Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: Motion 31 draft text V04.4, extra notes

Vincent Lefevere wrote:

On 2012-04-11 18:53:04 -0500, Nate Hayes wrote:

Vincent Lefevre wrote:
>How can you consider 1 / [0,1] without unbounded intervals?
You've already agreed [1,+OVR] as a family of intervals is not the same
thing as an unbounded interval but contains all possible solutions.


Do you mean that 1 / [0,1] returns [1,+OVR] based on this fact?
In such a case, [1,+OVR] is equivalent to an unbounded interval.

That has been a point of mine from the beginning: unbounded intervals are
not necessary.




>>Who cares if I can do 1/[0,1]=[1,+Inf] at Level 1 if I can't assume
>>   A + X = B + X
>>means A = B!!
>>
>>That is not an arithmetic I want to work with.
>
>If you do not work with unbounded intervals, you still have
> A + X = B + X ==> A = B
>
>I don't see any problem.


And I would add the the above does not work with families of intervals
such as [1,+OVR]. So, you are not solving anything by replacing
unbounded intervals by families of intervals.

It appears you are changing the subject, since I was speaking about Level 1
and now you are talking about Level 2.



Well, how am I to not work with unbounded intervals at Level 1 if the
standard requires they may be there?


Since your system works only with bounded intervals, you must have
some hypotheses that guaranty that unbounded intervals will never
occur (e.g. if you consider 1 / X, you need to know that X doesn't
contain 0). So, you can just ignore unbounded intervals globally.

It appears you are changing the subject again, for the same reasons
mentioned above.

Anyhow, at Level 2 there is no practical difference between Inf/OVR in the
interval arithmetics:
Decorations and compressed intervals can make the distinction that you
mention in both cases. For example, the full decorated result of 1 / [0,1]
may be
   ([1,+OVR],somewhereDefined)
and with compressed intervals the result may be either the bare interval
   [1,+OVR]
or the bare decoration
   somewhereDefined.
So nothing is lost over the current P1788 model, i.e., what you're talking
about isn't any argument in favor of unbounded intervals or against family
of intervals (in fact, its not really relevant at all).



I can't ignore anything the standard mandates unless I don't follow the
standard.


The standard mandates that unbounded intervals are supported by the
implementation, not that they will occur in the user application.

It mandates they are in the Level 1 math equations, which are then no longer
cancellative.



Development of Kaucher arithmetic *requires* cancellation property!!!


The standard is not about the Kaucher arithmetic anyway.

That's news to me. The name of P1788 is "Standard for Interval
Arithmetic"... and Kaucher arithmetic is "interval arithmetic".





>BTW, cancellation is invalid at Level 2.
I already pointed that out just the other day.


+ the fact that you do not want to work at Level 1, this makes it
useless.

I have never said I don't want to work at Level 1. I've said I want to work
in a Level 1 model that is cancellative. Please stop putting words in my
mouth.

Nate

P.S. The definition of a "straw man" is a counter-argument made to a
position not actually held by one's opponent.