[Pellet-users] cardonality restrictions produce erroneous taxonomy

[Michael Smith]

On Tue, 2008-05-27 at 14:07 +0200, Christina Tziviskou wrote:

> I want to include cardinality properties restriction,
> so I'm using *all* the following for a property:

For readability I'm restating using the OWL 2 functional syntax,
numbering the axioms, and naming the entities

1) EquivalentClasses( D SomeValuesFrom( p R ) )
2) EquivalentClasses( D MinCardinality( a p R ) )
3) EquivalentClasses( D MaxCardinality( b p R ) )

I don't know what numbers were used for the cardinality restrictions,
providing these might help some.  I've used (a,b) here

> The results is that Pellet does not produce the right taxonomy for the
> classes in the KB.
> Instead, If I use only one of the above (it does not matter which one),
> the taxonomy is correct.
> Even If I use only the second and third invocations without the first
> one, I keep taking a wrong taxonomy.

Incorrect in what way?  Can you provide your expectations and the
computed results for some specific cardinalities?

I think this may be a misunderstanding of how the equivalent class
axioms are going to interact.  Equivalence is transitive, so the 3
axioms above can be rewritten as the following

4) EquivalentClasses( D SomeValuesFrom( p R ) MinCardinality( a p R ) MaxCardinality( b p R ) )


Some interesting things about this equivalence:

+ If a == 0, the MinCardinality description is equivalent to owl:Thing,
but must also be equivalent the the existential, so all individuals in
the ontology will have p.R fillers and will be instances of D

+ If a == 1, the MinCardinality description is no different from the
existential restriction and can be ignored

+ If a > 1, the SomeValuesFrom and the MinCardinality restriction
interact to prohibit individuals with fewer than a fillers from using
the p property.

For all cases where a >= 1, the axioms collectively any individual using
the p property is a instance of the D class and must contain >= a
fillers and <= b fillers, all of which are instances of R.

Finally, you don't include domain and range axioms, but based on the
variable names you use, I think they may exist.  If so, there will be
additional interactions worth noting.

5) PropertyRange(p R)

Together with (4) above will cause D to be equivalent with owl:Thing for
all values of (a,b)

-- 
Mike Smith

Clark & Parsia