[sc34wg3] RM4TM issue : is role player always a set?

Lars Marius Garshol sc34wg3@isotopicmaps.org
23 Nov 2002 12:09:53 +0100

* Bernard Vatant
| Why so? My maths background tends to make me disagree with that.  I
| would like the RM to stand on a strong mathematical model, grounded
| in set theory.  That is the aim of the HG4TM proposal (see previous
| message)

* Sam Hunting
| We discussing, I think, a point where it is going to be "tricky" (as
| Lars says) to draw the line between SAM and RM.

I'm not so sure. The notion of a set is sufficiently well-defined that
separate definitions in the RM and the SAM need not worry us. A set is
a set is a set, as long as we are not worried by Russell's Paradox,
and I am not.
| On the one hand, the RM clearly uses the *concept* of set -- but
| without (so far) a mathematical definition of it.

Then I think the RM should make it clear that it is using the
mathematical notion.
| On the other hand, the SAM (at least in discussion, uses the *term*
| set in a non-mathematical sense -- for example, it speaks of sets as
| having duplicate members.

Yes and no. The unmathematical thing about the SAM is that time is
part of the model through the notion of changing values, and that is
what causes this seeming problem with sets. Once SAM processing is
complete no sets have duplicate values, but the current prose may
imply that the sets may at times contain duplicates. 

That's an editorial problem that needs to be ironed out, however, and
not something that will be present in the final standard.
| On the third hand, "grounded in set theory" means "grounded in set
| theory" means "grounded in a *particular* set theory." (see
| http://mathworld.wolfram.com/SetTheory.html). 

I wouldn't worry about this. A choice between set theories is made in
order to get the beneficial properties of a particular set theory, but
so long one doesn't need the differences one does not need to make a
particular choice, either.

The RDF Model Theory chooses ZF sets because it is a logical model
with an overriding need for consistency and so it chooses a set theory
designed for consistency. SAM as an implementor's model has no need
for these distinctions. All the SAM cares about is a) knowing when
something is a member of a set, b) avoiding duplicates, and c) being
able to enumerate the members of a set.

I don't fully understand the objectives of the RM4TM so I can't
comment on what it needs.
| I worry that by blessing a particular set theory in the RM, we would
| foreclose some options that would be useful to us in the future
| (fuzzy sets?).

I think answering this requires careful thought about what the RM4TM
is supposed to *do*. Will it be a problem to tighten it up in the
future? Will establishing a model theory for topic maps be left to a
separate specification? etc
| [Note also Bernard's careful comma, "mathematical model<EM>,</EM>
| grounded in set theory." Meaning that a mathematical model (if any)
| would need to support set theory, wihtout being necessarily equal to
| such a theory.]

A mathematical model might need to choose a particular set theory, yes.
A model theory would probably choose ZF, while a graph theory might
not need to choose, and something based on situation theory might be
in a third position for all I know.

| Clearly, it would be possible to standardize an assertion type for
| set/set member relationships that embodied a particular set theory
| and express that (I "assert") in RM4TM terms for applications. I
| don't think it should be normative, whether it goes in the RM or the
| SAM.

I think you are creating problems where none exist. The SAM uses sets
in one specific place: as the values of certain properties. This is
part of the notational framework that the SAM is built on and as long
as that framework does what the SAM needs it to do without having any
harmful side-effects there is no problem.

One chooses formalisms because they are useful, to meet certain ends,
and that's all. The formalisms used throughout the standards family do
*not* need to be consistent, so long as the whole ends up being

* Steven R. Newcomb
| The ontology defined by a TM Application can *even* decide that
| there are no subjects that are not sets.

I think we should be careful with how we use the word "ontology" so
that we do not wear it out and end up with a meaningless phrase. I
think we should reserve it for "a collection of typing and scoping
topics as used in one or more topic maps[1]".

What RM4TM calls a "TM application" is a "TM application" so we don't
need to use up the term "ontology" by applying it to something that
already has a defined term.

* Steven R. Newcomb
| Personally, I think that's a very extreme position.  I think it
| pollutes and colors the semantic space of the TM Application very
| severely, and I see no point in it (but maybe that's because you,
| Bernard, know something that I don't know).  I would hate to see the
| Standard Application take that position.  Why shouldn't a role
| player be allowed to be an individual subject, rather than a set of
| subjects with only one member?  For me, they are two different
| subjects.

* Sam Hunting
| As (in my own way) an implementor, I hate this, because of the lack
| of symmetry between individuals and sets of one member. But when I
| think about whether an individual qua indivuidual is the same
| subject, or a different subject from an individual as a member of a
| set, I am forced to agree that indeed there are two subjects (unless
| an application defines them to be otherwise....). ["I am me! I am
| not the set of one member that contains me!"]

Yup. This is also the slippery slope that leads towards Russell's
Paradox, by the way. One needs to tread carefully here, and I think
this is the right approach.

[1] ISO 13250:2002 sense.

Lars Marius Garshol, Ontopian         <URL: http://www.ontopia.net >
ISO SC34/WG3, OASIS GeoLang TC        <URL: http://www.garshol.priv.no >