Re: Motion P1788/M0013.02:ComparisonOperations : NO
John Pryce a écrit
There's something I don't understand in Dominique's email, see below.
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On 30 Apr 2010, at 11:11, Dominique Lohez wrote:
My vote is NO
Rationales
1) The comparison operations SHOULD be defined at defined at level 1 and then developed at level 2 and further
Such an approach would be consistent with the the methodology alway used in the working group up to now
2) The primitive operations provided by the standard MUST be be defined such that for any pair of intervals one and only one operation provided the true result.
I don't know what this sentence means.
Sorry , I really express my position in a too condensed formulation.
My point that the the comparison operations defined must be handle
ALL the relative position on an interval a with respect to an interval b.
Before going further let consider the case of real number comparisons
1) THE CASE OF REAL NUMBERS COMPARISON OPERATIONS
The extensive list of comparison operations is < , <= , = ,
>= , > , # , true , false
All the operations can be defined from three primitive operations
namely < , = , >
We have
a < b <=> a <b
a<= b <=> a<b || a=b
a=b <=> a=b
a>=b <=> a>b || a=b
a>b <=> a >b
a#b <=> a <b || a>b
true <=> a<b || a=b || a>b for any a and b
false <=> No disjunction
Furthermore we have
false <=> a <b && a=b for any a and b
false <=> a=b && a>b for any a and b
false <=> a<b && a>b for any a and b
Finally noting that
a>b <=> b<a
the number of primitive operations may be reduced to < and =
2) THE CASE OF INTERVAL COMPARISON OPERATIONS
I would like that the standard define primitive interval comparison
operation such that any comparison operation can be defined as an unique
disjunction of
primitive operations
This is meaningful since in contrast with numbers where only 6
comparisons (excluding true and false) has to be considered so that
all the comparison may be explicitly provided, the number of
interval comparison operation is considerably higher.
For example using the Allen's Work(quoted by Vladik Kreinovich
in his mail of 10th of April 10 ) as a starting point
http://en.wikipedia.org/wiki/Allen's_Interval_Algebra
we found that 13 primitive operations (7 if symmetry is taken into
account) and the number of comparison operations between interval
(including true and false) goes to 2^13
At this point I realize that choosing the primitive comparison is a
big challenge . I think however that this challenge must be
addressed, since you then specify what intervals may be compared, and
to what extent they may be compared.
3) For the shake of convenience further very often used relations MAY be defined
Please suggest what you would include here.
The point is now anecdotal. Of course the primitive comparisons are not
necessarily the most useful.
So some further very often used might added to the standard.
Sincerly,
Dominique LOHEZ
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Dr Dominique LOHEZ
ISEN
41, Bd Vauban
F59046 LILLE
France
Phone : +33 (0)3 20 30 40 71
Email: Dominique.Lohez@xxxxxxx