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Re: subclasses (RDF vocabulary definitions)

From: Frank Manola <fmanola@mitre.org>
Date: Thu, 21 Nov 2002 18:50:27 -0500
Message-ID: <3DDD7143.4080900@mitre.org>
To: "Richard H. McCullough" <rhm@cdepot.net>
CC: www-rdf-interest@w3.org, David Menendez <zednenem@psualum.com>, Brian McBride <bwm@hplb.hpl.hp.com>

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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Received on Thursday, 21 November 2002 18:33:34 GMT

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