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Re: Discussion paper: what are the level 2 datums?

Nate Hayes wrote:

Arnold Neumaier wrote:

Nate Hayes wrote:

Arnold Neumaier wrote:

3. Concerning the values of the other decoration trits, I think that
this is part of a general observation that not all combinations of trit
values make sense. Indeed, assuming the four trits
    v=valid,  d=-defined,  c=continuous,  b=bounded
(which are the indispensible ones) and the possible values
    + (True),  - (False),  and  0 (no claim),
only 10 combinations of trits are computationally relevant and should
be allowed:

    v d  c  b  | #cases
    - 0  0  0  | 1
    + -  0  0  | 1
    + 0  0  0- | 2
    + + +0 +0- | 6

(In particular, v is never 0 and c is never -.)
A further observation is that "v" is never + when all other decorations are 0, hence "v" (what I believe John is referring to as the "illform" bit) is completely unnecesary. 

This is not correct. +000 can arise:
  x = sign([-1,1]) is ([-1,1],++0+)
  y = sqrt(x)      is ([0,1],+000)
Thus v is needed.
I think we agree but the discrepancy is that the example is given in terms of trits (motion 8); but P1788 has now accepted tetrit for the "domain" decoration (motion 18). So by motion 18 this would give: 
   x = sign([-1,1])    is ([-1,1],domain:(T,F),continuous:F)
   y = sqrt(x)        is ([0,1],domain:(T,T),continuous:F)


I had been absent for a few months from the list, due to other heavy
commitments, and have still a backlog of about 850 unread mails from
the list....



Notice that this would be different from the invalid construction
   construct([-Infinity,-Infinity]) = (Empty,domain:(F,F),continuous:F)


Anyway, one must be able to conclude from the decoration whether or not
an interval is valid, and one needs at least operations extracting the four trits v d c b from a tetrit representation.
I'm fairly certain the only decorations IEEE 1788 needs are "defined", "continuous", and "bounded". 

We need all four. But we can dispense with the ohers.
If we were still using trits, then "v" might be needed. But since we are now using tetrits I believe "v" is not necessary.
Does the interpretational difference matter when there are only 10 different combinations that are useful? With tetrits it shoudn't be significantly more.
So one can probably map the trit formulation and the tetrit formulation equivalently to 10 (or 16) abstract decoration objects that are just organized differently by the two formulations.