Re: Cardinality Restrictions and Punning

Summary: I don't yet see any particular problems.

Note:  I also don't see that this is only related to cardinalities, as
related issues arise with things like

	ObjectPropertyAssertion(eg:p eg:a eg:a)
	ClassAssertion(eg:a DataAllValuesFrom(eg:p xsd:integer))

(The mention of cardinalities had lead me to think that the issue had
something to do with a punned name counting as more than one domain
element, but I now see that this is not the case.)

peter



From: Jeremy Carroll <jjc@hpl.hp.com>
Subject: Cardinality Restrictions and Punning
Date: Thu, 20 Dec 2007 13:56:08 +0000

> 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 .

I.e.,

ObjectPropertyAssertion(eg:p eg:a eg:a)
ClassAssertion(eg:a DataMaxCardinality(0 eg:p))

> 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 .


I.e.,  (more or less)

ObjectPropertyAssertion(eg:p eg:a eg:a)
ClassAssertion(eg:a ObjectMaxCardinality(0 eg:p))
+ something like EquivalentDataProperties(eg:p eg:p)

> 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 .

I.e., (more less than more)

ObjectPropertyAssertion(eg:p eg:a eg:a)
ClassAssertion(eg:a MaxCardinality(0 eg:p))
+ something like EquivalentDataProperties(eg:p eg:p)

> 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 .

I.e.,

ObjectPropertyAssertion(eg:p eg:a eg:a)
ClassAssertion(eg:a MaxCardinality(0 eg:p))

> 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 .

I.e., (more or less)

ClassAssertion(eg:a DataMaxCardinality(0 eg:p))

> Summary:
> 
> 1 vs 2 the object restriction is inconsistent, data restriction is  
> consistent, *in the DL semantics*. One triple differs between the two.
  	      *    [added]        *
> 
> 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

Same as in OWL Full?

> 3 vs 4
> 4 is inconsistent in OWL 1.1 DL, becuase the restriction is read as an 
> ObjectRestriction *again in the DL semantics*. 3 adds more triples,
                    *          [added]        *
> and so must also be inconsistent  
> in OWL 1.1 Full.
> 
> 3 vs 5
> 5 is 3 without two triples, but is consistent.

One possible way forward (which I'm not yet championing):

In OWL 1.1 Full, there is no distinction between object and data
properties.  The class extension of both owl:ObjectProperty and
owl:DataProperty is the same as that of rdfs:Property.  Note that this
does produce observable differences between OWL 1.1 DL and OWL 1.1 Full,
but only related to punning object and data properties.