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

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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