Re: RDF vocabulary definitions

The rdf-mt document http://www.w3.org/TR/2002/WD-rdf-mt-20021112/ 
says in Appendix A, "RDF Axioms":
    rdf:type(?x,?y)  iff  ?y(?x)
The triple translation is
    <?x> <rdf:type> <?y>  iff  <?x> <rdfs:subClassOf> <?y>
The KR translation is
    $x has type = $y  iff  $x isa* $y
============ 
Dick McCullough 
knowledge := man do identify od existent done
knowledge haspart list of proposition

  ----- Original Message ----- 
  From: Jon Hanna 
  To: www-rdf-interest@w3.org 
  Sent: Tuesday, November 19, 2002 9:50 AM
  Subject: RE: RDF vocabulary definitions



  > The two triples have the same meaning; either one implies the other.
  >
  > <_:MyClass> <rdf:type> <rdfs:Class>
  > <_:MyClass> <rdfs:subClassOf> <rdfs:Class>

  Are you sure?

  The first indicates that MyClass is a category of "thing" in some shape or
  form.
  The second indicates that MyClass is a category of category of "thing".

  I can see how one can say that the second implies the latter (since
  "category of thing" is itself a "thing"), but not how the first implies the
  former.

  I'd be grateful if you could explain this, preferably using either natural
  language or with reference to the RDFS closure concept described in rdf-mt
  (any other notation is likely to leave me at a loss).

  For the record, in terms of RDFS closures going from the latter to the
  former is easy once we add the triple <rdfs:Class> <rdf:type> <rdfs:Class>:

  <xxx> <rdfs:subClassOf> <yyy> .
  <aaa> <rdf:type> <xxx> .
  entails
  <aaa> <rdf:type> <yyy> .

  hence:

  <_:MyClass> <rdfs:subClassOf> <rdfs:Class> .
  <rdfs:Class> <rdf:type> <rdfs:Class> .
  entails
  <_:MyClass> <rdf:type> <rdfs:Class> .