Logical Rule Induction and Theory Learning Using Neural Theorem Proving

Abstract

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.

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Cited by in corpus (8)

• Logic Tensor Networks
• Learn to Explain Efficiently via Neural Logic Inductive Learning
• Feed-Forward Neural Networks Need Inductive Bias to Learn Equality Relations
• Neural Theorem Provers Do Not Learn Rules Without Exploration
• A Survey on Neural-symbolic Learning Systems
• SLD-Resolution Reduction of Second-Order Horn Fragments -- technical report --
• Neural Networks Enhancement with Logical Knowledge
• RuDaS: Synthetic Datasets for Rule Learning and Evaluation Tools