Issue 5.3

Heres a non-technical summary of the basic idea of how to resolve 
issue 5.3 along the lines currently being worked out. I am sending 
this now in case the issue comes up at the telecon.

1. The OWL 'universe' consists of some subclasses of the RDFS 
universe; the OWL vocabulary is restricted (by domain and range 
assertions, mostly) to this sub-universe (consisting of owl:Thing, 
owl:Class, owl:Property). However, exactly how the OWL universe 
relates to the RDFS universe is not yet specified.

2. The 'weak' meanings of the OWL vocabulary can be given without 
making any assumptions about the relationship between the OWL 
universe and the RDFS universe. These meanings correspond roughly to 
the DAML-style semantics that Peter refers to in issue 5.10, ie they 
do not incorporate any assumptions about the existence of classes 
that are not explicitly named. So they do not support many of the 
'intuitive' entailments that Peter has pointed out. (Though see 7. 
below.)

3. These weaker meanings can be applied to the entire RDFS domain if 
one wishes, ie it is perfectly coherent to assert things like

rdfs:Class rdfs:subClassOf owl:Class .

in order to claim that the OWL universe and the RDFS universe are the 
same. This allows the OWL vocabulary to be used (with its weak 
meaning) in situations where classes may be instances, for example.

3a. The 'Russell paradox' RDF graph is a simple contradiction in this 
semantics.

4. If one makes additional assumptions about the OWL universe, so 
that its various parts are disjoint in the ways described in the OWL 
MT, and that this restricted universe is closed under the various 
class constructors (such as union/intersection and restrictions) then 
one gets the 'strong' meanings of full OWL, but on a more restricted 
universe. This supports a lot more entailments and also allows 
efficient DL reasoners to work properly, providing a computational 
guarantee of inferential power, but only on a suitably restricted 
('layered') use of the OWL vocabulary. Still, many users may be happy 
to stay inside the restrictions in order to gain the extra utility.

4a. If you were to add these assumptions to the unrestricted RDFS 
universe, the Russell paradox graph would be a genuine paradox, since 
these semantic assumptions would require it to be true.

5. There is a syntactic criterion which can be applied to an OWL/RDF 
graph to detect when it 'fits' inside the restricted full-OWL 
category (and therefore it is kosher to use the stronger inference 
procedures on it) but the one I have is rather complicated and may be 
too expensive to use in practice. Probably a simpler criterion could 
be invented; I think Peter has one, but I can't follow the details. 
Of course, one way to say this would be to refer to the translation 
from the OWL abstract syntax, but it would be nice to have a quick 
check that could be applied directly to an RDF graph.

6. It is possible to transfer more of the 'strong' meaning to the 
unrestricted RDFS-wide use of the OWL vocabulary - for example, it is 
certainly harmless to add closure under unions and intersections - 
but determining the exact limits of this is a research problem. 
Basically, we have to invent a new formal set theory and prove it 
consistent. (My own view is that this isn't worth doing: if we need 
to get this technical in order to provide a web language for general 
use, we are barking up the wrong tree.)

7. I am pretty confident that (modulo minor bugs) this semantics 
agrees with the picture one would get by starting from the abstract 
syntax, applying Peter's MT to it, and then translating it into RDF. 
That is, it produces the same entailments on any OWL/RDF that is a 
translation of any well-formed abstract OWL. I confess however that I 
have not written out a detailed proof of this.

8. When all this is done by translation into Lbase (or equivalent), 
the 'weak' meanings correspond to straightforward FOL transcriptions 
of the semantic meanings, and the 'strong' meanings involve adding a 
number of extra comprehension axioms, most of them of the form
(forall <class, property> (exists <class> .....))

9. There are some unresolved issues about the need to 'strengthen' 
parts of the RDFS MT. We are working on those. They are not 
show-stoppers but we need to get the details right.

Write-up coming soon (Friday).

Pat

PS. Peter's help has gone from the acknowledgments stage to the 
co-author stage at this point, but he isn't responsible for *this* 
message and may want to disown parts of it.

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Received on Wednesday, 18 September 2002 20:51:51 UTC