mlsanityData to 14 Oct 2026

Defining neurosymbolic AI

arXiv 2507.11127 ↗First posted 15 Jul 2025cs.AIcited by 8

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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.

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

34 of 69 references.

References · 34

  1. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
  2. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 270
  3. 2020Neurosymbolic AI: The 3rd Wavecited by 255
  4. 2020Logic Tensor Networkscited by 199
  5. 2017Neural-Symbolic Learning and Reasoning: A Survey and Interpretationcited by 196
  6. 2017End-to-End Differentiable Provingcited by 161
  7. 2019Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoningcited by 151
  8. 2019Neural Logic Machinescited by 145
  9. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  10. 2023NeurASP: Embracing Neural Networks into Answer Set Programmingcited by 92
  11. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  12. 2020From Statistical Relational to Neuro-Symbolic Artificial Intelligencecited by 63
22 more
  1. 2023Scallop: A Language for Neurosymbolic Programmingcited by 63
  2. 2021DeepStochLog: Neural Stochastic Logic Programmingcited by 58
  3. 2020Neural-Symbolic Integration: A Compositional Perspectivecited by 45
  4. 2023Safe Reinforcement Learning via Probabilistic Logic Shieldscited by 42
  5. 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
  6. 2019NLProlog: Reasoning with Weak Unification for Question Answering in Natural Languagecited by 37
  7. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  8. 2019Neural Markov Logic Networkscited by 27
  9. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 25
  10. 2019Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architecturescited by 24
  11. 2018Inductive Learning of Answer Set Programs from Noisy Examplescited by 22
  12. 2019Integrating Learning and Reasoning with Deep Logic Modelscited by 21
  13. 2019A Boxology of Design Patterns for Hybrid Learning and Reasoning Systemscited by 20
  14. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  15. 2023Logic of Differentiable Logics: Towards a Uniform Semantics of DLcited by 15
  16. 2024NeSyA: Neurosymbolic Automatacited by 10
  17. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  18. 2022Neurosymbolic Motion and Task Planning for Linear Temporal Logic Taskscited by 6
  19. 2023Declarative Probabilistic Logic Programming in Discrete-Continuous Domainscited by 5
  20. 2023Neurosymbolic AI for Reasoning on Biomedical Knowledge Graphscited by 4
  21. 2025Valid Text-to-SQL Generation with Unification-based DeepStochLogcited by 3
  22. 2025Pi-NeSy: A Possibilistic Neuro-Symbolic Approachcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 5.

8 papers.

  1. 2025The DeepLog Neurosymbolic Machinecited by 5
  2. 2025CLAUSE: Agentic Neuro-Symbolic Knowledge Graph Reasoning via Dynamic Learnable Context Engineeringcited by 3
  3. 2026DeepLog: A Software Framework for Modular Neurosymbolic AIcited by 2
  4. 2025Symbolic Neural Generation with Applications to Lead Discovery in Drug Designcited by 0
  5. 2026A Sugeno Integral View of Binarized Neural Network Inferencecited by 0
  6. 2026A homotopy-type-theoretic generalization of neurosymbolic inferencecited by 0
  7. 2026From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and Howcited by 0
  8. 2026Rule-Based Languages for Neurosymbolic AIcited by 0