Learning to Reason over Neighborhoods: A Differentiable Guarded Logic Approach

Yizheng Zhao

Keywords: systematic generalization, inductive bias, guarded fragment, fuzzy sem

Abstract: Systematic generalization remains a well-recognized fundamental barrier for deep learning, especially in tasks requiring multi-hop relational reasoning. We posit this failure stems from a missing \emph{inductive bias} for local, compositional inference---a structure that is inherent to symbolic logic but absent in monolithic neural architectures. Our core insight is that the Guarded Fragment (GF)---a classic, decidable fragment of first-order logic---provides the ideal computational primitive for this paradigm. We reveal that its syntactic `guard' is not merely a constraint, but is formally equivalent to a mechanism for reasoning over local, relational neighborhoods. We operationalize this insight in \textsc{GuardNet}, the first framework to leverage GF as a principled inductive bias for neighborhood reasoning, featuring a novel dynamic domain strategy to prevent representational collapse. \textsc{GuardNet} employs a principled fuzzy semantics derived from Product t-norms, grounding it in theoretical soundness while enabling stable, end-to-end integration with neural architectures. On challenging benchmarks for knowledge base completion, \textsc{GuardNet} unlocks superior systematic generalization, succeeding on complex inferences where purely neural and prior neuro-symbolic systems falter. Our work demonstrates that classical logics can be reframed as a powerful inductive bias for modern representation learning, offering a principled pathway toward neural networks that can robustly reason.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 6296