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Re: ontology for rough set theory

From: Tara Athan <taraathan@gmail.com>
Date: Mon, 08 Feb 2010 10:28:12 -0800
Message-ID: <4B7057BC.5060806@gmail.com>
To: Uli Sattler <sattler@cs.man.ac.uk>, public-owl-dev@w3.org
Thanks for your help!

1. About the kind of sets:
 >is A and notA disjoint?
 >does not being a member of A imply being a member of notA?

Neither.  A thing can be both a member of A and "not" a member of A. It 
can also be neither.  The things that can belong to these sets don't 
have any inherent characteristics that lead them to belong to one class 
or another. So to fully define a set, two classes have to be specified- 
the class of things that are members and the class of things that are 
"not" members. I have been calling these properties isMemberOf and 
isComplementMemberOf because using "not" in a sense that is different 
from negation can get confusing.
Subset is a transitive and reflexive partial ordering and means the 
isMemberOf classes have a Subclass relationship AND the 
isComplementMemberOf classes have a Superclass relationship.
Complement is a symmetric relation where the isMemberOf and 
isComplementMemberOf classes are interchanged. There is a second 
transitive, reflexive partial ordering, isSameOrRougherThan, where both 
IsMemberOf and isComplementOf have a Superclass relationship.

And so on - I need to define union and intersection for a set of sets, 
determine if a set of sets is connected through pair-wise intersections 
and a number of other things that appear to me to require abstractions 
at a level above the ontology language itself, at least for DL. But if 
there is another way to approach this, I'm open to suggestions, as what 
I have done so far was way more complicated than I expected.

2. thanks for the tip about OPPL- looks like it will be very useful for 
this. I see OPPL 1 and OPPL 2 on the plugin list for Protege. Also on 
the OPPL page there is a download which includes Protege - are these 
installation methods equivalent? (that is, will I be missing something 
if I just install the OPPL plugins into Protege?)

3. I have tried Pellet in Protege, but I am having some troubles and 
can't get it to execute (I posted to pellet-users about this, no need to 
deal with that on this list).

4. Hermit looks interesting - at present, it looks like Hermit and 
Protege are mutually exclusive choices for me?  That is, from what have  
seen on the list , OWL ontologies that include DL Safe Rules cannot be 
opened in  P4?  And property-chains are not compatible with P3 or Hermit 
0.9.x, right?   So if I go with Hermit and use both property chains and 
DL Safe rules, then the ontology can only be opened in stand-alone 
Hermit 1.x? (These are all questions, I may have drawn wrong conclusions 
from what I read).

Tara

Uli Sattler wrote:
> Dear Tara,
>
> it seems to me as if you could be modeling things much more 
> straightforwardly in OWL, but first, could you let us know exactly 
> what kind of rought sets you want to implement:
>
> is A and notA disjoint?
> does not being a member of A imply being a member of notA?
>
> then, you might want to look into OPPL and rest assured, the Fact++ 
> implementors know about it crashing P4, and are working on it. Pellet 
> or Hermit are alternative reasoners.
>
> Cheers, Uli
>
>
> On 7 Feb 2010, at 22:09, Tara Athan wrote:
>
>> 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 18:28:40 GMT

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