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 logical structure) with formal logical machinery for self-reference. In this paper, we expand the cognitive power of $IFOL_B$ by using probability computation for currently unknown sentences, based on Nilsson's probability structure.
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 Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.
Blogger's Review: This paper delves into the probabilistic extension of neuro-symbolic AI, demonstrating how incorporating probability computation enhances logical reasoning capabilities. This integration offers fresh insights into the interpretability and decision-making abilities of AI systems, making it a noteworthy consideration, especially in complex reasoning scenarios with broad potential applications.