  We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for
both inductive learning and logic reasoning. NLMs exploit the power of both
neural networks---as function approximators, and logic programming---as a
symbolic processor for objects with properties, relations, logic connectives,
and quantifiers. After being trained on small-scale tasks (such as sorting
short arrays), NLMs can recover lifted rules, and generalize to large-scale
tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect
generalization in a number of tasks, from relational reasoning tasks on the
family tree and general graphs, to decision making tasks including sorting
arrays, finding shortest paths, and playing the blocks world. Most of these
tasks are hard to accomplish for neural networks or inductive logic programming
alone.
