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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 1 Aug 2007 13:45:00 -0500
Message-id: <p06230902c2d68327c984@[]>
>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!"    (01)

And such a reaction is simply a misunderstanding, or perhaps an 
example of the characteristically American intellectual weakness 
called math-phobia. The set D can *be* a set of horses. Sets can be 
sets of anything. To say that the universe is a set is, literally, to 
say nothing whatever about what kinds of thing are in the universe, 
since (to repeat, though it bears repetition) a set can be a set of 
anything. That is precisely why model theory is so general as a 
semantic theory: it imposes no conditions *at all* on the nature of 
the things in the universe of discourse (other than that there are 
some of them, i.e. that the universe is not empty.)    (02)

>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.    (03)

Quite.    (04)

>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.    (05)

Quite. And to emphasize the rather odd use of the "model" 
terminology, this can be precisely re-phrased using the language of 
model theory by saying that both the model (in your sense above) and 
the real bridge are models (in the sense of model theory) of the 
equations, i.e. they are both relational 'worlds' that make the 
equations true.    (06)

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