为神经符号机器人引入概率推理，提升未知命题的决策能力。
Probabilistic Extension of Neuro-Symbolic AGI Robots based on Belnap's Typed Intensional FOL
- 基于尼尔森概率结构，用神经网络计算未知命题的概率密度函数。
- 通过全局与局部对称变换，保持知识库一致性并支持实时决策。
- 适用于需要可解释性与自洽推理的高阶智能体系统设计。
基于 $IFOL_B$ 的神经符号人工智能结合了神经学习与符号推理，克服纯神经系统缺乏可解释性与逻辑结构的问题，并利用形式化逻辑机制实现自指。本文通过尼尔森的概率结构扩展 $IFOL_B$ 的认知能力，对当前未知命题进行概率计算。提出全局对称变换以保持知识库与逻辑推导的一致性，以及用于实时处理具体（子）问题的局部对称变换，仅涉及 $IFOL_B$ 的极小谓词子集。两种情形下，概率密度函数 $KI$ 均基于香农最大信息熵原则，由该概率神经符号 AGI 的神经网络实现。
原文摘要 · Abstract (English)
Neuro-symbolic AI based on $IFOL_B$ is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference. In this paper we expand the cognitive power of $IFOL_B$ by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the $IFOL_B$. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of $IFOL_B$ predicates. The computation of probability density function $KI$ in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.
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