Re: Re[2]: RDF vocabulary definitions

I have no trouble at all understanding concepts, concept-formation, classification, etc.  But I'm having trouble understanding the terminology being used in RDFS, because there are no clear definitions of terms.  The informal descriptions are helpful, but they leave many questions in my mind.

I read your paper, and I am interested in the "duality principle  in the classification theory" that you mentioned.  Could you tell me what that means?
============ 
Dick McCullough 
knowledge := man do identify od existent done
knowledge haspart list of proposition

  ----- Original Message ----- 
  From: Leonid Ototsky 
  To: Richard H. McCullough 
  Cc: www-rdf-interest@w3.org ; David Menendez 
  Sent: Wednesday, November 20, 2002 7:42 PM
  Subject: Re[2]: RDF vocabulary definitions


  Hello Richard,

  Thursday, November 21, 2002, 2:31:44 AM, you wrote:

  RHM> I have been frustrated in my attempts to pin down the meaning of "Class".  There are so many documents that I have trouble finding one which addresses my concerns, and almost as much trouble
  RHM> re-finding it later.

  RHM> The first documents that I found when I joined RDF-interest stated (paraphrasing), "Class is concept".  Another document that I found within the last hour stated (paraphrasing) "Class is the set
  RHM> of types", as you indicated based on your examination of RDF-MT.

  The "Class" problem was discussed long time ago in biology etc. It has
  much more interesting sides comparing current discussions in the ontology communities !
  See for example my paper "To keep abreast of the 21st century" -
  http://ototsky.mgn.ru/it/21abreast.htm

  Best regards,
   Leonid
  mailto:leo@mmk.ru and copy to leo@mgn.ru
  =====================================================
  Leonid Ototsky,
  http://ototsky.mgn.ru
  Chief Specialist of the Computer Center,
  Magnitogorsk Iron&Steel Works (MMK)- www.mmk.ru
  Russia
  =====================================================



  RHM>   ----- Original Message -----
  RHM>   From: Richard H. McCullough
  RHM>   To: www-rdf-interest@w3.org ; David Menendez
  RHM>   Sent: Wednesday, November 20, 2002 12:29 PM
  RHM>   Subject: Re: RDF vocabulary definitions


  RHM>   Your excursion into rdf-mt is only obscuring the facts, viz.

  RHM>       Thing, Class, Property are all classes.
  RHM>       class is an alias of concept.
  RHM>       RDFS "definition" of class is wrong.
  RHM>   ============
  RHM>   Dick McCullough
  RHM>   knowledge := man do identify od existent done
  RHM>   knowledge haspart list of proposition

  RHM>     ----- Original Message -----
  RHM>     From: David Menendez
  RHM>     To: www-rdf-interest@w3.org
  RHM>     Sent: Wednesday, November 20, 2002 9:49 AM
  RHM>     Subject: Re: RDF vocabulary definitions


  RHM>     At 7:58 AM -0800 2002-11-20, Richard H. McCullough wrote:
  RHM>       I suppose it would be less confusing to say that
  RHM>       Property is the class that all properties are subclasses of.
  RHM>       In the sense used in RDFS, every property is a class.
  RHM>       For example, hasSex is the class of pairs [person; sex]
  RHM>       and its individuals are [John Doe; male], [Jane Doe, female], ...


  RHM>     I think I understand your confusion: you and RDFS are using the word class in different ways.


  RHM>     An rdfs:Class is a thing which may be used as the value of rdf:type. The set of all members of a rdfs:Class is the set of all resources which have that rdfs:Class as a value of rdf:type.


  RHM>     As I understand RDF-MT:


  RHM>     I(X) is the interpretation of the resource identified by X


  RHM>     IEXT(I(X)) is the extension of a rdf:Property; a set of pairs of the form (subject, object). For example, IEXT(I(eg:hasSex)) = {(I(eg:john_doe), I(eg:male)), (I(eg:jane_doe), I(eg:female)),
  RHM> ...}


  RHM>     ICEXT(I(X)) is the extension of a rdfs:Class; a set of resources which belong to the rdfs:Class. For example, ICEXT(I(eg:Person)) = {I(eg:john_doe), I(eg:jane_doe), ...}


  RHM>     ICEXT(X) is defined as the set of Y such that (Y, X) is in IEXT(I(rdf:type)).


  RHM>     IC is defined as ICEXT(I(rdfs:Class)), the set of resources which represent classes. For all X in IC, ICEXT(X) is a subset of ICEXT(I(rdfs:Resource))


  RHM>     rdfs:Class and rdf:Property are members of IC. They represent distinct concepts which have different effects on the model.


  RHM>     To summarize:


  RHM>     eg:hasSex is a resource of the type rdf:Property
  RHM>     I(eg:hasSex) is the concept of the property "sex"
  RHM>     IEXT(I(eg:hasSex)) is the set of pairs corresponding to people and their sex


  RHM>     eg:Person is a resource of the type rdfs:Class
  RHM>     I(eg:Person) is the concept of personhood
  RHM>     ICEXT(I(eg:Person)) is the set of resources which are people
  RHM> --
  RHM> Dave Menendez - zednenem@psualum.com - http://www.eyrie.org/~zednenem/