S&AS: not enough type statements OWL Full-entailed from empty RDF graph

In my last review of S&AS, just before the decision to go 
to last call (see [1] and the discussion that followed)
I noted that in the definition of OWL interpretations
IC needs to be given more elements, to become completely
consistent with the editor's version of the RDF Semantics
It was agreed to take this up later when the next version
of the RDF Semantics document becomes more official.

However, only after the decision to go to last call
I realized that exactly the same changes can also be 
motivated by means of test cases, in a way that does not 
depend on the semantic theory.

Namely, a certain analogy between RDF entailment, 
RDFS entailment, and OWL Full entailment is not complete.
Recall that each RDF graph (including the empty RDF graph)
RDF-entails the RDF statement
  rdf:type rdf:type rdf:Property .,   and
RDFS-entails RDF statements like
  rdfs:domain rdf:type rdf:Property .
  rdfs:Class rdf:type rdfs:Class .
To summarize, each RDF(S) vocabulary element that is clearly a 
property or class, is defined as a property or class in this way 
with an entailed explicit RDF statement.

However, this holds to a large extent, but does not hold completely, 
for OWL Full.
From the empty graph, there is OWL Full-entailment of RDF statements 
  owl:sameIndividualAs rdf:type rdf:Property .
  owl:Thing rdf:type rdfs:Class .
and very many other statements like this, but it seems that the
following 12 statements are not OWL Full-entailed, given the
definition in the last call version of S&AS:

  owl:Class rdf:type rdf:Class .
  owl:Restriction rdf:type rdf:Class .
  owl:ObjectProperty rdf:type rdf:Class .
  owl:DatatypeProperty rdf:type rdf:Class .
  owl:AnnotationProperty rdf:type rdf:Class .
  owl:OntologyProperty rdf:type rdf:Class .
  owl:Ontology rdf:type rdf:Class .
  owl:AllDifferent rdf:type rdf:Class .
  owl:FunctionalProperty rdf:type rdf:Class .
  owl:InverseFunctionalProperty rdf:type rdf:Class .
  owl:SymmetricProperty rdf:type rdf:Class .
  owl:TransitiveProperty rdf:type rdf:Class .

It is interesting to note that the requirement that
ICEXT has IC as domain necessarily leads to exactly the correction
of these omissions.


For future reference I recall from my review the summary of changes 
required to S&AS :

Replace the sentence
>CEXTI is then defined as CEXTI(c) = ...
by the following two sentences:
"CI, the set of classes, is defined by
CI = {x in RI | <x,SI(rdfs:Class)> is in EXTI(SI(rdf:type)>}.
CEXTI is a mapping from CI to P(RI), defined for each
c in CI by CEXTI(c) = [exactly what is already in the text].

The first table, "Conditions concerning the parts of the OWL
universe and syntactic categories" needs to be completed
in connection with CI:  Each of the 11 empty cells in the
first column (SI(E) is in ...) needs to be filled with the
set CI.  Otherwise, as discussed before, many invocations
of CEXTI that occur later are are not clearly legal.
(For two of these cells, for rdfs:Datatype and rdf:List,
this amounts to a repetition from the RDF Semantics document.)

I believe that five more lines need to be added to this table,
for the following vocabulary elements
(the reason is, as before, that otherwise it is not clear
that various function invocations occurring later are legal):

If  E is                      .SI(E). .CEXTI(SI(E)).    and
  owl:Datarange                 CI       ?      ? subsetof CI
  owl:SymmetricProperty         CI       ?      ? subsetof IOP
  owl:FunctionalProperty        CI       ?      ? subsetof IOP
  owl:InverseFunctionalProperty CI       ?      ? subsetof IOP
  owl:TransitiveProperty        CI       ?      ? subsetof IOP
Where I put question mark it would be most natural to define new
specific sets, in analogy to many other sets already defined.

I checked that the appendix remains completely consistent: each 
invocation of CEXTI done there is legal when these changes 
are made.


(I am taking up the other point that Peter arose in connection with
my review of S&AS in relation to RDF Semantics, whether 
IC and ICEXT are part of the definition of RDFS-interpretation, 
on rdf-comments.)

Herman ter Horst


Received on Thursday, 10 April 2003 09:59:06 UTC