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extensions of the superrelations. In the example given earlier, we can define
airline distance as a subrelation of the general distance relation.
Similarly to attributes for concepts, each relation has a possibly empty
set of named parameters. If no named parameters are given, a unnamed,
ordered list is assumed. Each parameter is single-valued and can have a range
restriction in the form of a concept. As for concepts, a logical expression
defining the set of instances (
n
-ary tuples, if
n
is the arity of the relation) can
be specified.
6.1.6 Functions
A function is a special relation, with a unary range and an
n
-ary domain (the
parameters inherited from relations), where the range specifies the return
value. Functions can be used to represent and exploit built-in predicates of
common datatypes. Their semantics can be captured externally by means of
an oracle or the semantics can be formalized by assigning a logical expression
to a particular relation. The logical representation of functions is almost the
same as for relations. A typical example of the use of oracles is provided by
“built-ins”. These are functions such as “round” that are evaluated outside
the logical theory.
6.1.7 Instances
Instances are defined either explicitly or by a link to an instance store, i.e.
an external storage of instances and their values. Specified more formally in
MOF, an instance is made up of the following elements:
Class
instance
hasNonFunctionalProperties
type
nonFunctionalProperties
hasType
type
concept
hasAttributeValues
type
attributeValue
Instances of relations (with arity
n
) can be seen as n-tuples of instances
of the concepts that are specified as the parameters of the relation.
In general, instances do not need to be specified using an explicit notation
of the kind used above. In particular, when a huge number of instances exist,
a link to a data store can be used [73]. Basically, the approach is to integrate
large sets of instances which already exist on storage devices by means of
sending queries to external storage devices or oracles.
6.1.8 Axioms
An axiom is a logical expression together with its nonfunctional properties. A
detailed discussion of axioms can be found in Chapter 7.
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