Knowledge graph embedding aims to represent entities and relations in a knowledge graph as low-dimensional real-value vectors. Most existing studies exploit only structural information to learn these vectors. This paper studies how logical information expressed as RBox axioms in OWL 2 is used for embedding. The involvement of RBox axioms could prevent existing methods from learning predictive vectors. For example, the symmetric, reflexive or transitive relations can be declared by RBox axioms, but popular translation-based methods are unable to learn distinguishable vectors for multiple these relations in the ideal case. To overcome these limitations introduced by the involvement of RBox axioms, this paper proposes to enhance existing translation-based methods by logical pre-completion and bi-directional projection of entities. Experimental results demonstrate that these enhancements improve the predictive performance in link prediction and triple classification.
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