Innovation and Ontologies

164 Elements of Ontologies
4.1.1.2 Attributes
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Attributes (slots) are the properties of objects that constitute the object’s structure.
The set of attributes (also called slots) is usually defined with the class (Noy & McGuinness,
2001). After instantiation of the object, attributes contain attribute or slot values. This means that
concrete values of the attributes are defined; this procedure is called the binding of a variable to a
value. Hence, different instances of a class vary in their attribute values (Balzert, 2001a & 2001b;
Chandrasekaran, Josephson & Benjamins, 1999; Kastens & Kleine Buening, 2005; Lutz, 1997) 194 .
The instance ‘Bob Miller’ of the class ‘employee’ has the attribute value ‘185’ of the attribute ‘height’.
4.1.1.3 Relations
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Relations represent an association or interaction between two or more classes and
consequently associations between the instances of these classes 195 .
Relations can be seen as extensions of the attribute concept whose values are replaced by
pointers to other instances or classes. Without the possibility of specifying relations, the
definition of classes would not have the significance formal ontologies are expected to have.
Formally, a relation R is defined as a subset of the Cartesian product of n sets, i.e. R:
C1 x C2 x … x Cn, where all Ci’s represent classes. Binary relations are those with n=2.
Consequently, relations in an ontology are intensional, i.e. reflecting a particular state of affairs 196 .
Ris employed at : employee x enterprise indicates that the class ‘enterprise’ has the class ‘employee’ on its payroll.
Ris employed at = {(Bob Miller, ABC Company)} indicates that there is a relation such that the instance ‘Bob Miller’
of the class’ employee’ is on the payroll of the instance ‘ABC Company’ of the class ‘enterprise’.
A specific and elementary binary relation is inheritance (also called is-a relation) which is also
known from the object-oriented modeling paradigm (Balzert, 2001a & 2001b; Booch, Martin &
Newkirk, 1999; Brooks, 1986; Lutz, 1997; Rosenkranz, 2002). An is-a relation indicates that a
class (called subclass) is derived from another class (called upper class or superclass). Derived, in this
context, means that the subclass inherits all characteristics (attributes and relations) of its upper
class, but might override them or add additional ones.
194 For the sake of completeness, it must be noted that there exist also attributes whose values are the same for all instances of a class (so-called
class attributes) or are shared between several classes (so called local attributes) (Gómez-Pérez, Fernández-López & Corcho, 2002).
195 This definition is based on the various definitions (Balzert, 2001b; Chandrasekaran, Josephson & Benjamins, 1999; Kastens & Kleine
Buening, 2005; Lutz, 1997; Rosenkranz, 2002; Scheer, 1988; Gómez-Pérez, Fernández-López & Corcho, 2002).
196 Extensional relations, as they are indicated by Genesereth & Nilsson (1988) stand for mathematical relations and thus omit the meaning of the
relation (Guarino, 1995). Guarino (1998) even speaks of conceptual relations to stress that the simple term ‘relation’ is reserved for mathematical
relations.