# Defining neurosymbolic AI

arXiv: https://arxiv.org/abs/2507.11127 · HTML: https://mlsanity.com/paper/2507.11127/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 69 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 30 of 34)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [Neural Markov Logic Networks](https://mlsanity.com/paper/1905.13462/) (2019)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures](https://mlsanity.com/paper/1905.08550/) (2019)
- [Inductive Learning of Answer Set Programs from Noisy Examples](https://mlsanity.com/paper/1808.08441/) (2018)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [A Boxology of Design Patterns for Hybrid Learning and Reasoning Systems](https://mlsanity.com/paper/1905.12389/) (2019)
- [Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints](https://mlsanity.com/paper/2502.18237/) (2025)
- [Logic of Differentiable Logics: Towards a Uniform Semantics of DL](https://mlsanity.com/paper/2303.10650/) (2023)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [Neurosymbolic Motion and Task Planning for Linear Temporal Logic Tasks](https://mlsanity.com/paper/2210.05180/) (2022)

## Built on by (most cited first, 8 of 8)

- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [CLAUSE: Agentic Neuro-Symbolic Knowledge Graph Reasoning via Dynamic Learnable Context Engineering](https://mlsanity.com/paper/2509.21035/) (2025)
- [DeepLog: A Software Framework for Modular Neurosymbolic AI](https://mlsanity.com/paper/2605.10279/) (2026)
- [Symbolic Neural Generation with Applications to Lead Discovery in Drug Design](https://mlsanity.com/paper/2510.23379/) (2025)
- [A Sugeno Integral View of Binarized Neural Network Inference](https://mlsanity.com/paper/2604.17967/) (2026)
- [A homotopy-type-theoretic generalization of neurosymbolic inference](https://mlsanity.com/paper/2606.17851/) (2026)
- [From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How](https://mlsanity.com/paper/2607.22811/) (2026)
- [Rule-Based Languages for Neurosymbolic AI](https://mlsanity.com/paper/2610.07313/) (2026)

## Abstract (arXiv)

Neurosymbolic AI focuses on integrating learning and reasoning, in particular, on unifying logical and neural representations. Despite the existence of an alphabet soup of neurosymbolic AI systems, the field is lacking a generally accepted formal definition of what neurosymbolic models and inference really are. We introduce a formal definition for neurosymbolic AI that makes abstraction of its key ingredients. More specifically, we define neurosymbolic inference as the computation of an integral over a product of a logical and a belief function. We show that our neurosymbolic AI definition makes abstraction of key representative neurosymbolic AI systems.