Neural-Symbolic Architectural Axioms of Integration: A Manifesto

Connor Pryor, Lise Getoor
Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning, PMLR 284:322-342, 2025.

Abstract

The integration of neural and symbolic methods has long been viewed as a promising path toward more general, interpretable, and robust artificial intelligence. The past two decades have seen a rapid proliferation of neural-symbolic (NeSy) systems, spanning a wide range of architectures, reasoning strategies, and application domains. However, this growth has outpaced theoretical clarity: many existing approaches conflate the roles of learning, inference, and representation, leading to a fragmented field lacking principled foundations. In this work, we address this gap by proposing a set of architectural axioms of integration—formal, implementation-agnostic principles that define how neural and symbolic components can be coherently combined. These axioms abstract away from system-specific details and instead characterize the structural interface between neural perception and symbolic reasoning. Rather than introducing a new method, this work offers a foundation to organize, compare, and reason about the rapidly expanding space of NeSy approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v284-pryor25a, title = {Neural-Symbolic Architectural Axioms of Integration: A Manifesto}, author = {Pryor, Connor and Getoor, Lise}, booktitle = {Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning}, pages = {322--342}, year = {2025}, editor = {H. Gilpin, Leilani and Giunchiglia, Eleonora and Hitzler, Pascal and van Krieken, Emile}, volume = {284}, series = {Proceedings of Machine Learning Research}, month = {08--10 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v284/main/assets/pryor25a/pryor25a.pdf}, url = {https://proceedings.mlr.press/v284/pryor25a.html}, abstract = {The integration of neural and symbolic methods has long been viewed as a promising path toward more general, interpretable, and robust artificial intelligence. The past two decades have seen a rapid proliferation of neural-symbolic (NeSy) systems, spanning a wide range of architectures, reasoning strategies, and application domains. However, this growth has outpaced theoretical clarity: many existing approaches conflate the roles of learning, inference, and representation, leading to a fragmented field lacking principled foundations. In this work, we address this gap by proposing a set of architectural axioms of integration—formal, implementation-agnostic principles that define how neural and symbolic components can be coherently combined. These axioms abstract away from system-specific details and instead characterize the structural interface between neural perception and symbolic reasoning. Rather than introducing a new method, this work offers a foundation to organize, compare, and reason about the rapidly expanding space of NeSy approaches.} }
Endnote
%0 Conference Paper %T Neural-Symbolic Architectural Axioms of Integration: A Manifesto %A Connor Pryor %A Lise Getoor %B Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Leilani H. Gilpin %E Eleonora Giunchiglia %E Pascal Hitzler %E Emile van Krieken %F pmlr-v284-pryor25a %I PMLR %P 322--342 %U https://proceedings.mlr.press/v284/pryor25a.html %V 284 %X The integration of neural and symbolic methods has long been viewed as a promising path toward more general, interpretable, and robust artificial intelligence. The past two decades have seen a rapid proliferation of neural-symbolic (NeSy) systems, spanning a wide range of architectures, reasoning strategies, and application domains. However, this growth has outpaced theoretical clarity: many existing approaches conflate the roles of learning, inference, and representation, leading to a fragmented field lacking principled foundations. In this work, we address this gap by proposing a set of architectural axioms of integration—formal, implementation-agnostic principles that define how neural and symbolic components can be coherently combined. These axioms abstract away from system-specific details and instead characterize the structural interface between neural perception and symbolic reasoning. Rather than introducing a new method, this work offers a foundation to organize, compare, and reason about the rapidly expanding space of NeSy approaches.
APA
Pryor, C. & Getoor, L.. (2025). Neural-Symbolic Architectural Axioms of Integration: A Manifesto. Proceedings of The 19th International Conference on Neurosymbolic Learning and Reasoning, in Proceedings of Machine Learning Research 284:322-342 Available from https://proceedings.mlr.press/v284/pryor25a.html.

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