Logical Rule Induction and Theory Learning Using Neural Theorem Proving
  A hallmark of human cognition is the ability to continually acquire and
distill observations of the world into meaningful, predictive theories. In this
paper we present a new mechanism for logical theory acquisition which takes a
set of observed facts and learns to extract from them a set of logical rules
and a small set of core facts which together entail the observations. Our
approach is neuro-symbolic in the sense that the rule pred- icates and core
facts are given dense vector representations. The rules are applied to the core
facts using a soft unification procedure to infer additional facts. After k
steps of forward inference, the consequences are compared to the initial
observations and the rules and core facts are then encouraged towards
representations that more faithfully generate the observations through
inference. Our approach is based on a novel neural forward-chaining
differentiable rule induction network. The rules are interpretable and learned
compositionally from their predicates, which may be invented. We demonstrate
the efficacy of our approach on a variety of ILP rule induction and domain
theory learning datasets.
