Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law
This work identifies inherent limits of data-driven machine learning for rigorous logical reasoning, challenging the scaling law assumption for AI systems.
The paper demonstrates that supervised deep learning cannot achieve symbolic-level syllogistic reasoning due to fundamental limitations in training data and neural architecture, and shows that even GPT-5 fails to provide correct explanations despite 100% accuracy.
Sphere neural networks have achieved symbolic level syllogistic reasoning without training data, raising the question of where the limit of the scaling law for logical reasoning lies, i.e., whether data-driven machine learning systems can achieve the same level by increasing training data and training time. We show two methodological limitations that prevent supervised deep learning from reaching the symbolic-level syllogistic reasoning: (1) training data can not distinguish all 24 types of valid syllogistic reasoning; (2) end-to-end mapping from premises to conclusion introduces contradictory training targets between neural components for pattern recognition and logical reasoning. Beside theoretical analysis, we experimentally illustrate that Euler Net cannot achieve rigorous syllogistic reasoning. We further challenge the most recent ChatGPTs (GPT-5-nano and GPT-5) to determine the satisfiability of syllogistic statements in four surface forms (patterns): words, double words, simple symbols, and long random symbols, showing that surface forms affect the reasoning performance and that ChatGPT GPT-5 may reach 100% accuracy but still provide incorrect explanations. As empirical training processes are stopped after achieving 100% accuracy, we conclude that supervised machine learning systems will not attain the rigour of symbolic logical reasoning.