[Inquiry] Re: Introduction to Inquiry Driven Systems

[Jon Awbrey]

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INT.  Discursive Note 1

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EW = Elijah Wright
JA = Jon Awbrey

JA: 3.  Finally, I plan to develop a theory of qualitative differential
        equations, implement methods for their computation and their
        solution, and then apply the resulting body of techniques
        to two kinds of recalcitrant problems:

EW: jon, can you clear up what you mean by "qualitative differential equations"?
    i'm not familiar with that particular framing ... i think i just need
    definitions and context for what you're intending.

This is based on a report that I wrote for my dissertation committee,
and so I had tried to soft-peddle one of my favorite phrase-turners,
with the end result of stepping all over the point of it.

If I had my druthers ...

There is what is known as the "qualitative theory of differential equations",
where you have have systems that are described by differential equations over
real number spaces, but you only want to know the qualitative shape and flow
of the dynamics.  I will get some refs later.

But say that you start out instead with "qualitative" or "logical" pictures
of static situations, as in venn diagrams, that is, in boolean coordinates,
and then you turn the time on, letting "particles" in the cells of the
venn diagram start moving around.  You the want to develop the logical
analogue of differential equations, a cute name for which would be
the "differential theory of qualitative equations".

Also known as "differential logic".
There is a bit of exposition here:

http://www.altheim.com/cs/
http://www.altheim.com/cs/zol.html
http://www.altheim.com/cs/difflogic.html
http://www.altheim.com/cs/cactus.html

But I'm going to be returning to this in more detail soon.

I also have a paper "Differential Logic and Dynamic Systems" that
I can send you.  About 700 kb in Word 95, or 1700 kb in Word 2000.

Jon

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