Logic of Hypotheses Unifies Neurosymbolic Integration Approaches

A new paper introduces Logic of Hypotheses (LoH), a language that unifies two strands of neurosymbolic integration (NeSy): injecting hand-crafted rules into neural models and inducing symbolic rules from data. LoH extends propositional logic with a choice operator that has learnable parameters, allowing selection of subformulas from a pool. Using Gödel fuzzy logic and the Gödel trick, LoH formulas compile into differentiable computational graphs, enabling learning via backpropagation. The framework subsumes existing NeSy models while allowing arbitrary degrees of knowledge specification. The paper is available on arXiv (2509.21663v2).