Re: subclasses (RDF vocabulary definitions)

I don't think intension vs. extension is the issue here; the whole point is that the rdfs:subClassOf property does not rule out the alternative that the two Classes are identical, i.e., subsume the same group of individuals.

In reality, intension and extension are inseparable.

In RDFS, I don't think intension is considered.  I think rdf:type is still evaluated in terms of extension.

Whew, what a lot of "I think"s!
I'm just telling you how I understand it to be.
============ 
Dick McCullough 
knowledge := man do identify od existent done
knowledge haspart list of proposition

  ----- Original Message ----- 
  From: Frank Manola 
  To: Richard H. McCullough 
  Cc: www-rdf-interest@w3.org ; David Menendez ; Brian McBride 
  Sent: Thursday, November 21, 2002 3:50 PM
  Subject: Re: subclasses (RDF vocabulary definitions)


  Richard H. McCullough wrote:

  > Brian said:
  > 
  >   [[ll classes are subclasses of themselves.
  > <<this is true, but RDF Schema should use proper subsets instead of subsets.
  > Using subsets logically permits such absurdities as: the set of all men is
  > identical to the set of all animals.>>]]
  > 
  > I'm intrigued by that one.  We have a major flaw if that is true.  Care to
  > explain?


  I'm intrigued too, but I'd like to discuss this in terms of logical 
  entailments and extensions, rather than KR notation (and yes, I 
  understand the difference between subsets and proper subsets).

  Background:  This started with Brian saying:

  > A class A is a subclass of a class B if and only if all the members of A 
  > are also members of B.
  > All classes are subclasses of themselves.
  > <<this is true, but RDF Schema should use proper subsets instead of subsets.
  > Using subsets logically permits such absurdities as: the set of all men is
  > identical to the set of all animals.>>


  (with your comment delimited by <<>>).

  My impression is that the basic problem here is trying to consider 
  subclass as specifying an intensional rather than an extensional 
  relationship.  In RDFS, a class is a resource that represents the set of 
  things which have that class as the value of their rdf:type property. 
  Given that definition, it certainly could be true that at any given 
  point, the class Man (i.e., the set of things that have class Man as the 
  value of their rdf:type property) could be the same as (have the same 
  members as) the class Animal (the set of things that have class Animal 
  as the value of their rdf:type property).  However, there is no 
  specification that the two classes are (or could be) intensionally 
  identical.  All the Semantics spec (entailment rdfs9) says is that

  Man rdfs:subClassOf Animal
  aaa rdf:type Man

  entails

  aaa rdf:type Animal

  It does NOT say that

  Man rdfs:subClassOf Animal
  aaa rdf:type Animal

  entails

  aaa rdf:type Man

  Could you cast what you see as the problem is these terms?

  --Frank


  -- 
  Frank Manola                   The MITRE Corporation
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