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

Researchers propose a probabilistic extension of neuro-symbolic AGI robots based on Belnap's typed intensional first-order logic (IFOL_B), integrating neural networks for probability computation via Shannon's maximum information entropy. The approach introduces global and local symmetry transformations to preserve knowledge and enable real-time decisions, aiming to enhance cognitive power and overcome limitations of purely neural systems.

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.