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Re: Neumaier-Pryce proposed decoration system (v03.2)

Dominque Lohez wrote:

BTW bnd is not a level 1 concept
Any continuous function is bounded
if f (x) == 1/x

f ([-1, -0.1]) = ([-10,-1], saf)
f(-1,0]) = ((-infty, -1), con)

bnd might be a useful concept at level 2 to distinguish between the
representation of the level one intervals [0,1^10000] and [0,+infty)


I agree. This is a reason motion 25 has no "bounded" decoration. IMHO, Ian
McIntosh has presented the most viable way to handle this at Level 2, and
his method does not require decorations.




But even in that case con , daf and def are enough


An "undefined" decoration is still required.

Equating motion 25 and motion 26 terms, it should be:

   D4    ein    "empty input"
   D3    dac    "defined and continuous"
   D2    def    "defined"
   D1    con    "contained (possibly defined/undefined, etc.)
   D0    und    "undefined"

we then have linear quality order:

   D0 < D1 < D2 < D3 < D4

for property tracking and partial containment order:

   ein \subset dac \subset def \subset con
   und \subset con

for FTDIA.

Nate




Dominique


John Pryce a e'crit :

Nate

On 14 Jun 2011, at 05:18, Nate Hayes wrote:


One thing in v3.02 that puzzles me is the introduction of the decoration
"ein" as the "worst" decoration of the linear quality order (5).
...
It was in some offline discussions with the Gang of Ten a month or two
later
that Dominique suggested arithmetic operations on empty input should
give
the best decoration, not the worst.




I was also minded to make it the "best", for reasons I put forward in the
emails you mentioned, but Arnold at time of circulating v03.2 favoured
"worst". He is currently checking the FTDIA proof and updating it to the
new set of decorations. Let's see what he comes up with.

However: though the difference between best and worst seems somewhat
extreme, it is also possible this is not a serious show-stopper. ein is
rather an "outlier" as properties go, so a version of FTDIA may exist
with either choice of ein's position. I am suffering from FTDIA-fatigue
at present, so prefer to wait and check someone else's work.

John Pryce






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