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 log-ical background knowledge and the diffi-culty of scaling up inference. In contrast, low-dimensional embeddings (i.e. distri-butional 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-of-concept paper we address this by learning embeddings that simulate the behavior of first-order logic.