  We explore end-to-end trained differentiable models that integrate natural
logic with neural networks, aiming to keep the backbone of natural language
reasoning based on the natural logic formalism while introducing subsymbolic
vector representations and neural components. The proposed model adapts module
networks to model natural logic operations, which is enhanced with a memory
component to model contextual information. Experiments show that the proposed
framework can effectively model monotonicity-based reasoning, compared to the
baseline neural network models without built-in inductive bias for
monotonicity-based reasoning. Our proposed model shows to be robust when
transferred from upward to downward inference. We perform further analyses on
the performance of the proposed model on aggregation, showing the effectiveness
of the proposed subcomponents on helping achieve better intermediate
aggregation performance.
