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Motion P1788/M0035.01:OverflowBeforeUnbounded -- discussion period begins

P-1788:

Since Motion 35 has been made by Nate Hayes and
seconded by Svetoslav Markov, the discussion period now
begins, and will end after Saturday, May 26, 2012.
I append the motion, and I attach the corresponding
paper giving the rationale.

Discussion on this motion will proceed according to the rules for
position papers.

Juergen:  Please place the motion and associated information
           in the appropriate place on the web page, as
           you have aptly done in the past.

Acting secretary:  Please record the transaction in the minutes.

As usual, please contact me if you need the password to the private
area of the P-1788 web site.

Best regards,

Baker (acting as chair, P-1788)


On 05/03/2012 07:00 PM, Nate Hayes wrote:


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.

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--

---------------------------------------------------------------
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
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Attachment: overflow.pdf
Description: Adobe PDF document