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Re: RDF vocabulary definitions

From: David Menendez <zednenem@psualum.com>
Date: Wed, 20 Nov 2002 12:49:15 -0500
Message-Id: <a05111b0aba01711fd7c5@[10.0.1.2]>
To: <www-rdf-interest@w3.org>
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/
Received on Wednesday, 20 November 2002 12:47:53 GMT

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