Fernando Zhapa-Camacho

Fernando Zhapa-Camacho, Robert Hoehndorf

Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.

Fernando Zhapa-Camacho, Robert Hoehndorf

Generating vector representations (embeddings) of OWL ontologies is a growing task due to its applications in predicting missing facts and knowledge-enhanced learning in fields such as bioinformatics. The underlying semantics of OWL ontologies are expressed using Description Logics (DLs). Initial approaches to generate embeddings relied on constructing a graph out of ontologies, neglecting the semantics of the logic therein. Recent semantic-preserving embedding methods often target lightweight DL languages like $\mathcal{EL}^{++}$, ignoring more expressive information in ontologies. Although some approaches aim to embed more descriptive DLs like $\mathcal{ALC}$, those methods require the existence of individuals, while many real-world ontologies are devoid of them. We propose an ontology embedding method for the $\mathcal{ALC}$ DL language that considers the lattice structure of concept descriptions. We use connections between DL and Category Theory to materialize the lattice structure and embed it using an order-preserving embedding method. We show that our method outperforms state-of-the-art methods in several knowledge base completion tasks. Furthermore, we incoporate saturation procedures that increase the information within the constructed lattices. We make our code and data available at \url{https://github.com/bio-ontology-research-group/catE}.

Olga Mashkova, Fernando Zhapa-Camacho, Robert Hoehndorf

Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies based on high-dimensional ball representation of concept descriptions, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

Fernando Zhapa-Camacho, Robert Hoehndorf

Geometric embedding methods have shown to be useful for multi-hop reasoning on knowledge graphs by mapping entities and logical operations to geometric regions and geometric transformations, respectively. Geometric embeddings provide direct interpretability framework for queries. However, current methods have only leveraged the geometric construction of entities, failing to map logical operations to geometric transformations and, instead, using neural components to learn these operations. We introduce GeometrE, a geometric embedding method for multi-hop reasoning, which does not require learning the logical operations and enables full geometric interpretability. Additionally, unlike previous methods, we introduce a transitive loss function and show that it can preserve the logical rule $\forall a,b,c: r(a,b) \land r(b,c) \to r(a,c)$. Our experiments show that GeometrE outperforms current state-of-the-art methods on standard benchmark datasets.

Olga Mashkova, Fernando Zhapa-Camacho, Robert Hoehndorf

Ontology embeddings map classes, roles, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several optimization-based embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives and formulated evaluation methods for knowledge base completion. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

Jiaoyan Chen, Olga Mashkova, Fernando Zhapa-Camacho et al.

Ontologies are widely used for representing domain knowledge and meta data, playing an increasingly important role in Information Systems, the Semantic Web, Bioinformatics and many other domains. However, logical reasoning that ontologies can directly support are quite limited in learning, approximation and prediction. One straightforward solution is to integrate statistical analysis and machine learning. To this end, automatically learning vector representation for knowledge of an ontology i.e., ontology embedding has been widely investigated. Numerous papers have been published on ontology embedding, but a lack of systematic reviews hinders researchers from gaining a comprehensive understanding of this field. To bridge this gap, we write this survey paper, which first introduces different kinds of semantics of ontologies and formally defines ontology embedding as well as its property of faithfulness. Based on this, it systematically categorizes and analyses a relatively complete set of over 80 papers, according to the ontologies they aim at and their technical solutions including geometric modeling, sequence modeling and graph propagation. This survey also introduces the applications of ontology embedding in ontology engineering, machine learning augmentation and life sciences, presents a new library mOWL and discusses the challenges and future directions.