On Wednesday, 18 December 2013 at 20:45:44 UTC, Timon Gehr wrote:
Giving up Eg. ¬(A ∧ B) → ¬A ∨ ¬B is actually a sensible thing
to do in constructive logic.
It is common to give it up in fuzzy logic too, doesn't mean it is
the first thing to throw out.
Anyway, the point in the discussion above is that of having a
third value "uncertain"/"indeterminate" mapped to false and the
consequences of that.
You don't want:
a<b == a>b, so ordering overlapping intervals is indeterminate
It is sensible to allow explicit:
bool(indeterminate)==false
If you then have:
[a,b]<[c,d] => indeterminate
And define == by < then it follows that:
[a,b]==[a,b] => indeterminate for a!=b
and:
bool([a,b]==[a,b]) => false
and therefore you would want:
bool([a,b]!=[a,b]) => true
Which is kind of tricky to achieve unless you have two types of
indeterminate when I come to think of it, maybe you need
indeterminate and not_indeterminate if you allow casts to bool…
E.g. !indeterminate=> not_indeterminate and !not_indeterminate =>
indeterminate ?
Hm…
