mlsanityData to 7 Oct 2026

From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey

arXiv 2108.11451 ↗First posted 25 Aug 2021cs.AIcited by 72

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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.

Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). Builds on 57 of its 139 references that are in the map. First posted on arXiv 25 Aug 2021.

Builds on

57 of 139 references.

References · 57

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  11. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 389
  12. 2019The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervisioncited by 369
38 more
  1. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 267
  2. 2015A Review of Relational Machine Learning for Knowledge Graphscited by 264
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  4. 2020Logic Tensor Networkscited by 197
  5. 2019Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoningcited by 149
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50 most cited of 57 All 57 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 5; 2024: 14; 2025: 28; 2026: 19.

72 papers.

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  1. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
  2. 2021A Survey on Neural-symbolic Learning Systemscited by 39
  3. 2025Neuro-Symbolic AI in 2024: A Systematic Reviewcited by 36
  4. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  5. 2022VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programmingcited by 31
  6. 2022Neuro-Symbolic Entropy Regularizationcited by 27
  7. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 24
  8. 2024Interpretable Concept-Based Memory Reasoningcited by 17
  9. 2024Softened Symbol Grounding for Neuro-symbolic Systemscited by 16
  10. 2023Injecting Logical Constraints into Neural Networks via Straight-Through Estimatorscited by 12
  11. 2025Neurosymbolic Diffusion Modelscited by 12
  12. 2025A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfactioncited by 11
38 more
  1. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  2. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  3. 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
  4. 2024NeSyA: Neurosymbolic Automatacited by 9
  5. 2025Defining neurosymbolic AIcited by 7
  6. 2023Neurosymbolic AI and its Taxonomy: a surveycited by 6
  7. 2023Declarative Probabilistic Logic Programming in Discrete-Continuous Domainscited by 5
  8. 2024Understanding the Logic of Direct Preference Alignment through Logiccited by 5
  9. 2024Clinical Reasoning over Tabular Data and Text with Bayesian Networkscited by 4
  10. 2024CLEVR-POC: Reasoning-Intensive Visual Question Answering in Partially Observable Environmentscited by 3
  11. 2025A Learnability Analysis on Neuro-Symbolic Learningcited by 3
  12. 2025Grounding Methods for Neural-Symbolic AIcited by 3
  13. 2025The DeepLog Neurosymbolic Machinecited by 3
  14. 2023Knowledge Enhanced Graph Neural Networks for Graph Completioncited by 2
  15. 2024Aligning Generalisation Between Humans and Machinescited by 2
  16. 2025Inductive Learning of Robot Task Knowledge from Raw Data and Online Expert Feedbackcited by 2
  17. 2025Benchmarking graph construction by large language models for coherence-driven inferencecited by 2
  18. 2025A Neuro-Symbolic Framework for Sequence Classification with Relational and Temporal Knowledgecited by 2
  19. 2025Enhancing Symbolic Machine Learning by Subsymbolic Representationscited by 2
  20. 2025Neurosymbolic Object-Centric Learning with Distant Supervisioncited by 2
  21. 2025Neuro-Symbolic AI for Cybersecurity: State of the Art, Challenges, and Opportunitiescited by 2
  22. 2025Explainability of Large Language Models: Opportunities and Challenges toward Generating Trustworthy Explanationscited by 2
  23. 2022Modular design patterns for neural-symbolic integration: refinement and combinationcited by 1
  24. 2024IID Relaxation by Logical Expressivity: A Research Agenda for Fitting Logics to Neurosymbolic Requirementscited by 1
  25. 2024Declarative Design of Neural Predicates in Neuro-Symbolic Systemscited by 1
  26. 2024Quantum Algorithms for Weighted Constrained Sampling and Weighted Model Countingcited by 1
  27. 2025Standard Neural Computation Alone Is Insufficient for Logical Intelligencecited by 1
  28. 2025A Scalable Approach to Probabilistic Neuro-Symbolic Robustness Verificationcited by 1
  29. 2025MILP-SAT-GNN: Yet Another Neural SAT Solvercited by 1
  30. 2025Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformerscited by 1
  31. 2025DeepGraphLog for Layered Neurosymbolic AIcited by 1
  32. 2026Sample-Efficient Neurosymbolic Deep Reinforcement Learningcited by 1
  33. 2026DeepLog: A Software Framework for Modular Neurosymbolic AIcited by 1
  34. 2026Weakly Supervised Segmentation as Semantic-Based Regularizationcited by 1
  35. 2026First-Order Temporal Logic Tensor Networkscited by 1
  36. 2026From Token Probabilities to Semantic Constraints: Towards Declarative Probabilistic Evaluation of Language Modelscited by 1
  37. 2024Enhancing Computer Vision with Knowledge: a Rummikub Case Studycited by 0
  38. 2025Combining Planning and Reinforcement Learning for Solving Relational Multiagent Domainscited by 0

50 most cited of 72 All 72 (JSON)