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parid0508
| Wed, 20 Nov 2002 15:59:56
"equivalence relationship" or more exactly "equivalence relation" has
in my
mind the meaning it has in mathematics, a relation R which has the three properties of
reflexivity, symmetry and transitivity.
Which means, for all x, y, z in the domain of the relation:
1. xRx (reflexivity)
2. If xRy, then yRx (symmetry)
3. If xRy and yRz, then xRz (transitivity)
In that sense in fact sibling-ness is an equivalence relation only if it's understood as
"belong to the same set-of-siblings" (I do not find any substantive in english for the
french "fratrie", meaning the set of siblings in the same family.)
In that extended definition, I am a sibling of myself, though this can be questionable of
course.
But the exemple you give ("opposites") is definitely not an equivalence
relation, it lacks reflexivity and transitivity. A true equivalence
relation in geometry is for example "is parallel to" (for straight lines)
more exactly expressed as "has the same direction as". If, to express the
assertion "D1 is parallel to D2", I need two different role types, I give
up, and your long explanation keeps me only wondering. If indeed the
Subject Location Uniqueness Principle leads to such convoluted and
non-intuitive conclusions ... ... either you got wrong in your reasoning
(and I can't really judge on that, I'm afraid, because I'm lost in your
arguments) ... or the principles that lead to such conclusions are
questionable.
parid0508
| Wed, 20 Nov 2002 08:43:50
What you are saying in this is that this assertion has two distinct role types "Opposite of White" and "Opposite of Black". Similarly my brother and I are linked by two different role types "Brother of Ian" and "Brother of Martin" It is the pair of the role type and the role player that needs to be unique, not the role type itself. My conclusion is that the role type is not a distinguishing property. It is simply a property that allows you to identify sets of assertions that play a similar role in different assertion instances. The RM should not concern itself about the fact that the same role type occurs in different places. It should only concern itself with the uniqueness of role type/player pairs in specific instances. |