Logic of Hypotheses: From Zero to Full Knowledge in Neurosymbolic Integration

ICLR 2026 Conference Submission18367 Authors

Keywords: Neurosymbolic, Fuzzy Logic, Gödel Semantics, Rule Learning

TL;DR: The Logic of Hypotheses paper adds a differentiable choice-operator to Gödel fuzzy logic so gradient descent can pick discrete rule options, unifying knowledge injection and structure learning inside one neuro-symbolic model.

Abstract: Neurosymbolic integration (NeSy) blends neural‐network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of Gödel fuzzy logic and the recently developed Gödel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on the Visual Tic-Tac-Toe NeSy task, while producing interpretable decision rules.

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

Submission Number: 18367