Title: Can Data-driven Machine Learning Reach Symbolic-level Logical Reasoning? -- The Limit of the Scaling Law
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: logical reasoning, syllogism, scaling law

Abstract: With the qualitative extension of embedding representation and the method of explicit model construction, neural networks may achieve the rigour of symbolic level logic reasoning without training data, raising questions 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, a subset of logical 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 object recognition and logical reasoning. Taking the Euler Net as a representative supervised neural network, we experimentally illustrate the challenges common to all image-input supervised networks, namely, they struggle to distinguish all types of syllogistic reasoning and to identify unintended inputs. We further challenge the most recent ChatGPTs (gpt-5-nano and gpt-5) to determine the satisfiability of syllogistic statements in four surface forms: 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 reaching 100% accuracy, we conclude that supervised machine learning systems may follow scaling laws but will not reach symbolic-level logical reasoning.