Integrating Two Descriptions of Taxonomies
with Materialization
Alain Pirotte, Université catholique de Louvain,
Institut d’Administration et de
Gestion, Louvain-la-Neuve, Belgium
David Massart, European Schoolnet Office, Brussels, Belgium
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REFEREED
ARTICLE
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Abstract
This paper presents a precise correspondence between two views of
taxonomic hierarchies: an intensional view based on concepts and an
extensional view based on categories, i.e., subsets of the population
of individuals analyzed in terms
of these concepts. The correspondence is described with materialization, a generic
relationship defined for object-oriented and entity-relationship information
models. The paper
introduces materialization and shows how it provides a systematic bridge between
both views of taxonomies.
1 REAL-WORLD MODELING
We view the world of interest as consisting of
objects (i.e., things, individuals, ideas,
...) important enough to be distinguished from one another. Still,
for clarity, we will
say that the world is populated by individuals and we will reserve
the term object for the usual basic construct of object-oriented models.
The world can
be described in many ways. We are interested in precise intensional
descriptions, called schemas in the database culture, based on concepts that
are ideas or notions of various degrees of generality about individuals
and sets of
individuals in the world. Concepts are used, for example, for distinguishing
individuals
from other individuals or for characterizing the common properties
of similar
individuals. Categories are the extensional counterparts of
concepts. They serve to
classify the population of individuals in the world into subsets perceived
as interesting.
The activity of conceptual modeling builds such intensional
descriptions, also
called conceptual models. They are biased and incomplete symbolic images
of portions
of the world built with concepts. Conceptual models capture meaning
in a processable
form, in order to perform various tasks of symbolic manipulation regarded
as useful (e.g., understand, aggregate, transform information; generalize
available
information; make assumptions and explore their consequences).
Taxonomies
are conceptual models. Informally, a taxonomy is an organization
of concepts or of categories about individuals in the world structured
by an order
relation expressing the relative generality of the concepts or categories.
2 TWO DESCRIPTIONS OF TAXONOMIES
Taxonomies can be described
as hierarchies structured along two alternative dimensions:
-
a dimension of concepts, that structures the population
of individuals in
the world in terms of concepts organized along an intensional dimension
of
abstractness/concreteness. That is the method usually chosen to organize
scientific knowledge (e.g., biological organisms).
The hierarchy of concepts may be expressed as a hierarchy of classes
and
their instances (or metaclasses and their classes) structured by
the mechanism
of classification of usual object-oriented models. Concepts are progressively
refined by successive instantiations downwards in the hierarchy;
-
a dimension of populations, that characterizes
a collection of subsets of
individuals in the world as a hierarchy of classes and subclasses
structured by
the generalization abstraction of usual object-oriented models.
The dimension
of populations analyzes the overall population of interesting individuals
in
terms of smaller and smaller subsets downwards in the hierarchy.
Consider,
for example, the population of vehicles on the road in Belgium.
Figure
1 shows a view of the example based on concepts1.
This is the point of
view, for example, of the transportation board or of the accounting
office. These
agencies are not interested in individual vehicles, but rather in the
structure of tax
revenues, or in the regulation for driving licences and car insurance.
In that view,
the class of the most general concepts is Types of
vehicle. It has
three instances: class A vehicle (or truck), class
B vehicle (or car), and class
C vehicle (or bus), each
concept being characterized, for example, by a value for a type of
driving license and
for a type of insurance. The concept of car is in turn refined into
concepts of luxury
car, family car, and sports
car, which are instances of class Types
of car associated
with the class B concept. Then, the concept of family
car is in turn
refined as car
models, which are instances of class Types of family
car.
Figure 2 shows the same example in terms of categories of
world individuals,
namely sets of concrete vehicles2.
This is the point of view, for example, of the
registry office that issues individual driving licences or vehicle
plates, and collects
taxes. In that view, the top-level class Vehicles comprises
all the vehicles of interest.
It has three subclasses (Trucks, Cars, and Buses),
denoting the corresponding subsets
of vehicles, and so on. Figure 2 also shows two subclasses of class
Family cars,
distinguished by their model: Fiat Retro cars and 2CV
cars, and two
instances of
these classes, Guy’s 2CV and Nico’s fiat, denoting real
concrete cars.
Figure 1: Concept dimension of a taxonomy of vehicles 
Figure
2: Population dimension of a taxonomy of vehicles 3 TWO-FACETED CONSTRUCTS
In the population view of the taxonomy, the
properties of each class are derived from
its links with its superclasses through the inheritance mechanism of
generalization.
In the concept view, each concept c (like class
B or car) is an object,
which
is tightly bound to a class (Types of car)
whose instances (such as luxury car) are
objects denoting subconcepts of c. The taxonomy
of concepts is thus expressed as
a hierarchy of classes structured by the classification link of object-oriented
models.
Concepts are viewed alternatively as objects and as classes of their
subconcepts.
Two-faceted constructs make that double explicit.
Each two-faceted construct is a
composite structure associating an object and a class. The association
is underlined
by drawing each two-faceted construct as a class box adjacent to
an object box.
For example, in Figure 1, objects luxury
car, family
car, and sports
car are instances
of class Types of car, each object being
associated with a class in a two-faceted
construct (e.g., concept family car is associated
with class Types
of family car in a
two-faceted construct). Similarly, fiat Retro and 2CV,
which denote car models, are
instances of Types of family car. In object-oriented
terms, Types
of car, for example,
is a metaclass for objects fiat Retro and 2CV.
Thus,
each concept is a two-faceted construct with an object facet (a concept
is
an instance of a more abstract concept at the next higher level of
the taxonomy)
and a class facet (a concept is a class of refined concepts that
are its instances at
the next lower level).
