RE: Comments on decoration ill, intersection and union
John Pryce wrote:
> So it seems "max(dx,dy)" for intersectionDec should be "min(dx,dy)"; and
> "min(dx,dy)" for convexHullDec should be "the tightest decoration
containing dx and dy
> in the containment order". (I assume by "weakest" you mean the min,
because you
> say it is like an arithmetic operation.)
Where do you see "weakest"? It says "the tightest decoration" not "the
weakest decoration". This is not the same thing as the min.
Anyhow, applying these rules to Motion 42 still leads to problems:
In the Example 2 in section 8.8.8 for X=[-1,1], it gives:
U = f1(intersect([-1,1],[-oo,-2]))
= f1((Empty,dac)) // (Empty,dac) is contradictory by section
8.8.4
= (Empty,emp)
V = (f1([-1,1]),dac)
W = f1(intersect([-1,1],[2,+oo]))
= f1((Empty,dac)) // (Empty,dac) is contradictory by section
8.8.4
= (Empty,emp)
So there are still the intermediate results (Empty,dac), which by Motion 42
is a contradiction.
Taking convexHull of U, V and W and propagating the "tightest" decoration by
the containment order gives:
(f1([-1,1]),trv)
This at least is not incorrect (since trv decoration is always true), but it
is not useful or informative.
This demonstrates my point further: to remove the contradictions specified
in section 8.8.4, and also to compute the decoration that is both correct
and most informative, one needs to define an ein decoration as I have done
in the previous e-mails in this discussion. Without these changes, Motion 42
simply does not define the correct decoration system to make decorated set
operations useful, informative or free of contradictions.
Nate