mlsanityData to 14 Oct 2026

Logic Tensor Networks

arXiv 2012.13635 ↗First posted 25 Dec 2020cs.AI cs.LGcited by 199

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Cited by 39 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic distributed representations, reasoning is normally useful at a higher level of abstraction with the use of a first-order logic language for knowledge representation. As a result, attempts at combining symbolic AI and neural computation into neural-symbolic systems have been on the increase. In this paper, we present Logic Tensor Networks (LTN), a neurosymbolic formalism and computational model that supports learning and reasoning through the introduction of a many-valued, end-to-end differentiable first-order logic called Real Logic as a representation language for deep learning. We show that LTN provides a uniform language for the specification and the computation of several AI tasks such as data clustering, multi-label classification, relational learning, query answering, semi-supervised learning, regression and embedding learning. We implement and illustrate each of the above tasks with a number of simple explanatory examples using TensorFlow 2. Keywords: Neurosymbolic AI, Deep Learning and Reasoning, Many-valued Logic.

Key facts. Cited by 199 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Dec 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 19; 2023: 29; 2024: 43; 2025: 37; 2026: 64.

199 papers.

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  1. 2023Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directionscited by 125
  2. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  3. 2023Interpretable Neural-Symbolic Concept Reasoningcited by 57
  4. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
  5. 2022Deep Learning with Logical Constraintscited by 44
  6. 2024R2-Guard: Robust Reasoning Enabled LLM Guardrail via Knowledge-Enhanced Logical Reasoningcited by 43
  7. 2025Neuro-Symbolic AI in 2024: A Systematic Reviewcited by 38
  8. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  9. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
  10. 2023Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databasescited by 35
  11. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  12. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
38 more
  1. 2023Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentationcited by 29
  2. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  3. 2021Learning with Holographic Reduced Representationscited by 25
  4. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 25
  5. 2023Neural-Logic Human-Object Interaction Detectioncited by 25
  6. 2023Indoor and Outdoor 3D Scene Graph Generation via Language-Enabled Spatial Ontologiescited by 25
  7. 2024Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIcited by 24
  8. 2022Deep Symbolic Learning: Discovering Symbols and Rules from Perceptionscited by 21
  9. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  10. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
  11. 2024Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?cited by 18
  12. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  13. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  14. 2024Interpretable Concept-Based Memory Reasoningcited by 17
  15. 2023PyReason: Software for Open World Temporal Logiccited by 16
  16. 2024KLay: Accelerating Arithmetic Circuits for Neurosymbolic AIcited by 16
  17. 2023Logic of Differentiable Logics: Towards a Uniform Semantics of DLcited by 15
  18. 2023CuTS: Customizable Tabular Synthetic Data Generationcited by 13
  19. 2025Neurosymbolic Diffusion Modelscited by 13
  20. 2022Neuro-Symbolic Learning of Answer Set Programs from Raw Datacited by 12
  21. 2024The Role of Foundation Models in Neuro-Symbolic Learning and Reasoningcited by 12
  22. 2024Ontology Embedding: A Survey of Methods, Applications and Resourcescited by 12
  23. 2022Refining neural network predictions using background knowledgecited by 11
  24. 2021Faster-LTN: a neuro-symbolic, end-to-end object detection architecturecited by 10
  25. 2022Neuro-Symbolic Artificial Intelligence (AI) for Intent based Semantic Communicationcited by 10
  26. 2023Sem@K: Is my knowledge graph embedding model semantic-aware?cited by 10
  27. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  28. 2024NeSyA: Neurosymbolic Automatacited by 10
  29. 2025DMWM: Dual-Mind World Model with Long-Term Imaginationcited by 10
  30. 2022OG-SGG: Ontology-Guided Scene Graph Generation. A Case Study in Transfer Learning for Telepresence Roboticscited by 9
  31. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  32. 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
  33. 2024Metacognitive AI: Framework and the Case for a Neurosymbolic Approachcited by 9
  34. 2023Machine Learning with Requirements: a Manifestocited by 8
  35. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  36. 2025Defining neurosymbolic AIcited by 8
  37. 2022Enabling Verification of Deep Neural Networks in Perception Tasks Using Fuzzy Logic and Concept Embeddingscited by 7
  38. 2023Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraintscited by 7

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