# An Embedding-Based Approach to Repairing OWL Ontologies
## 5 Experiments
### Discussion and Limitations  
In this section, we discuss the main conclusions of our experiments. In particular, we analyze the main advantages and limitations of our proposed algorithms. According to our results, the following main conclusions can be derived:  
* Compared with other algorithms, BaseAlg can always find a minimal diagnosis, but it spent slightly more time than ScoreAlg and ShapAlg in most cases. Although no big difference in these algorithms' efficiency has been reflected by our experiments, computing diagnoses based on subsets of all MIPS should be more efficient than that based on all MIPS directly. Thus, when time is a problem for BaseAlg, ScoreAlg and ShapAlg would be preferred as they compute a diagnosis based on subsets of all MIPS. * When logical consequences are considered important, LogicAlg can be used to compute a diagnosis such that removing all axioms in the diagnosis will lose the least entailments. One main disadvantage of this algorithm is that computing entailments, even given types of entailments, may be very time-consuming. * In the case that the usage of entities is considered important, SigCosAlg and SigEucAlg are good choices, because they consider both syntax and semantics, and remove fewer axioms than the original signature-based algorithm SigAlg. These algorithms assign higher degrees to those axioms that have more syntactical overlapping with other axioms. The embedding-based algorithms further consider semantic relevance. * For the threshold-based algorithm, the threshold plays an important role. According to our observations, a value of around 0.5 is a good choice. Furthermore, the threshold-based algorithm with Euclidean Distance (i.e., ThrEucAlg) often removes fewer axioms than that with Cosine Distance (i.e., ThrCosAlg), but it cannot distinguish the difference of axioms when the threshold is more than 0.65. * Among the four pre-trained models, m1 is the most efficient one. This reflects that its embedding model \"paraphrase-multilingual-343 MiniLM-L12-v2\" outperforms other BERT models used in m2, m3, and m4, according to their efficiency. In addition, m4 provides more promising results with respect to the number of removed axioms. It is able to not only differentiate the axioms but also remove fewer axioms. Based on the discussion of the main results, we can summarize the following advantages of our proposed approach: (1) Our embedding-based approach provides a novel approach to considering semantic relationships among axioms. The source code of our implementations, together with the data set and experimental results, can be freely downloaded for reusing or retesting purposes. This approach is also a flexible framework to integrate different distance metrics and embedding models. (2) Integrating the embedding-based ranking strategy with existing ones may be a promising combination to enhance existing strategies' effectiveness. SigCosAlg and SigEucAlg are good examples. They combine the traditional signature-based ranking strategy with the embedding-based one and really reduce the number of axioms to be removed. (3) Through our experiments, we show that our embedding-based algorithm with the model m4 is a promising choice to remove relatively fewer axioms and differentiate the axioms with different degrees. Nevertheless, there exist several limitations to our study. (1) Computing similarities between axioms will be extremely time-consuming if too many axiom pairs are considered. Although this process can be performed offline, various strategies to choose axiom pairs should be considered. (2) It is not easy to select a suitable threshold for given incoherent ontologies. According to our experimental results, a suitable threshold has been recommended. However, it would be dynamically changed when the evaluated ontologies are updated. (3) It is not sufficient to evaluate the repair algorithms with the time and number of axioms to be removed.