Neural-Symbolic Architectural Axioms of Integration: A Manifesto

Connor Pryor, Lise Getoor

Keywords: NeSy, Neural-Symbolic, Neural Symbolic, NeSy Axioms

TL;DR: This paper introduces architectural axioms that formalize how neural and symbolic components integrate, providing a unifying theoretical foundation for the neural-symbolic field.

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.

Track: Main Track

Paper Type: Long Paper

Resubmission: No

Submission Number: 29