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

Arnold Neumaier wrote:

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....


I understand and sympathyse.
Jurgen has Motion 18 (tetrits) on the private web-page. I'd suggest taking a look at that if you get a chance. 





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. 

Agreed.
Any interval with a "domain" decoration (F,F) is invalid. This is also the "worst" state of a tetrit, i.e., by the propagation rules of tetrits it is impossible that (F,F) could ever be "absorbed", "lost", or "changed" into another state that is either better or worse. So it is the perfect state to represent invalid constructions and/or uninitialized interval variables. 

The new domain tetrit provides the four states:

   priority    tetrit    trit    meaing
   3            (T,F)    +       "is defined"
   2            (T,T)    0        "possibly defined"
   1            (F,T)    -        "is undefined"
   0            (F,F)             "nowhere defined, nowhere undefined"
The first three states and thier meaning are the same as the old trits. But with trits, there was not an equivalent of the (F,F) state, which essentially makes the distinction of "v" in the above example.
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. 

Tetrits simplify and reduce the number of "unusable" combinations.
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. 

Yes.

Nate Hayes