ontology for rough set theory

I have built an ontology for rough sets (hasMember and
hasComplementMember are not disjoint or covering) with properties such
as hasSubset and hasComplement.
I am using Protege 4 and Fact++.
I found out from the beginning about the restrictions on complex role
inclusions, but
I thought I would be able to  implement inference in one direction at
least (A hasSubset B entails certain things about the members of A & B,
where A,B are individuals sets) using  property chains. This worked for
hasSubset. The reverse direction (inferring A hasSubset B from
assertions about its members) I was able to implement using general
class axioms, inserting nominal classes and then duplicating the axioms
for all individual sets in the ontology.

But I was unable to implement hasComplement in this way: I had to resort
to general class axioms on nominal sets even for the first direction.

So I have a couple of questions:
1. This seems like it would be an ubiquitous issue in any situation
dealing with sets, collections etc.  Are there any existing ontologies
that address these issues so I could see how other people have dealt
with it?
2. Duplicating all those general class axioms is tedious, and I am only
considering it as a place holder for DL-Safe SWRL rules, or as a pattern
for an interface using OWL API. Are there any other options (tools) that
would make this easier on me?
3. P4 and Fact++ are driving me nuts because Fact++ crashes P4 every two
or three times that it runs, so I am constantly restarting P4. Any
suggestions for other tools would be welcome.

Thanks, Tara

Received on Monday, 8 February 2010 10:33:58 UTC