Re: position paper on comparisons
Vladik, P1788
On 17 Apr 2010, at 20:50, Kreinovich, Vladik wrote:
> P(a,bb) <=> possibly_b (a <= bb), meaning that a <= b for some value b from the interval bb
>
> This relation is equivalent to a <= b+
>
> This relation is true for some a and false for some other a. Now, a natural question is whether this statement is necessarly true for a in aa, i.e., whether it is true for all a from the interval aa. This new relation
>
> Necessary_a P(aa,bb) <=> necessary_a possibly_b (aa <= bb) is equivalent to a+ <= b+
>
> This type of combination is used in some approaches to solving linear equations: there is a control solution, tolerance solution, joint solution, etc., that differ by selecting quantifiers and their orders -- this was explored in modal interval arithmetic.
Thank you for reminding us of this. I was just trying to keep things simple, and certainly was not ignoring the usefulness of set relations that mix "exist" and "forall". I was much enlightened by your paper on such matters that you circulated to the group about a year ago.
Regards
John