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Re: P1788: Our first formal motion has entered its discussion period

Dear colleagues:

Concerning StandardizedIntervalNotation I would like to make two remarks:
(in this mail R stand for the set of real numbers and I for an interval set.) 

1. Of course basic to all considerations is the set of extended reals R*.
Interval arithmetic deals with closed and connected sets of real numbers (and nothing else). If an interval is bounded it is written as [a, b] with a, b elements of R. If it is unbounded it is written as (-oo, a] or [b, +oo) with a, b elements of R or (-oo, +oo) where the parantheses indicate that the bounds -oo and +oo are not elements of the interval. The set of all such intervals should be denoted by IR. Then 
{IR, +, -, *, /} is an exception free calculus.
So what do the proposed notations like IR* or *IR^n really mean? If we really consider intervals of IR* we would have to allow intervals like [-oo,-oo] and [+oo, +oo]. To be complete we would then have to define operations like [+oo, +oo] - [+oo, +oo] and so on. This opens a nightmare and brings all the IEEE 754 exceptions back into interval arithmetic where we do not need these.
2. Of course I am aware that the bounds of an interval a frequently are denoted by 'a\underline' and 'a\overline'. But I would plead alternatively also to allow the notation a_1 and a_2 for the bounds of the interval a. The notation with an index can easily be written in any typing system. This are the coordinates of the interval in the two dimensional plane and in a program this is usually the notation of the interval anyhow. 
.
Best whishes
Ulrich Kulisch




Ralph Baker Kearfott schrieb:

IEEE P1788 working group members,

Vladik Kreinovich has seconded our first formal motion (appended).
Therefore, consistent with 11.2 of our Policies and Procedures, we are
entering our three week discussion period.  Thus, the discussion period
ends, and voting begins (if no modifications have been made) after
January 21.

We will refer to this motion as "motion 1," to eliminate confusion
in case more than one motion is simultaneously being processed.
(Mr. Secretary:  I will assign numbers to motions in the sequence
in which they are put forward.)

Best regards,

Baker

P.S. Best wishes to all in the new year.

On 12/31/2008 1:40 AM, Kreinovich, Vladik wrote:

I am seconding it.

------------------------------------------------------------------------
*From:* stds-1788@xxxxxxxx on behalf of R. Baker Kearfott
*Sent:* ¨. 29/12/2551 5:48
*To:* stds-1788
*Subject:* P1788: Our first formal motion enclosed

IEEE P1788 members:

John Pryce, the technical editor for the final document we
will submit to our Sponsor, has put forth our first formal
motion, which I append, along with the rationale. To advance
this motion, I first need a second from someone. After that,
we will have the three-week discussion period, then the
3-week voting period, according to 11.2 of our policies and
procedures document.

Please:

1. Read the appended motion.

2. Proffer a "second" directly to the list, if you agree with
the motion.

Sincerely,

Ralph Baker Kearfott
(acting chair, P1788)
===============================================================
=====
Motion P1788/M0001.01_Proposer: J D Pryce
=====
The P1788 standard will initially use the notation proposed in
the paper "Standardized notation in interval analysis" by R.B.
Kearfott, M.T. Nakao, A. Neumaier, S.M. Rump, S.P. Shary, and P.
van Hentenryck, available at
http://www.mat.univie.ac.at/~neum/papers.html

This notation will be open to amendment after sufficient
experience of using it.

The standard will include a copy of the above paper (as possibly
amended) in an appendix.
=====

==Rationale==
As that paper itself says, interval notation is somewhat
fragmented at present. Here is the view of some experts who have
thought hard about this issue. We can do great service to
interval computation for many years ahead by helping to
disseminate their recommended practice, and following it
ourselves.

Rather than spend preliminary time debating whether we want to
amend the proposed standard notation, I think it is more
fruitful for us all to accept it as it is for now, and accept
the discipline of following its notation for future position
papers. In due course, either we are satisfied we can accept it
permanently, or some of us are so annoyed by its perceived
deficiencies that we have some constructive changes to make.

The motion does not say that all position papers SHALL use this
notation. I just strongly recommend this, so we get experience
of using it.
=====


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R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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