SUO: RE: Merged Ontology and Collection, Aggregate, Set, etc.

[Chris Partridge <chris_partridge@csi.com>]

Hi Ian,

Thanks for your description of the ontology - very useful. Can I deduce that
classes and sets are disjoint from what you say?

So within your 'Merged Ontology' paper (or whatever it is to be called) you
are following the 'collection as new category' option (as suggested by Pat
Hayes) rather than the collection described using privileged part option (as
proposed originally by Matthew West, but supported by me and  Nicola
Guarino). I am noting this as it is important - as I have said a number of
times - to note the architectural options selected.

You say:
"Some might object to this four-fold
classification on the grounds that it is ontologically promiscuous, but I
think this objection carries weight only when we are attempting to hone a
philosophical theory, not when we are endeavoring to build an engineering
artifact."

I think there is some talking at cross-purposes here. The kind of
ontological promiscuity I was objecting to in this case has an engineering
aspect. It introduces unnecessary complexity to the overall theory.
Philosophically there is nothing wrong with being ontologically promiscuous.
If you of an engineering bent, you prefer less promiscuity (less
complexity), unless it buys you some benefit elsewhere. Typically
philosophers (and maybe this is a rash generalization) who attach a high
value to science also prefer less promiscuity, for the same reason as
scientists, simpler more elegant theories.

Regards,
Chris




-----Original Message-----
From: owner-standard-upper-ontology@ieee.org
[mailto:owner-standard-upper-ontology@ieee.org]On Behalf Of Ian Niles
Sent: 16 February 2001 20:13
To: Standard-Upper-Ontology (E-mail)
Subject: SUO: Merged Ontology and Collection, Aggregate, Set, etc.



Hi All,

        This is a response to Chris Partridge's question about how the
notions of class, set, collection, aggregate, group, fusion, mereosum, etc.
are handled in the merged ontology.  Currently, there are three concepts
along these lines in the ontology, viz.  Class, Set, and MereologicalSumFn.
Class and Set are both subclasses of Abstract and, hence, their instances
have no location in space/time (accordingly, a class or a set does not cease
to exist when all of its members vanish).  The difference between a class
and a set, as I see it (note that this is not (yet) part of the merged
ontology) is that the latter is the purely extensional notion of set theory,
while class contains an intensional element.  In addition to being a set, a
class characterizes a natural kind, which is defined by an associated
property or conjunction of properties.  MereologicalSumFn, on the other
hand, is a binary function which takes physical objects as arguments and
gives a mereosum or fusion as the result.  The definitions of this function
and related concepts are given below for those that are interested (note
that the definitions are borrowed from Nicola Guarino's and Barry Smith's
work).  On the basis of the exchange between Matthew, Chis, and Pat, I
wonder if we should look into including a fourth notion in the merged
ontology, viz. the concept of a group.  Groups would be exemplified by
flocks of sheep, football teams, etc.  Like a class/set, a group would have
members (which can be added/removed), but, like mereosums, a group would
have a location in space/time.  Some might object to this four-fold
classification on the grounds that it is ontologically promiscuous, but I
think this objection carries weight only when we are attempting to hone a
philosophical theory, not when we are endeavoring to build an engineering
artifact.

-Ian

;; Definition of 'MereologicalSumFn'

(<=>
     (equal ?Z (MereologicalSumFn ?X ?Y))
     (forall (?W)
               (<=>
                    (overlaps ?W ?Z)
                      (or
                           (overlaps ?W ?X)
                             (overlaps ?W ?Y)))))

;; Definition of 'MaximalBoundaryFn'

(instance-of MaximalBoundaryFn UnaryFunction)
(nth-domain MaximalBoundaryFn 1 CorpuscularObject)
(range MaximalBoundaryFn CorpuscularObject)

(<=>
     (equal ?Z (MaximalBoundaryFn ?X))
     (forall (?W)
               (=>
                    (boundary ?W ?X)
                      (part-of ?W ?Z))))

;; Definition of 'ClosureFn' (of an object)

(equal
        (ClosureFn ?X)
        (MereologicalSumFn ?X (MaximalBoundaryFn ?X)))

;; Definition of 'connected'

 (<=>
        (connected ?X ?Y)
        (overlaps (ClosureFn ?X) (ClosureFn ?Y)))

;; Definition of 'SelfConnectedObject'

(documentation SelfConnectedObject "Something is a SelfConnectedObject just
in
case it does not consist of two or more disconnected parts.")

(<=>
        (instance-of ?X SelfConnectedObject)
        (forall (?Y ?Z)
                (=>
                        (equal ?X (MereologicalSumFn ?Y ?Z))
                        (connected ?Y ?Z))))