[sc34wg3] New SAM PSIs

[Murray Altheim]

Dmitry wrote:
> [Murray Altheim]
[...]
> I think that there are two different models which are discussed in this
> thread.
> 
> More precisely, I think that:
> 
> It is possible to create different models explaining "class-subclass","
> instance-class" relationships.
> 
> It is possible to create useful model (let's call it M0) of "class-subclass"
> ," instance-class" relationships that is not based on concept of extensions.
> This model does not have superclass-subclass loops by definition.

Understood -- this is my preferred model, to put it plainly. One
might call it a "theory of intensionality", i.e., class definition by
meaning, axiom or defining conditions.

[To be clear, I don't disagree with the *concept* of class definition
by extension, I just believe the concept of extension is being abused
in conflating superclass/subclass and superset/subset.]

One of things that this discussion (both public and privately) has
unearthed, is to what formal set theoretic model we in the topic
map community believe TM should follow. To my knowledge this has not
been discussed openly, and the discussion here seems to have brought
up a fair amount of ambiguity in terminology.

> Class-subclass model used in SAM (M1) is out of scope of M0, it is a
> different model with different "axioms". I guess one of the first "axioms"
> of M1 is that "A type is a set of individual subjects, each of which is an
> instance of the type."

I don't consider "type" or "class" as different terms (nor do I know of
any justification to do so in any set theory I'm familiar with), so your
statement could be reworded as

    "A class is a set of individual subjects, each of which is an
     instance of the class."

Which is to me not a correct statement. A class is not a set, nor a
kind of set. A type or class is a specification (or definition)
defining membership in a set. You could reword the statement as

    "A class is defined by a set of individual subjects, each of
     which is an instance of the class."

But this is simply the definition of class-definition-by-extension,
which we've discussed previously. I note (via private communication)
that the decision in the SAM draft considers "type" as "intensional"
and "class" as extensional, but I would like somebody to provide some
references for a statement such as that (i.e., whose school of thought?)
as I don't think that convention is at all widespread. In looking at
the OWL Guide one can read:

    In OWL Full a class can be treated simultaneously as a collection
    of individuals (the class extension) and as an individual in its
    own right (the class intension).

And sorry, but that just sounds to me like nonsense, based on the
definitions I have of set, collection, class, and individual (I
assume "individual" and "instance" are synonyms -- more ambiguous
terminology?). The statement makes sense substituting "set" for
"class", not as is.

> M0 and M1 use the same terms "class", "subclass", "type", "subtype" but
> because of different "axioms" these terms have different meaning.  It is
> "difficult" to discuss M1 and M0 as one model.

Not difficult -- I would say they are simply different models.
There are different logics out there, different terminologies.
As you may correctly surmise, I find DL's use of terminology
extremely problematic (i.e., counterintuitive to me), and also
counter to most other uses of these terms that I'm aware of.

> Question that I have: Do we want to discuss M0 if we know that
> SAM is based on M1?

A more important question is whether or not the SAM should be
based on "M1" -- I don't see where that decision was made for the
entire community, and it's a big decision. Lars Marius has added
it to the SAM issue list as a technical issue, but it's very
important to keep separate the political and technical sides here.

To my understanding, OWL was a "significant compromise" on the part
of those involved in the Web Ontology WG who didn't arrive on
the scene from the Description Logics community. It might be noted
that DL is not the majority of the KR community, just one subset with
money, and OWL only one possible representation language among many
others.

If topic maps are in some way to be defined by the SAM, are we
comfortable defining topic map semantics in terms of Description
Logics merely in order to buy political or marketing weight? I'd
much prefer this be a technical decision. Fads in KR come and go,
and in a few years DL will be gone, something else will have stepped
into the fore. If you don't believe that, look at the Obrst and
Lui historical diagram of the field in Jack Park's book on p.123;
it's a trendy little world we've entered.

I know of at least one of the Topic Map "fathers" who believes
this technology to have a long potential life, and I certainly
believe it myself. I'd hate to see us squander the semantics of
the model unnecessarily on political exigency, if that's not
too harsh a judgement on what definitions in the SAM mean for
topic map applications' ability to correctly perform reasoning.

As I said to Lars Marius privately, I think we should decide as
a community upon a set theoretic model based on technical merit,
and adopt the terminology of that school of thought if there is
an available formal language; if not, perhaps look for a different
school that has formalized their model and terminology. DL claims
its logical roots in first order logic -- FOL does not include set
theory, so they're in their own territory in this regard.

I suppose whatever happens now, one can always redefine the PSI
set when the next trend comes along -- one of the benefits of
Topic Maps is that if somebody disagrees with the semantics of
these PSIs, they can decide to define their own.

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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