  Knowledge Graphs (KG), composed of entities and relations, provide a
structured representation of knowledge. For easy access to statistical
approaches on relational data, multiple methods to embed a KG into f(KG) $\in$
R^d have been introduced. We propose TransINT, a novel and interpretable KG
embedding method that isomorphically preserves the implication ordering among
relations in the embedding space. Given implication rules, TransINT maps set of
entities (tied by a relation) to continuous sets of vectors that are
inclusion-ordered isomorphically to relation implications. With a novel
parameter sharing scheme, TransINT enables automatic training on missing but
implied facts without rule grounding. On a benchmark dataset, we outperform the
best existing state-of-the-art rule integration embedding methods with
significant margins in link Prediction and triple Classification. The angles
between the continuous sets embedded by TransINT provide an interpretable way
to mine semantic relatedness and implication rules among relations.
