Information Technology Reference
In-Depth Information
3 What are Collectives?
According to WCH, the main distinction between collectives and quantities is that the
latter but not the former are said to be
homeomeros
wholes [8]. In simple terms, ho-
meorosity means that the entity at hand is composed solely of parts of the same type
(
homo
=same,
mereos
= part). The fact that quantities are homeomeros (e.g., all sub-
portions of wine are still wine) causes a problem for their representation (and the
representation of relationships involving them) in conceptual modeling. In order to
illustrate this idea, we use the example depicted in figure 2.a below. In this model, the
idea is to represent that a certain portion of wine is composed of all subportions of
wine belonging to a certain vintage, and that a wine tank can store several portions of
wine (perhaps an
assemblage
of different vintages). However, since Wine is ho-
meomeros and infinitely divisable in subportions of the same type, if we have that a
Wine portion x has as part a subportion y then it also has as part all the subparts of y
[17]. Likewise, a wine tank storing two different “portions of wine” actually stores all
the subparts of these two portions, i.e., it actually stores infinite portions of wine. In
other words, maximum cardinality relations involving quantities cannot be specified
in a finite manner. As discussed, for instance in [20],
finite satisfiability
is a funda-
mental requirement for conceptual models which are intended to be used in informa-
tion systems. This feature of quantities, thus, requires a special treatment so that they
can be property modeled in structural conceptual models. A treatment that does not
take quantities to be mere aggregations (
mereological sums
) of subportions of the
same kind but integral wholes unified by a characterizing relation of
topological
maximal self-connectedness
[17].
responsible for
1..*
1
Group of Visitors
Guide
*
*
Fig. 2.
Representations of a Quantity (a-left) and a Collective (b-right) with their respective
parts in UML conceptual Models
As correctly defined by WCH, collectives are not homeomeros. They are com-
posed of subparts parts that are not of the same kind (e.g., a tree is not forest). More-
over, they are also not infinitely divisible. As a consequence, a representation of a
collection as a simple aggregation of entities (analogous to an enumerated set of enti-
ties) does not lead to the same complications as for the case of quantities. Take, for
instance, the example depicted in figure 2.b, which represents a situation analogous to
the one of figure 2.a. Different from the former case, there is no longer the danger of
an infinite regress or the impossibility of specifying finite cardinality constraints. In
figure 2.b, the usual maximum cardinality of “many” can be used to express that a
group of visitors has as parts possibly many other groups of visitors and that a guide
is responsible for possibly many groups of visitors.
Nonetheless, in many examples (such as this one), this model of figure 2.b implies
a somewhat counterintuitive reading. In general, the intended idea is to express that,
