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Re: DTTF: darkest africa

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 30 May 2002 10:56:56 -0400
To: jjc@hplb.hpl.hp.com
Cc: www-webont-wg@w3.org
Message-Id: <20020530105656D.pfps@research.bell-labs.com>

From: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Subject: DTTF: darkest africa
Date: Thu, 30 May 2002 10:30:35 +0100

[...]

> I suggest that we should identify the dark graphs
> of web ont. These being the graphs that we treat
> as of undefined semantics rather than consistent
> or inconsistent. These being marked on the map
> as unmapped.
> 
> Possible text would be:
> 
> [[[
> RDF graphs are assigned a truth value true or
> false depending on whether they have any interpretations
> according to a model theory.

This is not consistent with how the RDF model theory works.  Given an RDF
or RDFS interpretation and an RDF graph, the RDF model theory assigns a
truth value to the graph in that interpretation.  This is very different
from assigning a syntactic structure the value false without reference to
an interpretation.

> RDFS Model Theory assigns all graphs true.

This is definitely not true.  It is true that in every RDF graph has 
an RDFS interpretation (and thus an RDF interpretation) in which the RDF
graph is assigned true.

> OWL Model theory assigns certain RDF graphs the value
> false because they are self-contradictory in OWL.

Well, there is no OWL model theory as of yet, but let's disregard that.

If the OWL model theory works in the same way as the RDF model theory, then
it will first define the notion of an OWL interpretation, and then assign
truth values to (some) RDF graphs in these interpretations.  Some such
graphs, may have no OWL interpretations for which they are assigned true.
This is very different from assigning a syntactic structure the value false
without reference to an interpretation.

> There are some graphs which cause particular problems
> to the current OWL model theory, and this version
> of OWL leaves their interpretation as undefined.
> These graphs are known as 'dark graphs'.

Which version of OWL?  Are you suggesting that the OWL model theory go to a
multi-valued semantics?  If so, you need to lay a *lot* of groundwork.  It
doesn't seem so, but I'm not sure.

> More precisely, an implementation should issue a
> warning message indicating that the semantics of
> such graphs is undefined, and that there wil[l] be
> interoperability problems. 

There are several possibilities here:

1/ The problematic graphs can be determined syntactically, in which case it
   would be better to simply say that they are syntactically illegal.
2/ The problematic graphs have to be determined semantically, in which case
   you are almost certainly asking for a multi-valued semantics.

> Having done so, an
> implementation may treat a dark graph as 
> having entailments of the implementation's
> chosing. The simplest behaviour is to treat the 
> graph as self-contradictory.

Well, this doesn't really follow, nor is it desirable.  There may be many
different reasons for a graph to have an ``undefined'' or unknown meaning.
However, if you admit such graphs, it is far better to precisely say how
they behave with respect to OWL as opposed to letting each implementation
treat them differently.  In any case, ``treating [a] graph as
self-contradictory'' doesn't indicate anything about how the graph should
be treated.

> Dark graphs are identified because either they
> directly contain a dark triple, or because they 
> RDFS entail a dark triple.

> Dark triples are triples that match any of the 
> following (using * as a wildcard).
> 
> (owl:* does not match owl:Thing)
> 
> * rdfs:subClassOf owl:* .
> * owl:sameClassAs owl:* .
> * rdfs:subPropertyOf owl:* .
> * rdfs:subPropertyOf rdf:type .
> * rdfs:subPropertyOf rdfs:subPropertyOf .
> * rdfs:subPropertyOf rdfs:subClassOf .
> * rdfs:subPropertyOf rdfs:range .
> * rdfs:subPropertyOf rdfs:domain .
> * owl:samePropertyAs owl:* .
> * owl:samePropertyAs rdf:type .
> * owl:samePropertyAs rdfs:subPropertyOf .
> * owl:samePropertyAs rdfs:subClassOf .
> * owl:samePropertyAs rdfs:range .
> * owl:samePropertyAs rdfs:domain .
> * owl:onProperty rdf:type .
> * owl:onProperty rdfs:subPropertyOf .
> * owl:onProperty rdfs:subClassOf .
> * owl:onProperty rdfs:domain .
> * owl:onProperty rdfs:range .
> * owl:onProperty owl:* .
> * owl:toClass owl:* .
> * owl:toClass rdf:Property .
> * owl:hasClass owl:* .
> * owl:hasClass rdf:Property .
> * owl:sameIndividualAs owl:nil .
> * owl:equivalentTo owl:* .
> * owl:equivalentTo owl:* .
> * owl:equivalentTo rdf:type .
> * owl:equivalentTo rdfs:subPropertyOf .
> * owl:equivalentTo rdfs:subClassOf .
> * owl:equivalentTo rdfs:range .
> * owl:equivalentTo rdfs:domain .
> * owl:equivalentTo owl:nil .
> 
> 
> These either allow an ontology to attempt to
> describe itself or try and extend the OWL language.
> ]]]

Huh?  You are now saying that the behaviour of OWL graphs that include

	ex:person owl:sameClassAs owl:ABCDEF

is undefined?  Why?  What is wrong with this?

> I suspect my list is incomplete, the rules for
> completing it are:
> - when in doubt add the triple
> - the only reason for not adding the triple is
>   + it seems genuinely useful
> and
>   + it expresses something that can be expressed
>     in mainstream description logic.
> I am assuming that the List vocabulary is in the
> owl namespace. Otherwise it would need to be
> explicitly treated in the black list. 

I don't understand this rationale for making triples dark.  I don't
understand the rationale for identifying triples as dark in this way.  I
don't understand the implications here of making triples dark.

> Of course, we could address the RDFS layering issue
> simply by deciding that all the dark graphs identified
> above are contradictions. Then we would respect all
> their RDFS entailments (trivially). I wouldn't like
> that much but could live with it, and would prefer it
> to making RDF Model Theory non-normative.

Huh?  

> If we wanted to stress conformance with RDFS then
> we would have slightly different text
> 
> [[[
> implementation may treat a dark graph as 
> having its RDFS entailments and any others
> of the implementation's chosing. The simplest
> implementation is to treat a dark graph as
> self-contradictory.
> 
> ]]]
> 
> (I doubt there would be group consensus for that).
> 
> If we wished to stress the dangers of paradox we
> would have text
> 
> [[[
> implementors should note that at least some
> dark graphs appear self-contradictory in
> interesting ways e.g.
>   testA, testB, testC
> ]]]

> Jeremy

I don't think that this proposal can lead to a solution of the layering
paradoxes.  I certainly don't see any such solution above.

Peter F. Patel-Schneider
Received on Thursday, 30 May 2002 10:57:48 GMT

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