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cycles in rdfs:subClassOf, cyc gels, extensionality of classes

From: Daniel Mahler <mahler@cyc.com>
Date: Wed, 27 Jun 2001 12:55:33 -0500
Message-ID: <15162.7701.961576.625155@mcallister.cyc.com>
To: Dan Connolly <connolly@w3.org>
Cc: Stephen Reed <reed@cyc.com>, www-rdf-logic@w3.org
Dan Connolly writes:
 > Stephen Reed wrote:
 > > 
 > > In the Cyc ontology ...
 > 
 > speaking of Cyc's ontology and DAML, I was very interested
 > to see Cyc's upper ontology in DAML:
 > 
 > 	http://www.cyc.com/cyc-2-1/cyc.daml
 > 
 > and the surrounding docs:
 > 	http://www.cyc.com/cyc-2-1/toc.html
 > 
 > But this gave me pause:
 > 
 > |  <rdf:Description rdf:about="&o;genls">
 > |          <samePropertyAs rdf:resource="subClassOf"/>
 > |  </rdf:Description>
 > 
 > first, because of typo/bug (of a very common variety,
 > due to an RDF syntax misfeature*1). That should be
 > 	rdf:resource="http://www.w3.org/2000/01/rdf-schema#subClassOf"


I thought subClassOf was in the DAML namespace as well;
it is referenced in the DAML spec.
Both our documents should be declared to be in the DAML namespace
in the header so that daml elements do not need to be qualified.
This a genral point for clarification:
do RDF(S) entities also exist in the DAML namespace.
it seems there could be different answers,
depending on wether  or not

* the are refernced in the DAML spec
   eg: http://www.daml.org/2001/03/reference.html#subClassOf-def
* DAML modifes their definition
  eg if antisymmetry gets dropped

 > or, since you've evidently decided entities aren't too ugly to use,
 > 	rdf:resource="&rdfs;subClassOf"

The document was generateted with SiSPAC/RDF API,
which sets up entities for namespaces.
That is why they have self documenting names like &o; :) .

 > 
 > But more substantively... because cyc's genls is
 > explicitly *not* extensional, and rdfs:subClassOf,

 > 

As I understand it,
in Cyc genls is extensional,

(genls A B) is just a macro for
(forall ?x (isa ?x A) (isa ?X B)).
 
Collection/Class identity is not.

 > per the DAML semantics, is explicitly extensional:

That bit I missed.
However, I think that will make DAML difficult to use,
given that most DAML agents have to operate
under resource bounded conditions.
If such agents have to believe classes to be equal
whenever they do not know of an individual that distingushes them,
they may end up making stronger inferences than intended.
It would seem to force the logic DAML to be non monotonic
since until you populate your domain with idividuals,
in particular it means that all classes start out being equal
to the (extensionally unique) empty class
until they are asserted to have members.

 > [[[
 > Warning: The RDF Schema specification demands that the subclass-relation
 > between
 >      classes must be acyclic. We believe this to be too restrictive,
 > since a cycle of subclass
 >      relationships provides a useful way to assert equality between
 > classes. Consequently,
 >      DAML+OIL (March 2001) places no such restriction on the subClassOf
 > relationship between
 >      classes;
 > ]]]

I thought this restriction had already been lifted in DAML.
There was discussion of lifting it for some time.
It would be good if formal relationship between RDF and DAML was specified.
At the last PI meetings there was not much agreement on wether
the DAML spec actually formally imports the RDF spec.

 > 
 > --        DAML+OIL (March 2001) reference description
 > http://www.daml.org/2001/03/reference.html#subClassOf-def
 > Wed, 11 Apr 2001 19:52:35 GMT
 > 
 > note the <=>, as opposed to =>
 > 
 > [[[
 > Ax32.    (<=> (PropertyValue subClassOf ?csub ?csuper) 
 >            (and (Type ?csub rdfs:Class)
 >                 (Type ?csuper rdfs:Class)
 >                 (forall (?x) (=> (Type ?x ?csub) (Type ?x ?csuper)))))
 > ]]]
 > 
 > --        DAML+OIL Axioms
 > http://www.daml.org/2001/03/axiomatic-semantics.html
 > Sun, 04 Mar 2001 17:32:03 GMT

This is consistent, if not identical with Cyc.
It is the antisymmetry of subClassOf that is different.
Note that antisymmetry is not included in the DAML+OIL
axiomatic semantics
ie there is no

(=> (and (subClassOf ?x ?y)
         (subClassOf ?y ?x))
    (sameClassAs ?x ?y))

axiom.

 > So... in saying that cyc gels is the same property
 > as rdfs:subClassOf, technically, you are licensing
 > the inference from
 > 	(and (cyc:genls X Y) (cyc:genls Y X))
 > to
 > 	(daml:sameClassAs X Y)

 > Was that on purpose? Were you aware of DAML's interpretation
 > of rdfs:subClassOf?

I was working under the assumtion that 
the antisymmetry restriction was or at least was about to be relaxed
for DAML even if not for RDF. 

 > Perhaps you sort of avoided the issue by making sure
 > there are no cycles in the genls tree in the
 > ontology you released?

I did not check. If antisymmetry is here to stay,
then I will have to change the mediating vocabulary.
(even if the ontlogy we released is acyclic,
this is only a contingent accident)

 > 
 > This is particularly important/timely because the
 > RDF Core WG is starting to discuss some nearby issues...
 > 
 >   Opening RDF Schema issues: rdfs-domain-and-range,
 >      rdfs-domain-unconstrained Dan Brickley (Tue, Jun 26 2001) 
 >   http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2001Jun/0482.html
 > 
 > We haven't gotten to this particular issue yet, but
 > we're likely to soon:
 > 
 >   Issue rdfs-no-cycles-in-subClassOf: Cycles of subClassOf properties
 > are prohibited.
 >   raised Wed, 14 Jun 2000 by Michel Klein
 >   http://www.w3.org/2000/03/rdf-tracking/#rdfs-no-cycles-in-subClassOf

I wholeheartedly agree

regards
Daniel Mahler


 > 
 > *1 re the syntax misfeature, as evidence that this is
 > a known bug/misfeature, and for backlink purposes...
 > http://www.w3.org/2000/03/rdf-tracking/#rdfms-qnames-as-attrib-values
 > 
 > -- 
 > Dan Connolly, W3C http://www.w3.org/People/Connolly/
 > 
Received on Wednesday, 27 June 2001 13:55:36 GMT

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