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Re: [ontolog-forum] Logic, Datalog and SQL

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 9 Feb 2007 12:26:22 -0600
Message-id: <p06230900c1f269c8cc64@[]>
>I'd rather not stir up more debate on this topic, but I
>would like to say that one can make a good case for the
>claim that there is general notion of model that includes
>both as special cases.
>  > Oh, sure. But here you are using "model" in what I
>  > called the model-2 sense, right, rather than the Tarskian
>  > sense used in "model theory". Then this becomes the
>  > Korzybskian slogan that the map is not the territory:
>  > which is true, of course.
>In my 1984 book, I mentioned with approval an observation by
>Carl Adam Petri, of Petri-net fame.  At the end of this note
>is a copy of the passage in which I summarize Petri's point.
>I still believe there is an important core meaning of _model_
>that is common to these uses of the word, to the term "mental
>model", and to the Craik-Minsky notion of the brain as a
>machine for building models.    (01)

Ah, this may be the root of our longstanding 
difference of opinion here. I think (as I said in 
an email response a few days ago) that the usages 
of "model" in "model theory" and "modelling" 
(respectively realization and prototype) are at 
best unrelated, and at worst almost directly 
opposite in meaning. The trouble is that if you 
analyze the way that simulations work, they are 
often (usually) symbolic structures built of 
software. That is, the simulation-model consists 
of symbols. If you now apply Tarskian semantics 
to those symbolic structures, the Tarskian sense 
of 'model' - the realization-model - treats the 
first, simulation, model as the axioms and the 
world it describes as being a realization of it. 
This makes the world be the realization of the 
simulation, and now our wires are irremediably 
crossed. But I really think this is just a matter 
of crossed terminology, rather than anything 
deeper.    (02)

So I would urge that Petri got this wrong. There 
isn't a common basis here (well, there might be 
between 1 and 3, but not including 2); there is 
instead a regrettable but not uncommon clash 
between two different technical usages from 
different fields.    (03)

But let us agree, both having re-stated our views 
resoundingly, to not stir up any further debate 
on this, lest everyone except us leave the 
mailing list :-)    (04)

Pat    (05)

>  From J. F. Sowa (1984) _Conceptual Structures_, Addison-Wesley,
>Reading, MA, p. 20:
>The word _model_ has multiple meanings in engineering, logic, and common
>speech. Petri (1977) noted three different meanings in the phrases model
>of an airplane, model of an axiom system, and model farm:
>      * Simulation. A model airplane is a simplified system that
>simulates some significant characteristics of some other system in the
>real world or a possible world.
>      * Realization. A model for a set of axioms is a data structure for
>which those axioms are true. Consistent axioms may have many different
>models, but inconsistent axioms have no model.
>      * Prototype. A model farm is an ideal or standard for evaluating
>other less perfect farms or for designing new ones.
>Petri maintained that a common basis should be found for these three
>different ways of modeling.
>Petri, Carl Adam (1977) "Modelling as a communication discipline,"
>in H. Beilner & E. Gelenbe, eds., _Meaning, Modelling, and
>Evaluating Computer Systems_, North-Holland Publishing Co.,
>Amsterdam, pp. 435-449.
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>    (06)

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