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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 -.)
For example, the reason for excluding the case + 0 0 + is:
If something is possibly undefined, how can it be surely bounded?
How can undefined things have any property?
I agree.This is also why a "defined and continuous" decoration only needs to be a single bit and not a tetrit; and why I believe Motion 22 -- along with its proposed amendment -- should be passed.
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.
All that is needed to represent an invalid construction such as [-Infinity,-Infinity] is to set the interval portion of the decorated interval to Empty and the decoration portions such that all attributes "d" "c" "b" are set to thier worst state, i.e., the "domain" tetrit should be (F,F) and "continuous" should be F, etc.
I'm fairly certain the only decorations IEEE 1788 needs are "defined", "continuous", and "bounded".
....although I do have doubts and reservations about "bounded." But I don't have strong feelings one way or the other on that and am waiting to see how future discussions on the topic shake out.
Nate Hayes