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

Understand

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 $\Delta$.