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.