See related work (section 2) of Wu 2020

Zhang et al 2020 - Neural, Symbolic and Neural-Symbolic Reasoning on Knowledge Graphs

Neural Module Networks

Murray & Krishnamurthy 2016 - Probabilistic Neural Programs

Hu et al 2016 - Harnessing Deep Neural Networks with Logic Rules

Evans & Grefenstette 2017 - Learning Explanatory Rules from Noisy Data Introduces Differentiable Inductive Logic Programming, which is trained using backpropagation. DILP provides “data efficiency and generalisation beyond what neural networks can achieve on their own.”

Evans et al 2018 - Can Neural Networks Understand Logical Entailment?

Wang & Poon 2018 - Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision (summary here, from Wang 2019)

Wang et al 2019 - Evidence Sentence Extraction for Machine Reading Comprehension Uses Deep Probabilistic Logic

Cohen et al 2020 - Tensorlog: A probabilistic database implemented using deep-learning infrastructure

Wu et al 2020 - Deep Weighted MaxSAT for Aspect-based Opinion Extraction See the related work

Feng et al 2022 - Neuro-symbolic Natural Logic with Introspective Revision for Natural Language Inference

Qian et al 2022 - Limitations of Language Models in Arithmetic and Symbolic Induction

William W. Cohen

Knowledge-Enhanced Methods

Neural Module Networks

Neural Program Induction

Probabilistic Logic