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From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey

Paper · 2021 · Giuseppe Marra, Sebastijan Dumančić, Robin Manhaeve et al.

Summary

Neurosymbolic AI (NeSy), which combines neural networks with symbolic reasoning, and statistical relational AI (StarAI), which combines logic with probabilistic graphical models, both aim to unify learning and reasoning. Yet the two communities have developed largely separately. This survey by Marra, Dumančić, Manhaeve and De Raedt (KU Leuven, TU Delft, Örebro University) bridges that gap. Its starting point is the StarAI literature, whose core concepts turn out to apply to NeSy as well.

The authors propose seven shared dimensions for describing any system in either field. Each dimension gets an accessible introduction to the underlying logic or probability concepts, written for readers from a neural-network background, along with illustrative methods. Representative frameworks are then classified in a comparison table.

The paper reports no new data or experiments. Its contribution is a common conceptual vocabulary and taxonomy. This matters because it reveals analogies between the two fields, shows where techniques can transfer from one to the other, and points to dimensions that remain underexplored. The survey closes with a list of open research challenges.

Key points

  • The seven dimensions are:
    • proof-based vs model-based inference
    • logic syntax (propositional, relational, first-order)
    • semantics, including fuzzy and probabilistic extensions
    • parameter vs structure learning
    • symbolic vs subsymbolic representations
    • the mix of logic, probability and neural paradigms
    • learning task type
  • Table 1 classifies 22 logic-based frameworks, among them DeepProbLog, DeepStochLog, ∂ILP, NTP, LTN, NeurASP, NeuralLP, Scallop, TensorLog and SBR.
  • The scope is deliberately limited. The survey takes a logical perspective, works with clausal logic, and covers prototypical systems rather than aiming for completeness.
  • Inference is contrasted in two views.
    • Proof-theoretic inference searches for proofs of a query, compactly represented as AND/OR trees.
    • Model-theoretic inference searches for truth assignments that satisfy a theory.
  • Open challenges include:
    • clarifying NeSy semantics, which the authors compare to the early "alphabet soup" of competing statistical relational formalisms
    • the inconsistent choice of t-norm fuzzy logics
    • structure learning that still depends on user-written templates
    • scalable inference
    • data efficiency
    • learning symbolic representations

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Fields, topics and concepts

📚 Shelves 2The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 works

💡 Concepts 1Key ideas and methods explained on our concept pages.Artificial intelligence · 49 works

Cite

Cite as Giuseppe Marra, Sebastijan Dumančić, Robin Manhaeve and Luc De Raedt. 2021. From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey. arXiv:2108.11451.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2108.11451 · arXiv 2108.11451

@misc{marra2021statistical,
  title = {{From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey}},
  author = {Giuseppe Marra, Sebastijan Dumančić, Robin Manhaeve and Luc {De Raedt}},
  year = {2021},
  doi = {10.48550/arxiv.2108.11451},
  eprint = {2108.11451},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2108.11451}
}

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