In section 3.2 of the submitted paper, we use the conclusion that "the transitive relation can be represented as the union of transitive closures of of all transitive chains." S1, S2, and S3 datasets of Counties are separated by '/'. Our model is implemented in Python 3.6 using Pytorch 1.1.0. We list the best hyper-parameter setting of Rot-Pro on the above datasets in Table 2. The fully expressive of BoxE refers to that it is able to express inference patterns, which includes symmetry, anti-symmetry, inversion, composition, hierarchy, intersection, and mutual exclusion.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities.

In section 3.2 of the submitted paper, we use the conclusion that "the transitive relation can be represented as the union of transitive closures of of all transitive chains." S1, S2, and S3 datasets of Counties are separated by '/'. Our model is implemented in Python 3.6 using Pytorch 1.1.0. We list the best hyper-parameter setting of Rot-Pro on the above datasets in Table 2. The fully expressive of BoxE refers to that it is able to express inference patterns, which includes symmetry, anti-symmetry, inversion, composition, hierarchy, intersection, and mutual exclusion.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities.

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the above relation patterns. Experimental results show that the proposed Rot-Pro model effectively learns the transitivity pattern and achieves the state-of-the-art results on the link prediction task in the datasets containing transitive relations.