Linear Reasoning vs. Proof by Cases: Obstacles for Large Language Models in FOL Problem Solving
arXiv:2602.20973v1 Announce Type: new Abstract: To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning, neglecting other parts such as proof by contradiction and proof by cases, which are crucial for investigating LLMs' reasoning abilities. To address this limitation, we first introduce a novel first-order logic (FOL) dataset named PC-FOL, annotated by professional mathematicians, focusing on case-based reasoning problems. All instances in this dataset are equipped with a manually written natural language proof, clearly distinguishing it from conventional linear reasoning datasets. Our experimental results over leading LLMs demonstrate a substantial performance gap between linear reasoning and case-based reasoning problems. To further investigate this phenomenon, we provide a theoretical analysis grounde
arXiv:2602.20973v1 Announce Type: new Abstract: To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning, neglecting other parts such as proof by contradiction and proof by cases, which are crucial for investigating LLMs' reasoning abilities. To address this limitation, we first introduce a novel first-order logic (FOL) dataset named PC-FOL, annotated by professional mathematicians, focusing on case-based reasoning problems. All instances in this dataset are equipped with a manually written natural language proof, clearly distinguishing it from conventional linear reasoning datasets. Our experimental results over leading LLMs demonstrate a substantial performance gap between linear reasoning and case-based reasoning problems. To further investigate this phenomenon, we provide a theoretical analysis grounded in graphical model, which provides an explanation for the observed disparity between the two types of reasoning problems. We hope this work can reveal the core challenges in the field of automated natural language mathematical proof generation, paving the way for future research.
Executive Summary
The article 'Linear Reasoning vs. Proof by Cases: Obstacles for Large Language Models in FOL Problem Solving' presents a critical evaluation of the capabilities of Large Language Models (LLMs) in solving First-Order Logic (FOL) problems. The authors introduce a novel dataset, PC-FOL, focused on case-based reasoning problems, and demonstrate a substantial performance gap between linear reasoning and case-based reasoning problems. Through a theoretical analysis grounded in graphical models, the authors provide an explanation for the observed disparity. This work highlights the core challenges in automated natural language mathematical proof generation, paving the way for future research. The study's findings have significant implications for the development of LLMs and their applications in mathematics and artificial intelligence.
Key Points
- ▸ Introduction of a novel FOL dataset, PC-FOL, focusing on case-based reasoning problems
- ▸ Demonstration of a substantial performance gap between linear reasoning and case-based reasoning problems
- ▸ Theoretical analysis using graphical models to explain the observed disparity
Merits
Strength in Novel Dataset
The introduction of PC-FOL provides a valuable resource for evaluating LLMs' reasoning capabilities, addressing the limitation of existing datasets that primarily focus on linear reasoning.
Insightful Theoretical Analysis
The use of graphical models to explain the observed disparity between linear and case-based reasoning problems provides a deeper understanding of LLMs' limitations and potential avenues for improvement.
Demerits
Limitation in Dataset Size
The size of the PC-FOL dataset is not explicitly mentioned, which may limit the generalizability of the findings and the conclusions drawn from the study.
Lack of Comparative Analysis with Human Performance
The study does not compare the performance of LLMs with human performance on the PC-FOL dataset, which would provide a more comprehensive evaluation of LLMs' reasoning capabilities.
Expert Commentary
The study presents a valuable contribution to the field of LLMs and their applications in mathematics and artificial intelligence. The introduction of the PC-FOL dataset provides a critical evaluation of LLMs' reasoning capabilities, highlighting the need for more advanced reasoning capabilities. The theoretical analysis using graphical models provides a deeper understanding of LLMs' limitations and potential avenues for improvement. However, the study's limitations, including the size of the dataset and the lack of comparative analysis with human performance, should be addressed in future research.
Recommendations
- ✓ Future research should focus on developing more advanced LLMs capable of handling complex reasoning tasks, including case-based reasoning.
- ✓ The development of more comprehensive evaluation frameworks, including comparative analysis with human performance, is essential for a more accurate assessment of LLMs' capabilities.
