Re: RDF vocabulary definitions

Re: RDF vocabulary definitionsDavid
I appreciate your effort.  I'm afraid I was erroneously venting my frustration on you.  I apologize for that.

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 re-finding it later.

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 of types", as you indicated based on your examination of RDF-MT.

Just referring to your summary, perhaps you didn't recognize one of its consequents:

    hasSex  type  Property    implies    Property  subClassOf  Class
============ 
Dick McCullough 
knowledge := man do identify od existent done
knowledge haspart list of proposition

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


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

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

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


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


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


    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.


    As I understand RDF-MT:


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


    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)), ...}


    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), ...}


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


    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))


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


    To summarize:


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


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