Re: the "set paradigm" is harmful
Kreinovich, Vladik schrieb:
I think what Svetoslav has in mind is that, e.g., Taylor arithmetic is
automatically excluded by this definition, since in Taylor arithmetic,
the main object is not an interval but rather a tuple consisting of real
numbers (coefficients of the Taylor polynomial) + the Taylor bounds for
the remainder.
Taylor arithmetic is a model for operating with uncertain _functions_,
not one for operating with intervals, interpreted as uncertain
_numbers_. Thus the standard should have to say nothing about it.
It doesn't make sense to standardize all possible formats that people
used in the past (or might use in the future) to get interval
enclosures.
The task is only to standardize interval arithmetic, such that others
who define more complex data types like Taylor models know what they
can rely upon.
If we should start catering for Taylor models we only open a can
of worms.
Then we need to look at _all_ kinds of representing functions,
various versions of centered forms, various versions of affine
arithmetic, various versions of polynomial enclosures (Taylor models
are not the only ones), etc., and we'll never reach agreement.
Arnold Neumaier