Arnold Neumaier wrote:
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.