[sc34wg3] New SAM PSIs

[Murray Altheim]

Lars Marius Garshol wrote:
> * 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.

I have been reading everything and *attempting* to listen to what
you are saying. As for classes and sets, I've been reading in the
subject night and day for the past year, so I really don't need a
review. I just finished writing one.

> 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.

I think you're now missing my point: the "superclass-subclass loop"
is simply wrong. The whole idea only makes sense in terms of "superset-
subset loop." I'm not focusing on sets, I'm saying the concept put
forth is illogical, regardless of what OWL does, it's illogical.

> * 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.

You were fine until you said "that's a kind of equivalence." If
that's as far as OWL went, fine. But in reading the OWL spec and
the W3C list archives this goes beyond simply saying they have the
same extensions; it is making a statement about the classes based
on the equivalence of extensions, which is where the problem lies.
I don't know if you remember me mentioning that this was being
justified on their list via things like RDF and Java's handling
of classes, which is a different domain entirely (eg., subclassing
in Java is different than set theory's definitions).

If I'm misinterpreting the OWL spec, imagine how many others will
do so. *sigh*

> | 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.

Well, we've had a difficulty in communicating a difficult bunch of
concepts over email. Not always the most efficient means of doing
this obviously. I'm glad that even though we both seem to get
frustrated with each other we keep trying... :-)

Murray

......................................................................
Murray Altheim                  <http://kmi.open.ac.uk/people/murray/>
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK

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