>>  mixed.
>>  The real semantics or meanings of any symbolism or notation is
>  > defined by
>>  ontology;
>
>Silly me, I've been thinking that the real semantics of any symbolism
>is defined by, you know, its *semantics*.
>
>-chris
>
>
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```
Received on Wednesday, 1 August 2007 16:31:44 UTC

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