Cardinality Restrictions and Punning

Hmmm, this is tricky, harder than I thought.

Some examples. I'm struggling as to the discussion.


Example 1:
Consistent:
[punning on eg:p]

eg:a rdf:type owl:Thing .
eg:a eg:p   eg:a .
eg:p rdf:type owl:ObjectProperty .
eg:p rdf:type owl:DataProperty .
_:r rdf:type owl:DataRestriction .
_:r owl:maxCardinality "0"^^xsd:int .
_:r owl:onProperty eg:p .
eg:a rdf:type _:r .

Example 2:
Inconsistent.

eg:a rdf:type owl:Thing .
eg:a eg:p   eg:a .
eg:p rdf:type owl:ObjectProperty .
eg:p rdf:type owl:DataProperty .
_:r rdf:type owl:ObjectRestriction .
_:r owl:maxCardinality "0"^^xsd:int .
_:r owl:onProperty eg:p .
eg:a rdf:type _:r .


Example 3 - not in OWL 1.1 DL, because mapping rules don't apply.
Who knows whether this is consistent or not, and how we would go about 
an OWL Full semantics. I think it should be inconsistent in OWL Full.

eg:a rdf:type owl:Thing .
eg:a eg:p   eg:a .
eg:p rdf:type owl:ObjectProperty .
eg:p rdf:type owl:DataProperty .
_:r rdf:type owl:Restriction .
_:r owl:maxCardinality "0"^^xsd:int .
_:r owl:onProperty eg:p .
eg:a rdf:type _:r .


Example 4
Inconsistent

eg:a rdf:type owl:Thing .
eg:a eg:p   eg:a .
eg:p rdf:type owl:ObjectProperty .
_:r rdf:type owl:Restriction .
_:r owl:maxCardinality "0"^^xsd:int .
_:r owl:onProperty eg:p .
eg:a rdf:type _:r .

Example 5
Consistent

eg:a rdf:type owl:Thing .
eg:p rdf:type owl:DataProperty .
_:r rdf:type owl:Restriction .
_:r owl:maxCardinality "0"^^xsd:int .
_:r owl:onProperty eg:p .
eg:a rdf:type _:r .



Summary:

1 vs 2 the object restriction is inconsistent, data restriction is 
consistent. One triple differs between the two.

1,2 vs 3 if we don't specify object restriction or data restriction, 
using owl:Restriction with punning declarations, then we are outside the 
scope of OWL 1.1 DL, but OWL 1.1 Full semantics needs to say something

3 vs 4
4 is inconsistent in OWL 1.1 DL, becuase the restriction is read as an 
ObjectRestriction. 3 adds more triples, and so must also be inconsistent 
in OWL 1.1 Full.

3 vs 5
5 is 3 without two triples, but is consistent.