Re: Do I have a second? Overflow, New Motion

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

That's fine with me; or if you wish to continue this will be our motion:

-------------------------------------------

As described in the accompanying position paper, P1788 shall change the
existing Level 1 and Level 2 model to the three-tiered level structure as
described in Section 2. Specifically, this means the following:

   -- The "mathematical intervals" at Level 1 are defined to be the classic
set of nonempty, closed and bounded intervals; this is the level of
"mathematical regularity" (MR) for interval arithmetic. The FTIA, infimum,
supremum, midpoint and radius are all defined as in Section 2.1.

   -- In Level 1a, FTIA is extended to unbounded intervals and the empty
set according to (4) and (5); this is the level of "algebraic closure" (AC)
for interval arithmetic. More specifically, an unbounded interval is
interpreted as a family of intervals parameterized (virtually) by an
overflow threshold, as defined and explained in Section 2.2.

   -- Level 2 is defined as in Section 2.3; this is the level of "interval
datums." The maximal real element of each interval datum format defines the
concrete value of each corresponding overflow threshold at Level 1a.

   -- All of the "infinities" in the current model are changed to
"overflow", i.e., lower-case omega.

   -- The midpoint operation is defined at Level 1a and Level 2 for all
nonempty intervals as a real number (we suggest something similar to what is
discussed in Section 3.2, but we leave the actual definition for a future
motion); the midpoint of an empty interval is left to a future motion.

-------------------------------------------

Sincerely,

Nate

P.S. One of our engineers found a type-o (the natural domain D_f of a real
function should be a "subset of" R^n, not an "element of"), so I attach a
corrected version.



----- Original Message ----- 
From: "Ralph Baker Kearfott" <rbk@xxxxxxxxxxxx>
To: "Michel Hack" <mhack@xxxxxxx>
Cc: "stds-1788" <stds-1788@xxxxxxxxxxxxxxxxx>
Sent: Thursday, May 03, 2012 3:47 PM
Subject: Re: Do I have a second? Overflow, New Motion


> OK, I guess that's reasonable,  if that's OK with Nate.
>
> Baker
>
> On 05/02/2012 01:18 PM, Michel Hack wrote:
> > As Baker's P.S. indicates, there is as yet no actual motion on
> > the table, so I don't understand what a "second" would be about!
> >
> > Nate's position paper is well-written btw, and I will post a few
> > comments soon.  But at this point it is just a position paper,
> > and we don't need a motion to put this into the public list of
> > position papers.  (It may become the Rationale for an upcoming
> > motion, of course.)
> >
> > Michel.
> > ---Sent: 2012-05-02 18:23:52 UTC
>
>
> --
>
> ---------------------------------------------------------------
> Ralph 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
> ---------------------------------------------------------------

Attachment: overflow.pdf
Description: Adobe PDF document