[topicmapmail] Superclass-subclass indentation in the Omnigator

[Murray Altheim]

Steve Pepper wrote:
[...]

 > The other problem is that of confusing superclass-subclass with
 > class-instance, as the following example illustrates:
 >
 > (1)  Steve is a homo sapiens       (1a)
 >      A homo sapiens is an ape      (1b)
 >      Therefore Steve is an ape
 >
 > (2)  Steve is a homo sapiens       (2a)
 >      Homo sapiens is a species     (2b)
 >      Therefore Steve is a species
 >
 > The conclusion drawn in (1) is correct, whereas that drawn in (2)
 > is not. Why? Because (1b) is a superclass-subclass relationship,
 > whereas (2b) is a class-instance relationship. They look almost
 > identical, but they have quite different semantics and properties.

Actually, Steve, you are not an ape. You are a human.

A bit of background:

   Kingdom Animalia
     Phylum Chordata
       Class Mammalia
         Order Primates
           Superfamily Hominoidea
             Family Pongidae
               Genus Homo
                 Species Homo sapiens

Not to pick too many nits in what is a casual conversation, but
your example points out a very common mistake in modeling that
is perhaps a good thing to note. Even the above taxonomy is
incomplete, as it *could* have listed the suborder (Anthropoidea)
or the infraorder (Catarrhini). You are mixing casual names for
animals with their taxonomical structure, something a lot of
zoologists do too. Eg., there are a lot of birds here in the UK
that simply aren't the same birds as in the US, such as the
"robin". Then again, that last sentence is likely not true unless
those birds happened to fly across the Atlantic (I should have
been more specific, since I meant species or "kinds" of birds,
not individual birds).

One of the things I've been (actually) enjoying in my research is
finally getting down to reading some of the Charles Sanders Peirce
materials, as well as things about various forms of logic. One of
the things I find in both the Peirceans and others such as Jon
Awbrey is that they try to emphasize knowledge domains. There's a
good paper on this called "Pragmatic semiotics and knowledge
organization" by Torkild Thellefsen and Martin Thellefsen (I'm
trying to locate a web copy), that expresses the issue that *all*
knowledge is contextualized, ie., that concepts have their meaning
only within a given knowledge domain. This issue pervades all
communication right down to the very words we use. As stated in
the Thellefsen's paper, they "are against an objective understanding
of knowledge because we believe that knowledge is created within
contexts, and indeed, it creates contexts."

Even the word "class" is problematic. We've created a set of
PSIs for XTM that express superclass-subclass and class-instance
relationships, but we did it absent any specific domain. These
terms mean different things in different domains, and I'm as
guilty as anyone is playing loosely with the terminology. The
concept of "class" is quite different in OO programming than it
is from zoological taxonomy, and different even within various
forms of formal logics).

So the word "ape" is not a taxonomical term but simply a common
name. The error was in "a homo sapiens is an ape", as you were
mixing the domains of common names with taxonomy, as well as
using "a homo sapiens" rather loosely -- perhaps "an instance
of the species homo sapiens" or "an animal whose species is
homo sapiens". If you had said "the species homo sapiens within
the order of primates" you'd not be mixing knowledge domains.
But I don't really mean to ruin the fun of logical fallacies;
maybe Steve you really are an ape, or just maybe you deserve
your own species. :-)

Like I said, I don't mean this message as a slam on anyone, just
a gentle reminder that these types of errors generally occur due
to a lack of expressive precision as well as ignoring the lexical
and terminological contextualization that occurs due to knowledge
domains, which themselves don't always have very firm boundaries.
Knowledge modeling is a hell of a lot more difficult to do
correctly than at first glance, as I'm finding out lately. Jon
Awbrey has been trying to express these ideas, and I don't feel
I'm particularly good (yet) at doing so. Basically, binary
relations (in topic map parlance, unscoped associations) should
be considered imprecise. It's just that suddenly models begin
to look rather more complicated, rather more like the real world.

   Differential Logic, Zeroth Order Logic, The Cactus Patch
     by Jon Awbrey
   http://www.altheim.com/cs/

If I can find a reference to an online version of the Thellefsen's
article, I'll pass it along.

Murray


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

            If you're the first person in a new territory,
            you're likely to get shot at.
                                                     -- ma