# Augmenting Neural Networks with First-order Logic

arXiv: https://arxiv.org/abs/1906.06298 · HTML: https://mlsanity.com/paper/1906.06298/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2019.

## Built on by (most cited first, 30 of 51)

- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
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- [Incorporating Domain Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2103.00180/) (2021)
- [Symbol-LLM: Towards Foundational Symbol-centric Interface For Large Language Models](https://mlsanity.com/paper/2311.09278/) (2023)
- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [GLoRE: Evaluating Logical Reasoning of Large Language Models](https://mlsanity.com/paper/2310.09107/) (2023)
- [DomiKnowS: A Library for Integration of Symbolic Domain Knowledge in Deep Learning](https://mlsanity.com/paper/2108.12370/) (2021)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [Do Large Language Models Understand Logic or Just Mimick Context?](https://mlsanity.com/paper/2402.12091/) (2024)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [DMWM: Dual-Mind World Model with Long-Term Imagination](https://mlsanity.com/paper/2502.07591/) (2025)
- [Learning Constraints and Descriptive Segmentation for Subevent Detection](https://mlsanity.com/paper/2109.06316/) (2021)
- [Does External Knowledge Help Explainable Natural Language Inference? Automatic Evaluation vs. Human Ratings](https://mlsanity.com/paper/2109.07833/) (2021)
- [Exploring Distantly-Labeled Rationales in Neural Network Models](https://mlsanity.com/paper/2106.01809/) (2021)
- [Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Study](https://mlsanity.com/paper/2107.13646/) (2021)
- [AI Descartes: Combining Data and Theory for Derivable Scientific Discovery](https://mlsanity.com/paper/2109.01634/) (2021)
- [AdaLoGN: Adaptive Logic Graph Network for Reasoning-Based Machine Reading Comprehension](https://mlsanity.com/paper/2203.08992/) (2022)
- [AutoML in The Wild: Obstacles, Workarounds, and Expectations](https://mlsanity.com/paper/2302.10827/) (2023)
- [Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learners](https://mlsanity.com/paper/2404.19696/) (2024)
- [The Need for Verification in AI-Driven Scientific Discovery](https://mlsanity.com/paper/2509.01398/) (2025)
- [EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic](https://mlsanity.com/paper/2408.08133/) (2024)
- [A Solver-Free Framework for Scalable Learning in Neural ILP Architectures](https://mlsanity.com/paper/2210.09082/) (2022)
- [Logic Rules as Explanations for Legal Case Retrieval](https://mlsanity.com/paper/2403.01457/) (2024)
- [A Novel Multi-Task Learning Approach for Context-Sensitive Compound Type Identification in Sanskrit](https://mlsanity.com/paper/2208.10310/) (2022)
- [Augmenting deep neural networks with symbolic knowledge: Towards trustworthy and interpretable AI for education](https://mlsanity.com/paper/2311.00393/) (2023)
- [Exploiting T-norms for Deep Learning in Autonomous Driving](https://mlsanity.com/paper/2402.11362/) (2024)

## Abstract (arXiv)

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this paper, we present a novel framework for introducing declarative knowledge to neural network architectures in order to guide training and prediction. Our framework systematically compiles logical statements into computation graphs that augment a neural network without extra learnable parameters or manual redesign. We evaluate our modeling strategy on three tasks: machine comprehension, natural language inference, and text chunking. Our experiments show that knowledge-augmented networks can strongly improve over baselines, especially in low-data regimes.