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      <title-group>
        <article-title>Direct computation of diagnoses for ontology alignment?</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Kostyantyn Shchekotykhin</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Philipp Fleiss</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Patrick Rodler</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gerhard Friedrich</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Alpen-Adria Universita ̈t</institution>
          ,
          <addr-line>Klagenfurt, 9020</addr-line>
          <country country="AT">Austria</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Modern ontology debugging methods allow efficient identification and localization of faulty axioms in an ontology. However, in many use cases such as ontology alignment the ontologies might include many conflict sets, i.e. sets of axioms preserving the faults, thus making ontology diagnosis infeasible. In this paper we present a debugging approach based on a direct computation of diagnoses that omits calculation of conflict sets. The evaluation results show that the approach is practicable and is able to identify a fault in adequate time.</p>
      </abstract>
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    <sec id="sec-1">
      <title>-</title>
      <p>the algorithm attempts to reconstruct the tree by reusing the remaining valid diagnoses.
In the direct approach limiting the number of diagnoses used to compute a query to
some reasonable number. e.g. n = 10 results in a small size of the search tree, thus,
using less memory in comparison to the standard approach.</p>
      <p>
        We evaluated the direct ontology debugging technique using aligned ontologies
generated in the framework of OAEI 2011 [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. These ontologies represent a real-world
scenario in which a user generated ontology alignments by means of some
(semi)automatic tools. The Conference test suite we included 146 classifiable ontologies and
computed 1, 9 and 30 diagnoses with both HS-TREE and INV-HS-TREE. For 133
ontologies both approaches were able to compute the required amount of diagnoses. In the
experiment where only 1 diagnosis was requested, the direct approach outperforms the
HS-TREE as it was expected. In the next two experiments the time difference between
the approaches decreases. However, the direct approach was able to avoid a rapid
increase of computation time for very hard cases. In the 13 cases HS-TREE was unable to
find all requested diagnoses in each experiment. Within 2 hours the algorithm calculated
only 1 diagnosis for csa-conference-ekaw and for ldoa-conference-confof it
was able to find 1 and 9 diagnoses, whereas INV-HS-TREE required 9 sec. for 1, 40
sec. for 9 and 107 sec. for 30 diagnoses on average.
      </p>
      <p>
        Moreover, in the first experiment we evaluated the efficiency of the interactive direct
debugging approach applied to the 13 “hard” ontologies. We selected the target
diagnosis randomly among all diagnoses that included only invalid alignments suggested by a
system. The latter can be computed using the set of correct alignments provided by the
organizers of OAEI 2011. In the experiment the used the Entropy scoring function [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]
with prior fault probabilities of axioms corresponding to aliments set to 1 v, where
v is the confidence value of the matcher. All axioms of the aligned ontologies were
assumed to be correct and were assigned small probabilities. The debugging was then
applied to the set of all alignments returned by a matcher. The experiment shows that
the system was able to identify the target diagnosis efficiently requiring less than 4 sec.
in 75% of all cases to compute a query. The system’s performance decreased only in
the cases when a reasoner required much time to verify the consistency of an ontology.
      </p>
      <p>In the second scenario we applied the direct method to unsatisfiable and classifiable
within 2 hours ontologies, generated for the Anatomy problem. The source ontologies
O1 and O2 include 11545 and 4838 axioms correspondingly, whereas the size of the
alignments varies between 1147 and 1461 axioms. The target diagnosis selection
process was performed in the same way as in the first experiment. The results of the
experiment show that the target diagnosis can be computed within 40 second in an average
case. Moreover, INV-HS-TREE slightly outperformed HS-TREE.</p>
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