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Re: interpretation of instance and subclass

From: Benja Fallenstein <b.fallenstein@gmx.de>
Date: Fri, 14 May 2004 00:09:37 +0300
Message-ID: <40A3E411.1020200@gmx.de>
To: "Burkett, Bill" <WBurkett@modulant.com>
Cc: www-rdf-interest@w3.org

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Burkett, Bill wrote:
| The problem I have is an apparent contradiction in the latter two
| statements with respect to m.  As a member of C, members of M are
| *not* also members of C.

If x is a member of X, which is a member of C, this does not imply that
x is a member of C.

However, it doesn't preclude it either. In itself, it doesn't say
anything about whether x is a member of C or not. Both is possible.

It's simply an unrelated statement:

~    a member b; b member c

says (in RDF) nothing about whether a is a member of c or not.

You seem to imply that from "m member M; M member C" it follows that "m
not member C." This is *not* correct. If it were, then there would be a
paradox, but it isn't so.

| As a subclass of C, members of M *are* also
| members of C.

This is correct.

| Is this where we find the Incompleteness of our
| rdf/rdfs representational langauge?  Is this an inherent
| paradox/contradiction that we just have to live with?

I don't think there's a paradox or contradiction on the formal level.

| You've stressed the importance of a "metaclass", Benja.  Is there some
| aspect of this term that I'm failing to understand in my understanding
| of this situation?

I don't think that's the problem -- I think the problem is that you
think that "looking at it from a certain angle,"

~    a  rdf:type  b
~    b  rdf:type  c

seems to you to imply that

~    a  NOT rdf:type  c

However, that implication is simply not true, looking at it from any
angle. The first two statements are simply independent of the third --
as indepent as

~    A  foaf:knows  B

is from

~    A  foaf:familyName  "Griffin"

Your "As a member of C, members of M are *not* also members of C" is
along the level of "As someone who knows B, A does not have the family
name 'Griffin'" -- it's correct when you interpret it in a kind of weird
way, but it's not correct if interpreted as "If A knows B, then A cannot
have 'Griffin' as their family name."

Does this help?
- - Benja
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Received on Thursday, 13 May 2004 17:10:10 GMT

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