# Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains

arXiv: https://arxiv.org/abs/2006.08480 · HTML: https://mlsanity.com/paper/2006.08480/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 16 of 16)

- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Machine Learning Methods in Solving the Boolean Satisfiability Problem](https://mlsanity.com/paper/2203.04755/) (2022)
- [Dividing and Conquering a BlackBox to a Mixture of Interpretable Models: Route, Interpret, Repeat](https://mlsanity.com/paper/2307.05350/) (2023)
- [Differentiable Rule Induction with Learned Relational Features](https://mlsanity.com/paper/2201.06515/) (2022)
- [Towards Safe Autonomous Driving Policies using a Neuro-Symbolic Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2307.01316/) (2023)
- [Neural-Symbolic VideoQA: Learning Compositional Spatio-Temporal Reasoning for Real-world Video Question Answering](https://mlsanity.com/paper/2404.04007/) (2024)
- [Neurosymbolic Graph Enrichment for Grounded World Models](https://mlsanity.com/paper/2411.12671/) (2024)
- [A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectives](https://mlsanity.com/paper/2503.18213/) (2025)
- [Semantic Objective Functions: A distribution-aware method for adding logical constraints in deep learning](https://mlsanity.com/paper/2405.15789/) (2024)
- [Deep Algorithmic Question Answering: Towards a Compositionally Hybrid AI for Algorithmic Reasoning](https://mlsanity.com/paper/2109.08006/) (2021)
- [Syntactic Requirements for Well-defined Hybrid Probabilistic Logic Programs](https://mlsanity.com/paper/2109.08283/) (2021)
- [Tackling Shortcut Learning in Deep Neural Networks: An Iterative Approach with Interpretable Models](https://mlsanity.com/paper/2302.10289/) (2023)
- [Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspective](https://mlsanity.com/paper/2210.01344/) (2022)
- [A Novel Neural-symbolic System under Statistical Relational Learning](https://mlsanity.com/paper/2309.08931/) (2023)
- [Towards Developing Ethical Reasoners: Integrating Probabilistic Reasoning and Decision-Making for Complex AI Systems](https://mlsanity.com/paper/2502.21250/) (2025)

## Abstract (arXiv)

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains.