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

arXiv 2607.13073 ↗First posted 12 Jul 2026cs.AIcited by 0

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

Neuro-symbolic AI based on IFOLB 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 IFOLB by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the IFOLB. 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 IFOLB 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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 5 of its 43 references that are in the map. First posted on arXiv 12 Jul 2026.

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2025A Comparative Study of Neurosymbolic AI Approaches to Interpretable Logical Reasoning5 Aug

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2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 774
2022Strong-AI Autoepistemic Robots Build on Intensional First Order Logiccited by 3
2025Intensional FOL over Belnap's Billatice for Strong-AI Roboticscited by 2
2026Neuro-Symbolic Strong-AI Robots with Closed Knowledge Assumption: Learning and Deductionscited by 1

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