Re: equivalentTo / sameClassAs / sameIndividualAs puzzle

From: pat hayes (
Date: 07/09/01

>On Mon, 9 Jul 2001, Jeff Heflin wrote:
> > Ian Horrocks wrote:
> > >
> > > On July 7, Dan Brickley writes:
> > > >
> > > > I was concerned mostly with the classes case as I'm thinking about the
> > > > subClassOf cycles issue. Reading on, same goes for samePropertyAs,
> > > > sameIndividualAs; it seems equivalentTo is the odd one out, by talking
> > > > about 'terms'.
> > >
> > > You are reading more into the use of "terms" than was intended. It is
> > > just an attempt to be vague/general w.r.t. the kinds of thing that are
> > > being stated to be equivalent.
> > >
> >
> > I think the definition for equivalentTo should say that "X is an
> > equivalent resource to Y," where resource is as defined in RDF. Since
> > RDF resources can be classes, properties or anything else given a URI,
> > this is compatible with the various subproperties of equivalentTo.
> > sameIndividualAs is different from equivalentTo because the set of DAML
> > individuals do not include classes or properties.
>Aha! That's it. From reading the spec, it wasn't entirely clear to me
>what DAML+OIL terms individuals. The schema definition suggests its a
>synonym for 'thing':
>	<Property rdf:ID="sameIndividualAs">
>	<rdfs:label>sameIndividualAs</rdfs:label>
>	<rdfs:comment>
>	for sameIndividualAs(a, b), read a is the same individual as b.
>	  </rdfs:comment>
>	<rdfs:subPropertyOf rdf:resource="#equivalentTo"/>
>	<rdfs:domain rdf:resource="#Thing"/>
>	<rdfs:range rdf:resource="#Thing"/>
>	</Property>
>Could someone explain to me which things precisely are considered
>individuals? I gather properties and classes are out of the
>picture. Any others?

My understanding is that 'individual' is synonymous with 'DAML+OIL 
object' and simply means anything in the semantic domain. The use of 
'individual' for anything in the domain of quantification is a 
familiar convention in logic, but maybe it needs to be spelled out 
for a wider audience.

As far as I am concerned, this does not in fact *rule out* properties 
and classes; those things could be individuals in some 
interpretations that satisfy the model-theoretic rules. The model 
theory just says that AD is 'a set', without saying that this set 
must not contain come particular category of things. In particular, 
it could contain some of its own subsets. However, there is no way to 
state in DAML+OIL any conditions that would force classes or 
properties to be in the universe of discourse, so it would be 
consistent to insist, as a kind of overall semantic strategy,  that 
they never are. This means that one can have several different model 
theories which all 'fit' the language equally well but reflect 
different metaphysical assumptions, which in turn means that the 
language is limited in what it can ultimately say, perhaps not 

This is in fact very like the situation in model theory for ordinary 
first-order logic, where it is often assumed that the universe does 
not contain any properties or relations; but the normal semantic 
rules do not, in fact, require this restriction.

Pat Hayes

IHMC					(850)434 8903   home
40 South Alcaniz St.			(850)202 4416   office
Pensacola,  FL 32501			(850)202 4440   fax

This archive was generated by hypermail 2.1.4 : 04/02/02 EST