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 as components of 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. 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. We achieve new state-of-the-art performances with signficant margins in Link Prediction and Triple Classification on FB122 dataset, with boosted performance even on test instances that cannot be inferred by logical rules. The angles between the continuous sets embedded by TransINT provide an interpretable way to mine semantic relatedness and implication rules among relations.
We propose TransINT, a novel and interpretable KG embedding method that isomorphically preserves the implication ordering among relations in the embedding space in an explainable, robust, and geometrically coherent way.