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机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究基于$IFOL_B$的神经符号人工智能，通过概率计算扩展其认知能力，引入全局和局部对称变换，利用神经网络基于香农最大信息熵计算概率密度函数$KI$，实现对未知句子概率计算及相关实时决策。
AI 中文摘要
基于$IFOL_B$的神经符号人工智能是结合神经学习和符号推理的一种方式，旨在克服纯神经系统的局限性（如缺乏可解释性和逻辑结构），并借助形式逻辑机制进行自我参照。本文基于$IFOL_B$的尼尔森概率结构，通过对当前未知句子进行概率计算来扩展$IFOL_B$的认知能力。引入了保持当前知识库和逻辑推导的全局对称变换，以及用于涉及$IFOL_B$谓词非常严格子集的具体（子）问题实时决策的局部对称变换。此概率神经符号通用人工智能的神经网络基于香农最大信息熵提供两种情况下概率密度函数$KI$的计算。
英文摘要
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.
Comments37 pages
