  Knowledge graph embedding models have gained significant attention in AI
research. Recent works have shown that the inclusion of background knowledge,
such as logical rules, can improve the performance of embeddings in downstream
machine learning tasks. However, so far, most existing models do not allow the
inclusion of rules. We address the challenge of including rules and present a
new neural based embedding model (LogicENN). We prove that LogicENN can learn
every ground truth of encoded rules in a knowledge graph. To the best of our
knowledge, this has not been proved so far for the neural based family of
embedding models. Moreover, we derive formulae for the inclusion of various
rules, including (anti-)symmetric, inverse, irreflexive and transitive,
implication, composition, equivalence and negation. Our formulation allows to
avoid grounding for implication and equivalence relations. Our experiments show
that LogicENN outperforms the state-of-the-art models in link prediction.
