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### EL Embeddings: Geometric construction of models for the Description Logic EL ++

An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can be used for machine learning, similarity search, or similar tasks. We address the problem of finding vector space embeddings for theories in the Description Logic $\mathcal{EL}^{++}$ that are also models of the TBox. To find such embeddings, we define an optimization problem that characterizes the model-theoretic semantics of the operators in $\mathcal{EL}^{++}$ within $\Re^n$, thereby solving the problem of finding an interpretation function for an $\mathcal{EL}^{++}$ theory given a particular domain $\Delta$. Our approach is mainly relevant to large $\mathcal{EL}^{++}$ theories and knowledge bases such as the ontologies and knowledge graphs used in the life sciences. We demonstrate that our method can be used for improved prediction of protein--protein interactions when compared to semantic similarity measures or knowledge graph embedding

The increasing amounts of semantic resources offer valuable storage of human knowledge; however, the probability of wrong entries increases with the increased size. The development of approaches that identify potentially spurious parts of a given knowledge base is thus becoming an increasingly important area of interest. In this work, we present a systematic evaluation of whether structure-only link analysis methods can already offer a scalable means to detecting possible anomalies, as well as potentially interesting novel relation candidates. Evaluating thirteen methods on eight different semantic resources, including Gene Ontology, Food Ontology, Marine Ontology and similar, we demonstrated that structure-only link analysis could offer scalable anomaly detection for a subset of the data sets. Further, we demonstrated that by considering symbolic node embedding, explanations of the predictions (links) could be obtained, making this branch of methods potentially more valuable than the black-box only ones. To our knowledge, this is currently one of the most extensive systematic studies of the applicability of different types of link analysis methods across semantic resources from different domains.

### OWL2Vec*: Embedding of OWL Ontologies

Semantic embedding of knowledge graphs has been widely studied and used for prediction and statistical analysis tasks across various domains such as Natural Language Processing and the Semantic Web. However, less attention has been paid to developing robust methods for embedding OWL (Web Ontology Language) ontologies. In this paper, we propose a language model based ontology embedding method named OWL2Vec*, which encodes the semantics of an ontology by taking into account its graph structure, lexical information and logic constructors. Our empirical evaluation with three real world datasets suggests that OWL2Vec* benefits from these three different aspects of an ontology in class membership prediction and class subsumption prediction tasks. Furthermore, OWL2Vec* often significantly outperforms the state-of-the-art methods in our experiments.

### Large-scale Taxonomy Induction Using Entity and Word Embeddings

Taxonomies are an important ingredient of knowledge organization, and serve as a backbone for more sophisticated knowledge representations in intelligent systems, such as formal ontologies. However, building taxonomies manually is a costly endeavor, and hence, automatic methods for taxonomy induction are a good alternative to build large-scale taxonomies. In this paper, we propose TIEmb, an approach for automatic unsupervised class subsumption axiom extraction from knowledge bases using entity and text embeddings. We apply the approach on the WebIsA database, a database of subsumption relations extracted from the large portion of the World Wide Web, to extract class hierarchies in the Person and Place domain.

### Ontology-based n-ball Concept Embeddings Informing Few-shot Image Classification

We propose a novel framework named ViOCE that integrates ontology-based background knowledge in the form of $n$-ball concept embeddings into a neural network based vision architecture. The approach consists of two components - converting symbolic knowledge of an ontology into continuous space by learning n-ball embeddings that capture properties of subsumption and disjointness, and guiding the training and inference of a vision model using the learnt embeddings. We evaluate ViOCE using the task of few-shot image classification, where it demonstrates superior performance on two standard benchmarks.