Training Relation Embeddings under Logical Constraints

We present ways of incorporating logical rules into the construction of embedding based Knowledge Base Completion (KBC) systems. Enforcing “logical consistency” in the predictions of a KBC system guarantees that the predictions comply with logical rules such as symmetry, implication and generalized transitivity. Our method encodes logical rules about entities and relations as convex constraints in the embedding space to enforce the condition that the score of a logically entailed fact must never be less than the minimum score of an antecedent fact. Such constraints provide a weak guarantee that the predictions made by our KBC model will match the output of a logical knowledge base for many types of logical inferences. We validate our method via experiments on a knowledge graph derived from WordNet.