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Dear Juergen,
Dear prof Kulisch,
To Juergen: By:
" I see the danger that every system of interval arithmetic claims to be
1788 conforming, at least as a special flavor."
it seems you mean the "systems of interval arithmetic" mentioned
in the letter prof Kulisch: " Real intervals, set-based intervals, standard
intervals, classical intervals, common intervals, conventional
intervals, wrap around intervals, Kaucher and modal intervals,
and so on."
I have a question:
How can I learn about all the enlisted types of intervals
with all the different "flavours" between them? Which are
the remaining "so on" intervals ?
My comments. In the above list I see only two main types of intervals:
--- the usual intervals (under different names: "Real intervals, set-based
intervals, standard intervals, classical intervals, common intervals,
conventional intervals, wrap around intervals (?)", and
--- "Kaucher and modal intervals", (which is the same)
Putting Kaucher/modal intervals in such a long list of "intervals"
makes me think that something in your letters is not connected
just to science.
Juergen, you are an author of a paper based on Kaucher arithmetic:
Wolff v. Gudenberg, J., Determination of Minimum Sets of the Set of
Zeros of a Function, Computing 24, 1980, 203–212.
and you know very well the unique role of Kaucher arithmetic.
What is the point of speaking about "every system of interval arithmetic"?
Which "systems of interval arithmetic" do you have in mind? Which
are the systems that you can put on the same plane as Kaucher's one?
Kaucher interval arithmetic is the unique possible
group extension perserving inclusion - the main
interval property. In the same way as real arithmetic is the
unique possible extension to the arithmetic over nonnegative
numbers perserving the distributive law.
Taking into account that many people in this forum do not know
well-enough this topic, makes me to conclude that your mentioning the
"many competing interval systems" is sort of obfuscation tactics, aiming to
devaluate the special role of Kaucher arithmetic.
I hope that this is not the case. I hope that a primary aim of this
forum is first to educate us in the various aspects of interval arithmetic
and then to take correct decisions.
I urge the participants who know too little algebra to learn a bit more
about the relation between a monoid and a group, in particular between
(\R^+, +) and (\R, +) and to think why the IEEE standard mentions
real numbers (nonnegative plus negative), despite the fact that it
actually specifies operations on signed-magnitute reals, that is on
nonnegative numbers.
The relation between usual interval arithmetic and Kaucher arithmetic
is precisely the same. Kaucher (interval) arithmetic is for standard (interval)
arithmetic the same as real (number) arithmetic is for nonnegative numbers
arithmetic.
Best regards,
Svetoslav
On 30 Jun 2012 at 14:49, J"urgen Wolff von Gudenberg wrote:
Date sent: Sat, 30 Jun 2012 14:49:56 +0200
From: J"urgen Wolff von Gudenberg <wolff@xxxxxxxxxxxxxxx
WUERZBURG.DE>
To: John Pryce <j.d.pryce@xxxxxxxxxxxx>,
stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: dangerous motion 35
> John, P1788
> It is indeed an interesting task to analyze the relations of various
> interval flavors, how they include each other, define commonly many
> operations but also show contradictions in others.
> This discussion should not be performed under the framework of P1788,
> because firsty we do not have the time and secondly
> I see the danger that every system of interval arithmetic claims to be
> 1788 conforming, at least as a special flavor.
> I think P1788 will only be accepted if it is presented by a clear and
> unique formulation of level 1 and a mapping to machine intervals in level 2
> furthermore a simple and reproducible specificaton of operations in
> level 3 will enhance the dissemination
>
> Juergen
> --
> o Prof. Dr. Juergen Wolff von Gudenberg, Lehrstuhl fuer
> Informatik II
> / \ Universitaet Wuerzburg, Am Hubland, D-97074 Wuerzburg
> InfoII o Tel.: +49 931 / 31 86602
> / \ Uni E-Mail: wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> o o Wuerzburg
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