Faithful Logical Reasoning via Symbolic Chain-of-Thought (AI summary)

Key Points

1. The paper proposes a novel Symbolic Chain-of-Thought (SymbCoT) framework, which is a fully LLM-based approach that integrates symbolic expressions and logical rules with Chain-of-Thought (CoT) prompting to enhance the logical reasoning capabilities of large language models (LLMs).

2. Unlike existing solutions that rely on external symbolic solvers, SymbCoT is entirely facilitated by LLMs, encompassing both the initial translation from natural language to symbolic format and the subsequent reasoning process.

3. SymbCoT combines the strengths of symbolic forms and natural language expressions, enabling precise reasoning calculations while fully interpreting implicit information and capturing rich contexts.

4. SymbCoT introduces a plan-then-solve architecture for CoT reasoning, where the original complex problem is first decomposed into smaller, more manageable sub-problems, resulting in a more structured and trackable problem-solving process.

5. SymbCoT also devises a retrospective verification mechanism to validate the correctness of the symbolic translations and the logical reasoning steps, ensuring the faithfulness and reliability of the overall process.

6. Experimental results on 5 standard datasets using both First-Order Logic and Constraint Optimization symbolic expressions demonstrate that SymbCoT significantly outperforms the vanilla CoT method and achieves state-of-the-art performance.

7. The paper highlights that the more complex the logical reasoning task, the more pronounced the improvement of SymbCoT over vanilla CoT, further underscoring the benefits of the proposed approach.

8. SymbCoT offers better robustness against translation errors and more human-understandable explanations compared to existing solutions that rely on external symbolic resolvers.

9. The paper presents SymbCoT as the first fully LLM-based logical reasoning framework that combines symbolic expressions and rules with CoT prompting, showcasing the potential of LLMs to achieve robust logical reasoning capabilities without the need for external reasoning tools.

Summary

The paper introduces a novel framework called SymbCoT that aims to enhance the logical reasoning capabilities of large language models (LLMs). SymbCoT integrates symbolic expressions and logic rules with the Chain-of-Thought (CoT) technique, which encourages LLMs to explicitly consider intermediate steps during problem-solving.

Limitations of CoT
The authors argue that while CoT has shown promise in improving LLM reasoning, it is inherently limited in handling logical reasoning tasks that heavily rely on symbolic expressions and rigid deducing rules. Logical reasoning demands precise logical calculations, which natural language expressions in CoT often fall short of supporting.

SymbCoT Framework
To address this, SymbCoT combines the strengths of symbolic forms and natural language expressions. It first translates the natural language context into a symbolic format, then derives a step-by-step plan to solve the problem using symbolic logical rules. This plan-then-solve architecture helps break down complex problems into more manageable sub-problems. Additionally, SymbCoT includes a verifier module that checks the translation and reasoning chain for correctness.

Evaluation Results
Through thorough evaluations on 5 standard datasets, the authors demonstrate that SymbCoT significantly outperforms the vanilla CoT approach, consistently refreshing the current state-of-the-art performance. The authors claim that SymbCoT advances in more faithful, flexible, and explainable logical reasoning compared to existing methods.

Technical Contribution
A key technical contribution is the fully LLM-based nature of SymbCoT, showing that LLMs can achieve robust logical reasoning capabilities without relying on external reasoning tools. This offers better robustness against translation errors and more human-understandable explanations than prior solutions that use external solvers.

Integration of Symbolic and Natural Language
Furthermore, the paper highlights the importance of integrating symbolic and natural language expressions, enabling precise reasoning calculations while fully interpreting implicit information and capturing rich contexts. The plan-then-solve architecture and the verification mechanism also enhance the faithfulness of the reasoning process.

Role in Artificial General Intelligence
The authors emphasize the crucial role of logical reasoning in realizing artificial general intelligence (AGI) and the growing interest in applying CoT for this purpose. By introducing SymbCoT, this work pioneers the development of the first symbolic CoT specifically designed for logical reasoning, fully harnessing the capabilities of LLMs.

Reference: https://arxiv.org/abs/2405.183...