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 two NeSy tasks with a perceptual component.

翻译：神经常识符号集成（NeSy）融合了神经网络学习与符号推理。该领域可分为两大方向：将人工规则注入神经模型的方法，以及从数据中归纳符号规则的方法。本文提出假设逻辑（LoH），一种新型语言，它统一了这两个方向，实现了数据驱动的规则学习与符号先验及专家知识的灵活集成。LoH在命题逻辑语法基础上扩展了一个选择算子，该算子具有可学习参数，能从备选子句池中选择子公式。通过使用模糊逻辑，LoH中的公式可直接编译为可微计算图，从而通过反向传播学习最优选择。该框架涵盖了一些现有NeSy模型，同时支持任意程度的知识规范。此外，采用哥德尔模糊逻辑及最新发展的哥德尔技巧，所得模型可离散化为布尔值硬函数而性能无损。我们对这类模型进行了实验分析，在表格数据和两个含感知组件的NeSy任务上取得了优异结果。