[sc34wg3] RM4TM and symmetrical relations

[Sam Hunting]

On Wed, 20 Nov 2002, Bernard Vatant wrote:

> [Bernard Vatant]
> > > how do I express sibling-ness or any other equivalence relationship if:
> > > 1. A single membership is not allowed.
> > > 2. Having two c-nodes of the same type in an assertion is not alllowed.
> 
> [Steve Newcomb]
> > By "equivalence relationship" I'm going to assume that
> > you mean "relationships in which there's no semantic
> > difference between the role types". Such as opposites.
> 
> Not exactly. "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)

I think there are some assumptions being made here:

1. That expressing (rather than *enabling* the expression of) equivalence
relationships is a task for the RM, rather than for an application.

My understanding is that equivalence relations apply to sets
(http://mathworld.wolfram.com/EquivalenceRelation.html). Are you saying
that the RM should define sets? And do equivalence relations apply to all
sets that any application might wish to define -- for example, fuzzy sets?

2. My understanding is that neither assertions nor associations have truth
values (though presumbaly some applicatons could confer truth values on
some (types of) a-node for example). When I see language like "if ... then
..." it makes me think of propositions, that do have truth value. Are you
saying that RM assertions or SAM associations have truth values?

> In that sense in fact sibling-ness is an equivalence relation only if
> it's understood as 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
                                                            ^^^^^^^^^ 
Not a "principle", an "objective." You might think of the objective as the
end or goal, and principles as guidelines for making design decisions
about how to achieve the objectives. For example, in arguing against
"convolutedness", you suggest a principle.

> leads to such convoluted and non-intuitive conclusions ... ... either

Well, you need to either (1) show that the suggested solution does not
meet the objective, (2) show that the violations of principle involved in
meeting the objective are so egregious that the objective is not worth
meeting, or (3) abandon the Subject Location Uniqueness Objective
altogether -- which would be like an indexer saying "Oh, it's OK that
there are several index entries that refer to the same subject -- it's too
much trouble to put in the See's and See als's, and anyhow, the reader
will never notice." So far, I'm not sure which alterntaive you've chosen.

Sam Hunting
eTopicality, Inc.

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