Re: modal intervals
Svetoslav Markov wrote
[in ''Edge case conversions, exceptions to IEEE FPA'']:
> standardization of proper interval arithmetic would be
> equivalent to standardization of nonnegative reals.
In contrast to the reals, which form a field,
the same is not the case for Kaucher intervals.
For example, the distributive law fails.
Kaucher intervals form a complicated algebraic structure,
not really simpler than that for ordinary intervals.
Thus your analogy completion of R^+ to R vs. completion of
intervals to Kaucher intervals is poor.
> I believe that a standard for Kaucher interval arithmetic will be simpler
> than one for proper intervals, as there will be no need to check
> whether an interval (as input data or computational result) is
> proper or not.
Input is a tiny part of interval computations, and output will
be automatically proper if the input is.
However, computations are more complex, since in most operations
one needs to check whether an interval is proper or not.
Thus whether or not to include modal intervals or Kaucher arithmetic
will depend on whether the extra compexity is compensated by
sufficiently increased practical usefulness.
Arnold Neumaier