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
