18
Apart from classes, we also consider a set of relations
R.
Definition [Relation]. For ontology
O, a relation
r
a
∈ R as
r
a
= (
n, c
s
, c
o
, ϕ
, J),
with
n is the string representing the name of the relation,
c
s
is the subject class,
c
s
∈ C,
c
o
is the object class,
c
o
∈ C,
ϕ
∈ {true, f alse}, indicating whether the relation is functional, and
J is the set of
relation instances,
J ⊆ I
s
× I
o
.
2
A relation can be conveniently expressed as the triplet
[
c
s
]
n [
c
o
]. For example,
[person] was born in [city] is instantiated with [Vincent van Gogh] was born in
[Zundert].
For
non-functional relations (i.e. ϕ
≡ f alse), instances in the subject class can
be related to multiple instances in the object class. For example, a person may
have multiple professions, a painter can belong to more than one art movement
and
Radiohead can be considered to be related to various other musical artists. For
some relations on the other hand, the number of instances in the object class related
to a subject instance may be restricted. In practice, this distinction is viable for all
relations considered in this work. We will return to the consequences of this choice
in Chapter 3.
Finally, we define the relation instances.
Definition [Relation Instance]. For relation
r
a
= (
n, c
s
, c
o
, J) in ontology
O, a
relation instance
j ∈ J is a pair (
i, i
0
), where
i is an instance of the subject class
c
s
, and
i
0
is an instance of the object class
c
o
.
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