Information propagates downwards by turning attribute
values of the object facet
into constant attributes of the class facet (i.e., class attributes
whose value is the
same for all class instances). For example, Types
of vehicle could
have a licence type attribute, with value type B for object class
B. An attribute with
the same name licence type is then a class attribute
for class Types
of car with
a constant value B for
all its instances. All subconcepts of class B in
the taxonomy similarly have a licence
type attribute with value B.
4 MATERIALIZATION
Materialization [PZMY94] is a binary relationship between
a class of categories and
a class of more concrete objects analyzed in terms of these categories.
Figure
3: An example of materialization.
Figure 3 shows a materialization between
classes Types of family car and Family
cars. A materialization link is drawn as a line with a “ ” on
the side of its more
concrete class.
Class Types of family car models
information that is typically supplied in the
catalog of a car dealer, such as model name, sticker
price, and available
options for
the engine size. Class Family
cars models information about individual
cars, such as manufacture date, serial number,
and owner.
Figure 4: Instances of Types of family
car and Family cars of Figure 3.
Figure 4 shows an instance of each
class (fiat Retro is an instance of Types
of family car and Nico’s fiat is an instance of Family
cars). The semantics
of materialization
expresses that each concrete car (such as Nico’s fiat) has exactly
one model (fiat
Retro), whereas there can be any number of cars of a given model.
The
semantics of the abstractness/concreteness relationship also expresses
that
each car is a concrete realization (or materialization) of a given
model, from which
it inherits properties in various ways. For example:
-
Nico’s fiat directly inherits the name and sticker
price of its
model fiat Retro;
-
Nico’s fiat has attributes (such
as engine
size) whose value
(1200) is one of the
options (1200 or 1300) offered by a multivalued attribute of the
same name in
object fiat Retro denoting the model of Nico’s fiat.
Of course,
in addition to the attributes propagated from its model fiat
Retro, Nico’s fiat has a value for the attributes manufacture
date,
serial number, and owner
of class Family cars.
More detail about the information-propagation
mechanisms of materialization
can be found in [PZMY94, DPZ02].
5 INTEGRATING CONCEPTS AND POPULATIONS
Figure 5 shows how materialization
can realize a correspondence between both views
of the taxonomy.
A first type of materialization (like Types of car —Cars labeled
(1) in the figure) establishes a systematic bridge between classes
of concepts in the
intensional view
and the corresponding classes of individuals in the extensional view.
Other similar
materializations include (see Figures 1 and 2): Types
of vehicle —Vehicles,
Types
of truck —Buses,
Types of luxury car —Luxury
cars, Types of
family car —Sports
cars.
Figure 5: Correspondences via materialization
Figure 5 also shows how both taxonomies merge at their bottom. The
materialization Types of family car —Family
cars, labeled (2) in the figure,
makes explicit
the semantics of the materialization of Figure 3 in terms of two-faceted
constructs,
and links of classification and generalization.
Object fiat Retro, an
instance of Types of family car, is the object facet of a twofaceted
construct whose class facet is class Fiat Retro cars,
a subclass of Family cars,
describing all the instances of Cars of
model fiat
Retro. 2CV is
another instance of Types of family car and Guy’s
2CV is
an instance of its class facet 2CV cars.
6
SUMMARY
This paper illustrates how the materialization mechanism can
establish a systematic
correspondence between two taxonomies for the same reality: an “intensional” taxonomy of concepts structured along a class/metaclass dimension
and an “extensional” taxonomy of populations
structured along a subclass/superclass dimension.
Materialization
establishes a bridge at every level of both hierarchies
between a
class of concepts on the intensional side and a class of individuals
of the application
domain on the extensional side. Materialization also establishes a link
between both taxonomies at their bottom
level.
Footnotes
1 Classes are drawn as rectangular
boxes and objects as rounded boxes; class names begin with an
uppercase letter, whereas object names are written in lower case. Dashed lines
denote instantiation
links (classification).
2 Solid lines denote
generalization links.
REFERENCES
[DPZ02] M. Dahchour, A. Pirotte and E. Zimányi. "Materialization
and its metaclass
implementation". IEEE Trans. on Knowledge and Data Engineering,
14(5): 1078-1094, 2002.
[PM99] A. Pirotte and D. Massart. "La matérialisation
pour réconcilier
deux descriptions
des taxinomies". In Proc. 7è Rencontres de la Société Française
de Classification, Nancy, France, September 1999.
[PZMY94] A. Pirotte,
E. Zimányi, D. Massart, and T. Yakusheva.
"Materialization:
a powerful and ubiquitous abstraction pattern". In J. Bocca, M. Jarke,
and C. Zaniolo, editors, Proc. of the 20th Int. Conf. on Very Large
Data
Bases, VLDB’94, pages 630–641, Santiago, Chile, 1994. Morgan
Kaufmann.
About the authors
Alain Pirotte is professor in computing science and information
at the Université catholique de Louvain, Louvain-la-Neuve, Belgium, and visiting professor
at the Université Libre de Bruxelles, Brussels, Belgium. He can be reached at pirotte@info.ucl.ac.be.
See also http://www.isys.ucl.ac.be/staff/alain/.
David Massart works
as a software engineer at the European Schoolnet Office
(http://www.eun.org/). He holds a Ph.D. in information science
from the Université Libre de Bruxelles, Brussels, Belgium. He also works as an expert
for the CEN/ISSS
workshop on learning technologies. He can be reached at david.massart@eun.org.
Cite this article as follows: Alain Pirotte, David Massart: "Integrating
Two Descriptions of
Taxonomies with Materialization", in Journal of Object Technology,
vol. 3, no. 5, May–June 2004, pp. 143-149. http://www.jot.fm/issues/issues
2004 05/article4
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