Probabilistic Extension of Neuro-Symbolic AGI Robots based on Belnap’s Typed Intensional FOL

基于贝尔纳普类型内涵一阶逻辑（Belnap’s Typed Intensional FOL）的神经符号通用人工智能（AGI）机器人的概率扩展

Abstract: 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 lack of logical structure) with formal logical machinery for self-reference.

摘要： 基于 $IFOL_B$（贝尔纳普类型内涵一阶逻辑）的神经符号人工智能，是一种结合神经学习与符号推理的方法，旨在通过形式逻辑机制实现自我指涉，从而克服纯神经网络系统（如缺乏可解释性和逻辑结构）的局限性。

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 $IFOL_B$.

在本文中，我们基于尼尔森（Nilsson）针对 $IFOL_B$ 的概率结构，通过对当前未知命题进行概率计算，扩展了 $IFOL_B$ 的认知能力。

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.

我们引入了全局对称变换，用以保持当前的知识库和逻辑推演；同时引入了局部对称变换，用于针对仅涉及 $IFOL_B$ 谓词极小子集的具体（子）问题进行实时决策。

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.

在这两种情况下，基于香农最大信息熵的概率密度函数 $KI$ 的计算，均由该概率神经符号通用人工智能（AGI）中的神经网络提供。