Natural logic offers a powerful relational conception of meaning that is a natural counterpart to distributed semantic representations, which have proven valuable in a wide range of sophisticated language tasks. However, it remains an open question whether it is possible to train distributed representations to support the rich, diverse logical reasoning captured by natural logic. We address this question using two neural network-based models for learning embeddings: plain neural networks and neural tensor networks. Our experiments evaluate the models' ability to learn the basic algebra of natural logic relations from simulated data and from the Word-Net noun graph. The overall positive results are promising for the future of learned distributed representations in the applied modeling of logical semantics.