Low-Dimensional Embeddings of Logic

Many machine reading approaches, from shallow information extraction to deep semantic parsing, map natural language to symbolic representations of meaning. Representations such as first-order logic capture the richness of natural language and support complex reasoning, but often fail in practice due to their reliance on logical background knowledge and the difficulty of scaling up inference. In contrast, low-dimensional embeddings (i.e. distributional representations) are efficient and enable generalization, but it is unclear how reasoning with embeddings could support the full power of symbolic representations such as first-order logic. In this proof-ofconcept paper we address this by learning embeddings that simulate the behavior of first-order logic.