We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.

中文翻译：

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逻辑神经网络

我们提出了一个新的框架，无缝地提供了神经网络（学习）和符号逻辑（知识和推理）的关键特性。每个神经元作为加权实值逻辑中公式的一个组成部分都具有意义，从而产生高度可解释的解开表示。推理是全方位的，而不是专注于预定义的目标变量，并且对应于逻辑推理，包括作为特例证明的经典一阶逻辑定理。该模型是端到端可微的，并且学习最小化了捕捉逻辑矛盾的新损失函数，从而对不一致的知识产生弹性。它还通过维护具有概率语义的真值界限来实现开放世界假设，从而对不完整的知识产生弹性。