arXiv:2607.13073v1 Announce Type: new 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 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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