# An Embedding-Based Approach to Repairing OWL Ontologies
## 6 Related Work  
Various algorithms to repair ontologies have been proposed. Existing algorithms generally consist of automatic repair algorithms and semi-automatic repair ones, or fine-grained ones and algorithms to delete whole axioms. Semi-automatic repair (e.g., [48; 49; 50; 51; 52]) requires an expert's participation to decide which recommended axioms should be removed. Most of these works focus on repairing ontology mappings interactively. When repairing ontology mappings, those confidence values associated with the correspondences could help an expert to make a decision. Fine-grained repair algorithms (e.g., [53; 54; 55; 56; 57; 58]) only remove or rewrite parts of an axiom instead of removing the entire axiom. When weakening axioms, various strategies such as using refinement operators, splitting axioms or applying the tableaux algorithm. In addition, a few works such as [55] consider weakening axioms with an expert's help. In this work, we focus on deleting complete axioms without interaction of experts. Many existing repair algorithms rely on ranking axioms by considering their syntax or logical influence. The authors in [22; 26; 59] ranked axioms by computing scores. A score of an axiom corresponds to the number of MIPS or conflicts which contain this axiom. This ranking strategy was implemented in ScoreAlg. The work in [27] proposed a signature-based ranking strategy and a logic-based one, which were used in SigAlg and LogicAlg, respectively. Furthermore, the latter can be extended to allow a user to specify a set of test cases that describe those desired entailments. The work in [25] introduced a graph-based method to debug and repair a DL-Lite ontology. The authors ranked an axiom with two strategies: one computed a score like ScoreAlg, and the other computed logic impact when removing an axiom, which is similar to the ranking strategy implemented in LogicAlg. The work presented in [45] proposed a novel ranking strategy and computed the penalty of an axiom in a conflict set as the sum of inverse proportions to the size of such sets. That is, if an axiom appears in one conflict set \(M\), the penalty of this axiom is \(\frac{1}{|M|}\). If it appears in \(n\) conflict sets, its total penalty should be the sum of \(n\) penalties. This ranking strategy has been implemented in ShapAlg. It indicated that different ranking strategies could be combined in some way to form a hybrid one, such as the strategy used in SWOOP [46]. Another type of ranking strategy makes use of external knowledge. The work in [27] also proposed another strategy by making use of provenance information like the authors or reasons for adding an axiom. For instance, an axiom created by a supervisor should be more important or reliable than that created by a subordinate. The authors in [45] designed two novel ranking strategies by using background context ontologies. Each axiom can be assigned a support to represent how much support for an axiom exists in the background knowledge. Although these strategies are very useful, background knowledge may not be always available. In this work, we do not consider using external information. Recently, several works ranked axioms in a special way. The work in [23] ranked axioms by providing their truth values based on an embedding model. The work in [60] dealt with the problem of resolving conflicts with a partial order of axioms. The authors considered that not all axioms were ranked in the same way, and thus the axioms cannot be compared directly. To deal with this problem, a general notion of logical inconsistency was defined, and a conflict was stratified into two parts. Finally, a prioritized hitting set was computed as a diagnosis. To conclude, most of the existing ranking strategies for ontology repair mainly rely on the syntax of axioms or logic entailments, while ignoring the semantics of axioms. Although there exist few works that consider the semantics of axioms, they may not be suitable to deal with complex types of axioms.