RE: Motion 42: NO
John Pryce wrote:
> IMO, any contradictions that Nate or anyone
> else sees in it are due to making a mixture of Nate's definitions and
assumptions with
> those of Motion 42. If anyone claims to have a contradiction, let's see
the details.
John, I would really like to see you explain, in specific detail, how the
following contradictions do not come directly from the definitions of the
decoration scheme in Motion 42:
Section 8.8.7 says decorated intersection operation may provide a decoration
min(dx,dy), where dx and dy are the decorations of the input operands. So
this gives:
([1,2],dac) intersect ([3,4],dac)
= ([1,2] intersect [3,4],min(dac,dac))
= (Empty,dac)
But by section 8.8.4 the empty set is not permitted to be decorated with
decoration dac because it says this would be a "contradiction". The text of
the specification therefore clearly allows implementations to give
contradictory results, as defined entirely by Motion 42 and no outside
source.
Are you denying this?
In Motion 42, Empty is an interval but (Empty,ill) is "not an interval." So
by this definition, (Empty,ill) is the "Empty interval" decorated with ill,
i.e., it is a "decorated interval". The motion therefore defines (Empty,ill)
as both a "decorated interval" and "not an interval" at the same time. I
don't agree this is reasonable, as you claim: it's like saying my dog is a
"furry dog" and "not a dog" all at the same time.
From a mathematical point of view the real function
f(x) = x + 0/0
is not defined for any real x, but for any interval X
f(X) = X + 0/0 = Empty.
If Empty is an interval, how can the Empty result be "not an interval?"
IMO, you are trying to have it both ways, when it must be one of two
mutually exclusive definitions:
-- Empty is an interval such that there is no definition of "not an
interval" in the standard; or
-- Empty is a valid mathematical object of the standard, but it is
not an element of overline-IR and therefore is "not an interval."
Looking forward to compressed interval arithmetic using only the definitions
provided in Motion 42, suppose the user specifies the threshold level such
that any operation that is not defined and continuous is considered to be an
error:
[1,2] \subseteq floor([5,6])
= [1,2] \subseteq ([5,6],def) // Full decorated result
= [1,2] \subseteq def // compress non-DAC result
= [1,2] \subseteq Entire // promote bare decoration def to
Entire
= true
How is this not a false positive, since [1,2] is not a subset of [5,6]
regardless if [5,6] is defined and continuous or not? By definitions in
Motion 42, how can the def decoration promote to anything other than Entire,
which is the cause of failure?
Nate