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The ordered set of concept types is denoted
T
C
, the set of relation types is denoted
T
R
and the
set of individual makers that are used to labeled the concept nodes is denoted
I
.
Fig. 7. Concept type hierarchy for TV programs
Figure 7 depicts an example of the hierarchy that contains the concept types used to describe
TV programs.
5.2.2 Basic conceptual graphs
Several families of conceptual graphs (CG) exist, that allow describing different kinds of
knowledge. Whithin this work, we focus on the basic graphs (defined in Chein & Mugnier
(2008)). Basic conceptual graphs are bipartite graphs containing concept and relation nodes.
Figure 6 gives an example of a basic graph. The rectangular boxes represent concept nodes
and the ovals represent relation nodes.
Conceptual graphs allow to express logical formulas. Any conceptual graph can thus be
translated into logic. The graph in Figure 6 for instance can be expressed in First Order Logic
as follows:
∃
x
,
∃
y
(
Content
(
x
)
∧
Title
(
”
TF
!
Jeunesse
”
)
))
A basic conceptual graph G is defined by a 4-uple over a vocabulary
V
∧
title
(
x
,”
TF
!
Jeunesse
”
)
∧
Text
(
y
)
∧
description
(
x
,
y
=(
T
C
,
T
R
,
I
)
:
G
=
(
C
G
,
R
G
,
E
G
,
l
G
)
and is such that:
•
is a finite undirected and bipatite multigraph.
C
G
is the set of concept nodes.
R
G
is the set of relation nodes, and
E
G
is the set of edges.
•
l
G
is a naming function of the nodes and edges of the graph
G
which satisfies:
1. A concept node
c
is labeled with a pair
(
C
G
,
R
G
,
E
G
)
(
(
)
(
))
(
)
∈
type
c
,
marker
c
, where
type
c
T
C
and
(
)
∈ I ∪ {∗}
.
2. A relation node
r
is labeled by
l
marker
c
is also called the type of
r
.
3. The degree of a relation node
r
is equal to the arity of
r
.
4. Edges incident to a relation node
r
are totally ordered and labelled from 1 to the arity
of
r
.
Given the order on
T
C
, the concept nodes that can be defined on a
T
C
×{I ∪{∗}}
(
r
)
∈
T
R
.
l
(
r
)
are partially
ordered by the generality relationship. For instance, as the the concept type
Text
is greater
(i.e. more general) than
Title
(see Figure 7) and the generic marker * is greater than any
individual marker of
I
, we have for instance:
≥
≥
“News”]
, but
[Text :
[Text:
*
]
[Text :
“News”]
[Title :
“News”]
and
[Title:
*
]
are not comparable.
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