模态逻辑神经网络
Modal Logic Neural Networks
AI总结：
模态逻辑神经网络结合深度学习与模态逻辑，通过可微逻辑护栏实现必要性与可能性推理，提升逻辑一致性和可解释性。
摘要：
我们提出了模态逻辑神经网络（MLNNs），一种将深度学习与模态逻辑的正式语义相结合的神经符号框架，使能够进行关于必要性和可能性的推理。基于克里普克语义学，我们引入了专门用于模态运算符□和◇的神经元，这些运算符在可能世界集上操作，使该框架能够作为可微的『逻辑护栏』。该架构高度灵活：世界之间的可及性关系可以由用户固定以强制执行已知规则，或者作为归纳特征由神经网络参数化。这使模型能够在从数据中学习逻辑系统的关系结构的同时，也在该结构内执行演绎推理。这种灵活的构造旨在提供灵活性。整个框架从端到端都是可微的，学习由最小化逻辑矛盾损失驱动。这不仅使系统能够抵御不一致的知识，还能使其学习非线性关系，从而帮助定义问题空间的逻辑。我们通过四个案例研究展示了MLNNs：语法护栏、多智能体认知信任、检测自然语言谈判中的构造欺骗，以及数独中的组合约束满足。这些实验展示了如何通过强制或学习可及性来增加逻辑一致性和可解释性，而无需改变底层任务架构。
英文摘要：
Neural Networks are indispensable to natural sciences and society. Their impact extends from applications in public health to workforce productivity. Here, we introduce Modal Logic Neural Networks (MLNNs) -- an end-to-end differentiable logical neural network realisation of modal logic which evaluates a learnable truth function across possible-world semantics. This neural architecture handles para-consistency and inconsistency via a learnable world accessibility relation and valuation function. Because the modality is fixed by which frame axioms the relation satisfies rather than by the operator, one differentiable engine covers the epistemic, doxastic, deontic and temporal readings, with applications from verification of reactive and distributed systems to legal discourse and microeconomic utility models. In this paper, we introduce a model of differentiable Kripke semantics, and establish their soundness, convergence, and structural guarantees. We show four applications, in which the learned relation reads as a trust matrix, an operating-regime embedding with safety bounds, a temporal precedence order, and a recovered constraint graph.
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