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