Action Item re Guide disjoint example

Suggested modifications to Guide re large number of disjoint subclasses.

Here is what I have come up with.  Minimally, we need to add PART 1.
PART 2 seems useful.  PART 3 is getting pretty verbose.  

I propose to include PARTs 1 and 2.  Corrections and comments welcome.

- Mike

[EXISTING] 

As the number of mutually disjoint classes grows, the number of
disjointness assertions grows proportionally to n<sup>2</sup>.
However, in the use cases we have seen, n is typically small.

[ADDITION PART 1]

When n is large, alternate approaches can be used to avoid quadratic
growth in the number of assertions.  One such method is illustrated in
the
<a
href="http://www.w3.org/TR/2003/CR-owl-test-20030818/proposedByIssue#I5.21-0
02">
OWL test suite
</a>

[ADDITION PART 2]

The illustrated method works as follows.  We describe a parent class
whose elements have a property with cardinality equal to one.  That
is, each instance must have one and only one value for this property.
Then, for every subclass of the parent we require that its instances
must have a particular unique value for the property.  In which case
none of the distinct subclasses can have members in common.

[ADDITION PART 3]

- The class Reptile is a subclass of things with exactly one
  family-name.

- The class Amphisbaenidae is a subclass of Reptile and its members have
  family-name 'Amphisbaenidae'.

- The class Crocodylidae is a subclass of Reptile and its members have
  family-name 'Crocodylidae'.

- The class Gekkonidae is a subclass of Reptile and its members have
  family-name 'Gekkonidae'.

Any member of the class Amphisbaenidae cannot also be a member
of the class Crocodylidae since their literal family-names are not
equal.  By repeating the family-name assertion for each subclass of
Reptile, where each class uses a distinct literal name, we can ensure
that all the subclasses of Reptile are disjoint using only order n 
assertions.


Michael K. Smith  PhD, PE
EDS - Austin Innovation Centre
98 San Jacinto
Austin, TX 78701
 
Phone:+1-512-404-6683
mailto:michael.smith@eds.com <mailto:michael.smith@eds.com>

Received on Thursday, 13 November 2003 13:05:57 UTC