[sc34wg3] New SAM PSIs

[Lars Marius Garshol]

* Murray Altheim
| 
| It is impossible unless you conflate "set" and "class", or believe
| that a superclass and subclass could have the same definition (I
| agree that this is nonsense, as Mary says, it has no bearing to
| reality).

Look, it would help if you started listening to what people are trying
to tell you. I'll make one more attempt: if there is a difference
between classes and sets it is that classes have an intension, whereas
sets only have members. Classes have extensions, the set of their
instances, which are like the members of sets.

So, to summarize:

  - classes have intensions (kind of like a definition of what it
    means to be an instance) and extensions (the set of instances),
    and

  - sets have members.

>From now on, let's ignore sets and focus on classes, because sets
aren't really relevant to this.
 
* Lars Marius Garshol
|
| Well, what you are saying with the loop is basically this: "these
| classes have different definitions, but they all have the same set
| of instances". There's nothing unreasonable about that.
 
* Murray Altheim
|
| Actually, there is, and this has been the most important point, that
| it's not just a fluffy equivalency mechanism, it could lead to
| erroneous conclusions.

Let's try again: if A is a subclass of B, then the extension of A is a
subset of the extension of B. We know nothing about the relationship
between their intensions. If we then also find that B is a subclass of
A, that means that the extension of B is a subset of the extension of
A. We still know nothing about the intensions, but we can now conclude
that the classes have the same extension.

In other words, we don't know that the classes are the same, but we do
know that their extensions are the same. That's a kind of equivalence,
and DAML+OIL and OWL *explicitly* allow this in order to allow people
to express this relationship between classes.
 
| To say that because two sets have the same instances, they are
| the same class, is an error in logic.

Yes. That's what I've been telling you.

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