![](bg6.png)
Figure 3: DL Reasoner calls in the 2D case.
Figure 4: DL Reasoner calls in the 4D case with logarithmic
scaling.
Both figures show that the inference calls of
Pareto is near to the optimal lower bound LOWER-
BOUND and considerably better than the typical
divide-and-conquer algorithm Pareto-0 in both 2D
and 4D. These results are reasonable for the proposed
pattern matching algorithm due to the depth of an on-
tology being typically smaller than 30 and the patterns
having typically a small amount of constraints.
We see that the amount of Pareto results, which
is around the half of the LOWERBOUND value, is
very small. For this set the degree of matching must
be computed with respect to the fusion function to
find the most optimal solution out of the set of Pareto-
optimal solutions. This search can be done without to
call the DL reasoner, since we already know that these
solutions are satisfied.
5 CONCLUSIONS
We have shown how to use ontological background
DL knowledge to overcome the problem of noisy and
imprecise data. Our tolerant pattern matching ap-
proach can even address erroneous or missing patterns
by successively abstracting them. The algorithm sub-
stantially reduced the amount of these inference calls
to the DL reasoner. It is correct, complete and needs
a number of inference calls close to the lower bound.
It can be parameterized to have the ability to infere
approximate results.
ACKNOWLEDGEMENTS
This work was supported by the German Federal Min-
istry of Education and Research (BMBF) under the
grant 01IS08022A.
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