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Motion P1788/M0002.01_ProcessStructure NO



I vote NO on motion 2.

I would vote "yes" if in the position paper P1788/PP008

lines 10+ to 12+ on page 2, saying:
"The levels framework, here proposed, does not give much help to 
discussing modal or Kaucher intervals, 
because these are more than "plain sets" (of numbers); but with minor 
changes it supports discussing 
Kahan-style wraparound intervals, which are plain sets."

and the sentence "It does not include Kaucher and modal intervals.", 
lines 5-,6-  on page 7.

are removed.

Rationale:
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1) the claim at lines 10+ to 12+ on page 2 is just not true. 
The lever framework, proposed in P1788/PP008, is fully compatible 
with the end-point representation of Kaucher intervals which present 
an algebraic completion of the set-theoretic intervals and
are considered as a canonical form of modal intervals.

2) The text marked for removal contradicts to
point 1c. from "3.1 Level 1 debates" of the position paper, which 
supposes Level 1 debates on support for 
other /Kaucher, modal/ interval models.
1c. from 3.1 says: "There are various ways in which the support of 
non-classical intervals could be done. The implementation of such a 
support may be not prescriptive but permissive."

The position paper suggests debates on  this topic also at Level 4 
debates (4c.) and at the Meta-level  debates (M-c). 

3) Taking the Vienna proposal as a background of the eventual 
interval standard, and because this proposal supports non-standard 
intervals, implies that at some time a discussion on 
non-standard intervals should take place.
The most reasonable interval model which might be relatively easy 
built on the non-standard intervals is Kaucher (modal) arithmetic.
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Evgenija Popova
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences