Is subclassing "strict order" or is it reflexive? RE: [sc34wg3] New SAM PSIs

[Lars Marius Garshol]

* Murray Altheim
| 
| On the one hand, and the error I think OWL is making, is that it
| seems to be talking about *members* of sets. So, if we have a set A
| and a set B whose members are all the same, they are identical sets.
| Eg., if we have 100 hominids and 100 primates, and they are the same
| 100 individuals, we can consider the two sets identical. We cannot,
| and I repeat, cannot, necessarily therefore consider the classes of
| primates and hominids as identical. They are not.

Murray, this is precisely what I tried to explain in
  <URL: http://isotopicmaps.org/pipermail/sc34wg3/2003-February/001107.html >

The classes are not identical because they may have different
intensions, even though their extensions are the same.

| A type hierarchy or taxonomy is strictly talking about the
| relationships between types or classes, not their instances. This is
| the point about extension and intension that Lars Marius brought up.

Extension == set of all instances. So you may have misunderstood me.
 
| This may be interpreted one of two ways. First, as a relationship
| between sets of individuals, secondly as essentially an argument
| about differences in labels, saying, for example, that "primate" in
| English and "primas" in German refer to the same class, or that two
| different labels for a specific star refer to the same star; we're
| not actually talking about a *difference* in classes, merely their
| labels, that within one context or domain a difference in label is
| not a difference in actual class, i.e., it does not constitute a
| different class but merely a different label for the same class.

I think you're missing the point about intensions. The intension is
not the label of the class, but something along the lines of the
definition of what the class is.
 
| Even if there is some mathematically-logical sense within which this
| is true, which I think I've demonstrated is not the case (unless
| we're talking about the relationships between classes of individuals
| and *not* the relationships between classes (ie., taxonomy), I still
| think this decision would be a mistake, since such "subtleties" are
| likely lost on 99% of the buying public (ie., developers and
| implementors).

Note that all we are saying is that it is allowed to do this. We're
not saying people have to do this, or even think about it. We're just
being clear that implementations are supposed to not detect this and
flag it as an error. (Though I imagine TMCL schemas might allow you to
disallow this in your own applications.)
 
| Based solely on the "principle of least surprise" I believe most
| people would intuitively disbelieve that a class can simultaneously
| have both a superclass and a subclass relationship to another class,
| [...]

I had the same reaction, and I've seen it in lots of people when
discussing this with them, but so what, really? Who do you think will
be upset by this in practice? How is it going to harm anyone?

-- 
Lars Marius Garshol, Ontopian         <URL: http://www.ontopia.net >
GSM: +47 98 21 55 50                  <URL: http://www.garshol.priv.no >