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

arXiv: https://arxiv.org/abs/2607.13073 · HTML: https://mlsanity.com/paper/2607.13073/

## Key facts

- No citing papers in the map yet (data through 14 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.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 5 of 5)

- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [A Comparative Study of Neurosymbolic AI Approaches to Interpretable Logical Reasoning](https://mlsanity.com/paper/2508.03366/) (2025)
- [Strong-AI Autoepistemic Robots Build on Intensional First Order Logic](https://mlsanity.com/paper/2212.07935/) (2022)
- [Intensional FOL over Belnap's Billatice for Strong-AI Robotics](https://mlsanity.com/paper/2508.02774/) (2025)
- [Neuro-Symbolic Strong-AI Robots with Closed Knowledge Assumption: Learning and Deductions](https://mlsanity.com/paper/2604.09567/) (2026)

## 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.