# An Embedding-Based Approach to Repairing OWL Ontologies
## 5 Experiments
### Data Set  
The data set comes from our previous work about benchmarking incoherent ontologies presented in [39]. Since the approach proposed in this paper considers the semantics of axioms, those ontologies with meaningless entity names are excluded from our experiments. For example, in ontology DICE-A, \"C521744\" is a class name and \"R19763\" is a property name. They are meaningless, and we do not consider such an ontology. Since the proposed algorithms compute all MIPS in an ontology, we do not consider those ontologies all of whose MIPS cannot be found within a limited time or memory. For instance, we choose the sub-ontology km1500-3500 instead of its complete version km1500. In this way, most of the existing incoherent ontologies (i.e., 13 incoherent ontologies) and 7 merged incoherent ontologies provided by [39] are chosen.  
Table 2 presents the details about the chosen incoherent ontologies. The ontology names that consist of three parts and are connected with two symbols of \"-\" indicate those ontologies constructed by merging two source ontologies and an alignment between them. Here, an alignment consists of a set of correspondences, and correspondence can be translated into an OWL axiom (see [39] for more details). Take ontology ALOD2 Vec-conf-ed as an example. Its name consists of ALOD2 Vec, confof and edas. ALOD2 Vec [40] is an ontology matching system, confof and edas indicate two source ontologies. This merged ontology is obtained by merging confof, edas, and the alignment generated by the system ALOD2 Vec. Similarly, the other 6 merged ontologies use the ontology matching systems ATBox [41], Lily [42], VeeAlign [43] and Wiktionary [44]. Those source ontologies come from the conference track provided by Ontology Alignment Evaluation Initiative ([[http://oaei.ontologymatching.org/2020/](http://oaei.ontologymatching.org/2020/)]([http://oaei.ontologymatching.org/2020/](http://oaei.ontologymatching.org/2020/)) accessed on 15 November 2022), which is a very popular platform to evaluate various ontology matching systems.  
From Table 2, we observe that dbpedia_2014 has a large TBox (i.e., 5763 axioms) and contains many SubObjectPropertyOf or SubDataPropertyOf axioms (i.e., 964 axioms). In its TBox, most axioms are used to describe the domains or ranges of the properties (nearly 5000 such axioms). As for ontologies MGED and Geograph, most of their axioms describe disjointness relations among the classes. For ontology km1500-3500, most of its axioms are subsumption, and there are also many disjointness axioms.  
Furthermore, the information about MIPS in a selected ontology can be seen in Table 3, where all MIPS are obtained from the work presented in [39]. It can be observed that ontology km1500-3500 has quite a lot of unsatisfiable concepts (i.e., 734), and most of the others have no more than 30 unsatisfiable concepts. For those ontologies containing more than 30 unsatisfiable concepts, they also contain many MIPS. For instance, km1500-3500 and Economy have 146 and 47 MIPS, respectively. For the found MIPS, the maximal size is no more than 16, and a MIPS often contains no more than 10 axioms on average. Overall, these ontologies have various numbers of MIPS, and the size of a MIPS varies differently (i.e., from 2 to 16).