# From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey

arXiv: https://arxiv.org/abs/2108.11451 · HTML: https://mlsanity.com/paper/2108.11451/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 139 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 30 of 57)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion](https://mlsanity.com/paper/1811.04441/) (2018)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)

## Built on by (most cited first, 30 of 72)

- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Neuro-Symbolic Entropy Regularization](https://mlsanity.com/paper/2201.11250/) (2022)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)
- [A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction](https://mlsanity.com/paper/2503.19466/) (2025)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [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)
- [On the Hardness of Probabilistic Neurosymbolic Learning](https://mlsanity.com/paper/2406.04472/) (2024)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Neurosymbolic AI and its Taxonomy: a survey](https://mlsanity.com/paper/2305.08876/) (2023)
- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [Understanding the Logic of Direct Preference Alignment through Logic](https://mlsanity.com/paper/2412.17696/) (2024)
- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [Clinical Reasoning over Tabular Data and Text with Bayesian Networks](https://mlsanity.com/paper/2403.09481/) (2024)
- [CLEVR-POC: Reasoning-Intensive Visual Question Answering in Partially Observable Environments](https://mlsanity.com/paper/2403.03203/) (2024)
- [A Learnability Analysis on Neuro-Symbolic Learning](https://mlsanity.com/paper/2503.16797/) (2025)
- [Grounding Methods for Neural-Symbolic AI](https://mlsanity.com/paper/2507.08216/) (2025)
- [Knowledge Enhanced Graph Neural Networks for Graph Completion](https://mlsanity.com/paper/2303.15487/) (2023)
- [Aligning Generalisation Between Humans and Machines](https://mlsanity.com/paper/2411.15626/) (2024)
- [Inductive Learning of Robot Task Knowledge from Raw Data and Online Expert Feedback](https://mlsanity.com/paper/2501.07507/) (2025)
- [Benchmarking graph construction by large language models for coherence-driven inference](https://mlsanity.com/paper/2502.13953/) (2025)
- [A Neuro-Symbolic Framework for Sequence Classification with Relational and Temporal Knowledge](https://mlsanity.com/paper/2505.05106/) (2025)

## Abstract (arXiv)

This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proof-based; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.