Information Technology Reference
In-Depth Information
The maximal join is composed of two components. First, it tests the compatibility of two
elements of the graphs and then fuses them actually. To define the maximal join operation,
Sowa defines several other operations that we detail hereafter.
Definition 5.9.
If a conceptual graph u is canonically derivable (see Sowa (2000)) from a conceptual
graph v, then u is called a specialization of v and v is called a generalization of u.
Definition 5.10.
Let two conceptual graphs u
1
and u
2
have a common generalization v with injective
projections P
1:
v
u
2
.P
1
and P
2
are
compatible projections
if, for each concept
c in v, the following conditions are true:
•P
1
→
u
1
and P
2:
v
→
have a common subtype,
• the referents of P
1
(
c
)
and P
2
(
c
)
(
)
(
)
c
and P
2
c
are either equal or one of them is undefined.
The definition of the maximal join of two graphs u1 and u2 given by Sowa in Sowa (1984) is
the following one.
Definition 5.11.
Let v be the most specific common generalization of the graphs u
1
and u
2
. There is
no generalization v
2
of u
1
and u
2
such as v is a sub-graph of v
2
.
P
1
and P
2
are two compatible injective projections of v in u
1
and u
2
.P
1
and P
2
are maximally
extended (P
1
and P
2
are maximally extended if they have no extension).
A join on these projections is called a
maximal join
.
There may be several possibilities of fusion between two observations, according to which
combinations of observed items are fused or not. This phenomenon is well manage by the
maximal join operator. As there may exist several maximally extended compatible projections
between two graphs, joining two graphs maximally may give several results, each one of them
being a fusion hypothesis.
However, using the maximal join only is not sufficient in order to fuse information as it enables
to fuse only strictly identical values. Figure 13 gives an example of such a case. Domain
knowledge must used in order to extend the notion of compatibility between concepts, so that
concepts with sufficiently similar referents can be be fused.
Fig. 13. Limitations of Maximal Join (1)
To do so, we use
Fusion Strategies
which are rules encoding domain knowledge and fusion
heuristics.
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