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subcollective-collective relation is transitive. That is, for all a,b,c, if M(a,b) and M(b,c)
then
¬
M(a,c), but if M(a,b) and C(b,c) then M(a,c).
4.
Asides from being intransitive, a member x of a collective W is atomic w.r.t. the
collective. This means that for if an entity y is part of x then y is not a member of W.
For the sake of illustration, we revisit in figures 6.a and 6.b two of the examples
discussed in this paper, explicitly representing them with the modeling primitives
proposed in table 1. As one can observe, we decorate the standard UML symbol for
aggregation with a C and an M to represent a subcollective-collective and member-
collective relations, respectively.
responsible for
«collective»
Association of Clubs
M
«kind»
Person
«collective»
Group of Visitors
1..*
1
Guide
*
C
C
{inseparable}
{inseparable}
2..*
1
1
«collective»
Club
M
ClubMember
«collective»
EnglishSpeakingSegment
«collective»
DutchSpeakingSegment
1..*
2..*
M
M
Person
2..*
2..*
EnglishSpeakingMember
DutchSpeakingMember
Fig. 6.
Examples of subcollective-collective and member-collective part-whole relations
5 Final Considerations
The development of suitable foundational theories is an important step towards the
definition of precise real-world semantics and sound methodological principles for
conceptual modeling languages. This article concludes a sequence of papers that aim
at addressing the three fundamental types of wholes prescribed by theories in linguis-
tics and cognitive sciences, namely, functional complexes, quantities, and collectives.
The first of these roughly correspond to our common sense notion of object and,
hence, the standard interpretation of objects (or entities) in the conceptual modeling
literature is one of functional complexes. The latter two categories, in contrast, have
traditionally been neglected both in conceptual modeling as well as in the ontological
analyzes of conceptual modeling grammars.
In this paper, we conduct one such ontological analysis to investigate the proper
representation of types whose instances are collectives, as well as the representation
of parthood relations involving them. As result, we were able to provide a sound onto-
logical interpretation for these notions, as well as modeling guidelines for their proper
representation in conceptual modeling. In addition, we have managed to provide a
precise qualification for the relations of
member-collective
and
subcollective-
collective
w.r.t. to both classical mereological properties (e.g., transitivity, weak sup-
plementation, extensionality) as well as modal secondary properties that differentiate
essential and inseparable parts. Finally, the results advanced here contribute to the
definition of concrete engineering tools for the practice of conceptual modeling. In
