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Knowledge Graphs (KG), composed of entities and relations, provide astructured representation of knowledge. For easy access to statisticalapproaches 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 KGembedding method that isomorphically preserves the implication ordering amongrelations in the embedding space. Given implication rules, TransINT maps set ofentities (tied by a relation) to continuous sets of vectors that areinclusion-ordered isomorphically to relation implications. With a novelparameter sharing scheme, TransINT enables automatic training on missing butimplied facts without rule grounding. On a benchmark dataset, we outperform thebest existing state-of-the-art rule integration embedding methods withsignificant margins in link Prediction and triple Classification. The anglesbetween the continuous sets embedded by TransINT provide an interpretable wayto mine semantic relatedness and implication rules among relations.

TransINT: Embedding Implication Rules in Knowledge Graphs with Isomorphic Intersections of Linear Subspaces