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

[Ian Niles <iniles@teknowledge.com>]

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))))