Level 1 description of decorations
Kreinovich, Vladik wrote:
[in: RE: Bare decorations (was ...level 2 datums)]
Maybe I am wrong, but the very fact that few people in the list jump into this discussion may be an indication that many of us are somewhat lost in the inter-relation between the purely math ideas and the technical details of IEEE implementations.
It may be a good idea to go back to "Level 1" (purely mathematical) description of decorations, to get a better understanding of the technical stuff that Nate, John, and Dan and discussing? Maybe we can get a (new version of) position paper explaining it? This will somewhat clarify all these things about bare decorations etc. and make the technical discussions more meaningful to us simple voters
On level 1, a decoration is just a finite set of properties,
and a decorated interval is a pair consisting of an interval
and a decoration, with some compbinations excluded since they don't
make sense. (Which ones depends on the ecoration model),
Arithmetic operations on decorated intervals are such that the interval
part does not depend on the decorations, and otherwise ''sensible''
in the sense of preserving the intended meaning of the decorations.
In particular, all arithmetic operations involving Empty as interval
part produce Empty as interval part, and all arithmetic operations
involving invalid as decoration part produce invalid as decoration part.
More is not specified on level 1.
Everything else depends on the decoration model and is so far
unspecified by the motions. There are many possibilities.
My recent posting under the thread ''Decorations and Motion 22''
suggested that the decorations are linearly ordered as 0,1,2,3,4,
the extremes being
dec=0 denoting safe (all desirable properties can be established)
dec=4 denoting an invald interval;
for more details see the first post in in that thread.
Currently I am discussing some variants offline with Nate Hayes.
Once we achieve agreement, there will be a motion on it.
One of the decorated intervals, namely (Empty,invalid), serves as
the NaI that John Pryce is asking for in his draft of a position paper.
But he wants to give it an additional separate existence, which is
both unneccesary and against the spirit of the whole decoration concept
as argued in the rationale for Motion 8 (which you'd read again to have
the context).
Arnold Neumaier