[Paper Review] Faithful Logical Reasoning via Symbolic Chain-of-Thought

Jundong Xu, Fei Hao+4 more|arXiv (Cornell University)|May 28, 2024

Logic, Reasoning, and Knowledge4 citations

TL;DR

This paper proposes SymbCoT, a fully LLM-based framework that enhances logical reasoning by integrating symbolic expressions and logic rules into Chain-of-Thought prompting. It translates natural language into First-Order Logic, applies symbolic reasoning with inference rules, and verifies results, achieving state-of-the-art performance across five datasets with improved faithfulness, flexibility, and explainability in logical reasoning tasks.

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.

Motivation & Objective

• To address the limitations of standard Chain-of-Thought in handling precise, rule-based logical reasoning that relies on symbolic expressions.
• To overcome the reliance on external symbolic solvers in existing LLM-symbolic integration methods, which limits flexibility and explainability.
• To develop a fully end-to-end LLM-driven system that performs symbolic translation, logical reasoning, and verification without external tools.
• To improve the faithfulness and correctness of logical reasoning by enforcing strict symbolic inference rules during the reasoning chain.
• To demonstrate that symbolic reasoning within CoT can outperform standard natural language CoT and existing hybrid systems on logical reasoning benchmarks.

Proposed method

• SymbCoT employs a four-module pipeline: Translator (converts natural language to symbolic logic, e.g., First-Order Logic), Planner (generates a step-by-step symbolic reasoning plan), Solver (applies logical inference rules like existential instantiation and conjunction elimination), and Verifier (validates translation and reasoning chain for correctness).
• The system uses LLMs to perform symbolic translation and reasoning, eliminating dependency on external symbolic reasoners, thus enabling full end-to-end LLM-based logical reasoning.
• Symbolic expressions are grounded in formal logic, allowing precise representation of premises and inferences, reducing ambiguity inherent in natural language rationales.
• The Planner module generates intermediate reasoning steps using symbolic inference rules, ensuring logical rigor and traceability.
• The Verifier module checks both the correctness of the symbolic translation and the validity of the reasoning chain, enhancing reliability and faithfulness.
• The framework supports both First-Order Logic and Constraint Optimization problems, enabling broad applicability across diverse logical reasoning tasks.

Experimental results

Research questions

• RQ1 Can integrating symbolic logic into Chain-of-Thought reasoning significantly improve the accuracy and faithfulness of LLMs in logical reasoning tasks?
• RQ2 Does a fully LLM-based symbolic reasoning system outperform existing hybrid approaches that rely on external symbolic solvers?
• RQ3 To what extent does symbolic CoT reduce overgeneralization and incorrect inferences compared to standard natural language CoT?
• RQ4 Can symbolic reasoning within CoT maintain explainability while improving logical rigor and correctness?
• RQ5 How does SymbCoT perform across diverse logical reasoning benchmarks, particularly in tasks requiring strict inference rules and symbolic manipulation?

Key findings

• SymbCoT achieves state-of-the-art performance across five standard logical reasoning datasets, consistently outperforming standard Chain-of-Thought and existing hybrid methods.
• The system demonstrates significantly improved faithfulness in reasoning, as verified by the internal verifier, reducing incorrect inferences due to overgeneralization.
• SymbCoT enhances explainability by making the reasoning chain fully traceable through symbolic inference rules, unlike black-box natural language rationales.
• The framework reduces reliance on external symbolic solvers, enabling a fully end-to-end LLM-based reasoning pipeline that is more flexible and maintainable.
• On the AR-LSAT and FOLIO benchmarks, SymbCoT correctly identifies the impossible schedule option (C) with a fully symbolic reasoning chain, demonstrating robustness in complex constraint reasoning.
• The verifier module successfully detects translation and reasoning errors, improving overall reliability and reducing false positives in logical inference.