[seek-kr-sms] Rendering DL in Growl/Proposed Growl change/Bertram's domain maps

[Serguei Krivov]

Hi,
I thought if we could use growl as an interface for a dl reasoner such
as RACE and I found that  we in fact have one more glitch in Growl
design. At present we have no way to render a general inclusion axiom
for two anonymous concepts i.e
 
(forall)R.C1    subclass-of     (exist) S.C2
 
Although this kind of  expressions   are not admissible in owl (but OK
for DL) there are yet valid owl statement which are not expressible in
growl:
 
Class(Teacher complete
 restriction(teaches  someValuesFrom(cource)))
 
This assert that class Teacher is equivalent to an anonimous class
restriction(teaches  someValuesFrom(cource)) and apparently this will
not be rendered properly in present growl.
 
Here is a  proposed change that would reconcile owl with DL languges and
in fact will bring growl very close to Bertram’s domain maps (in fact
those DMaps  inspired us to develop ontobrowser):
 
1.	Replace relation:     Class1 -----subclass-of--> Class2
by just one plain arrow   Class1------>Class2
 
2.	Do the same with instance-of arrows
3.	instead of using for equivalence of two classes something like
<--=--->   use simple double headed arrow  <---->. This would underline
the fact that equivalence is defined as existence of two opposite
subclass arrows.
4.	Allow to use oval restriction nodes as class nodes in that sense
that they may be targets for subclass arrows and equivalence arrows. Use
new subclass arrows in restriction as follows: Instead of
 

 
use the following:

Here the arrow from node MathCourse to oval restriction node ahould be
exactly the same arrow as one used for subclass-of and is-a arrows.
 
The advantages of this change is that the usage of subclass arrow make
semantics of the restrictions explicit. Say expression above in fact
says:
MathCourse  m " isTaughtBy.MathDeptStaffMember
or
(MathCourse subclass-of (for-all) isTaughtBy. MathDeptStaffMember
)
 
 so  (for-all) isTaughtBy. MathDeptStaffMember is not just a slot but a
superclass.
 
second it will be consistent with usage of oval property restriction
nodes as base nodes of anonymous classes in set theoretic operators like
the following

 
In this diagram the restriction node affiliatedWith used in the same
fashion as class node faculty.
 
Third, using simple double headed arrow for equivalence instead of using
“<--=-->” will reduce space. And now this equivalence arrow could
terminate on restriction nodes which would allow to render expressions
as
Class(Teacher complete
 restriction(teaches  someValuesFrom(cource)))
 
Fourth , using simple arrow for subclass and instance will considerably
reduce space.
 
Fifth, this change would enable to use growl as DL viewer.
 
 
Possible disadvantages:
1.We have been trying to maintain clean topology when two object nodes
are connected via relation node. It already has been broken. The
proposed change would break it further.
 
2.Usage Class1-->Class2 is not as explicit as usage 
 Class1 -----subclass-of--> Class2
 
But on the other hand it is very common to use simple arrows for
depicting subclass relations. Bertram’s domain maps  and also perhaps
TG plugin for protégé  are the examples.
 
Please let me know what you think about proposed changes. If I do not
get any negative response by Monday I will start implementing  the
changes. (Then I’ll also have to redraw all diagrams in growl paper)
 
Thanks,
Serguei
 
 
 
 
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