Conference Paper
Machine Learning

Symbolic Chain-of-Thought

Jundong Xu, Hao Fei, Liangming Pan, Qian Liu, Mong Li Lee, W. Hsu
May 28, 2024Annual Meeting of the Association for Computational Linguistics188 citations
arXivPDFDOI

188

Citations

13

Influential Citations

Annual Meeting of the Association for Computational Linguistics

Venue

2024

Year

Abstract

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

Analysis

Why This Paper Matters

Chain-of-Thought prompting has been a breakthrough for improving reasoning in large language models, but it often falls short on tasks requiring strict logical deduction and symbolic manipulation. This paper addresses a critical gap by introducing symbolic expressions and formal logic rules directly into the CoT pipeline. The proposed SymbCoT framework is significant because it does not require external solvers or fine-tuning—it operates entirely within the LLM, making it broadly applicable. By combining the flexibility of natural language with the rigor of symbolic logic, SymbCoT moves toward more reliable and interpretable AI reasoning.

Technical Contributions

  • Symbolic Translation: The first stage converts natural language context into a symbolic representation (e.g., First-Order Logic formulas or constraint optimization expressions), enabling precise manipulation.
  • Rule-Based Planning: The second stage uses the LLM to generate a step-by-step plan that applies symbolic logical rules, mimicking a formal proof or constraint solving process.
  • Verifier Module: A third stage checks the correctness of both the translation and the reasoning chain, reducing errors and improving faithfulness.
  • End-to-End LLM Framework: Unlike hybrid systems that call external symbolic solvers, SymbCoT keeps the entire reasoning process within the LLM, leveraging its generative capabilities while enforcing logical structure.

Results

SymbCoT was evaluated on 5 standard logical reasoning datasets covering First-Order Logic and Constraint Optimization. It consistently outperformed standard CoT prompting, achieving new state-of-the-art results. The paper reports "striking improvements" over CoT, though exact numeric metrics are not provided in the abstract. The system also demonstrated more faithful (less hallucinated), flexible (adaptable to different symbolic forms), and explainable (clear step-by-step symbolic derivations) reasoning.

Significance

This work represents a meaningful step toward neurosymbolic AI by embedding symbolic reasoning within LLM prompting. It shows that LLMs can be guided to perform formal logical deductions without external tools, which could democratize access to logical reasoning capabilities. The approach is particularly relevant for applications requiring verifiable reasoning, such as legal analysis, mathematics, and code generation. By making reasoning more faithful and explainable, SymbCoT addresses key trust and safety concerns in AI systems.

chain-of-thoughtlogical-reasoningsymbolic-reasoningllmpromptingfirst-order-logicconstraint-optimization
Large Language ModelsChain Of ThoughtPromptingReasoning

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