Semantic Knowledge Representations for Soft Data Fusion - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 20

Fig. 11. Processing similarity - results

Matching the two graphs, according to these couples of nodes, should also keep the structure
of the graphs. Arcs between nodes should not be deleted or modified. For instance, given that
( [Program] , [Entity: P1] ) and ( [Content] , [Content] ) are two couples of nodes
that are compatible, the edge between [Program] and [Content] must have an equivalent
between [Entity: P1] and [Content] , which is the case in our example. To do so, we
use projection search between the two graphs.
Definition 5.8. Let u =( ) =( ) be two basic conceptual graphs

defined on the same vocabulary V. A projection of v in u is a function P : V

C u , R u , E u , l u and v C v , R v , E v , l v

× → ( × ) ∪ V C u C v

( × ) of the nodes such that the arcs and their labels are preserved and the labels of the nodes can

be specialized.
•

R u R v

∀ ( ) ∈ ( ( ) ( )) = ( ) ∈ r u , i , c u u , P r u , i , P c u r v , i , c v v

•

∀

e

∈

C u

∪

R u , l v

(

P

(

e

)) ≤

l u

(

e

)

Fig. 12. Example projection between two graphs

Figures 12 depicts an example of projection. G 2 can be projected in the graph G 1 through the
projections P 1 and G 1 is more specific than G 2. We use injective projections. Two different
nodes of one graph have two different images in the other graph. Maximal join is a projection
based operation defined on conceptual graphs.