# Faithful Logical Reasoning via Symbolic Chain-of-Thought

arXiv: https://arxiv.org/abs/2405.18357 · HTML: https://mlsanity.com/paper/2405.18357/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 28 May 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [NExT-GPT: Any-to-Any Multimodal LLM](https://mlsanity.com/paper/2309.05519/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Video-of-Thought: Step-by-Step Video Reasoning from Perception to Cognition](https://mlsanity.com/paper/2501.03230/) (2024)
- [Structured Chain-of-Thought Prompting for Code Generation](https://mlsanity.com/paper/2305.06599/) (2023)
- [Reasoning Implicit Sentiment with Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.11255/) (2023)
- [Bidirectional Language Models Are Also Few-shot Learners](https://mlsanity.com/paper/2209.14500/) (2022)
- [Formal Specifications from Natural Language](https://mlsanity.com/paper/2206.01962/) (2022)
- [MultiTool-CoT: GPT-3 Can Use Multiple External Tools with Chain of Thought Prompting](https://mlsanity.com/paper/2305.16896/) (2023)
- [Scalable Qualitative Coding with LLMs: Chain-of-Thought Reasoning Matches Human Performance in Some Hermeneutic Tasks](https://mlsanity.com/paper/2401.15170/) (2024)
- [Reasoning in Large Language Models Through Symbolic Math Word Problems](https://mlsanity.com/paper/2308.01906/) (2023)
- [Reverse Multi-Choice Dialogue Commonsense Inference with Graph-of-Thought](https://mlsanity.com/paper/2312.15291/) (2023)

## Built on by (most cited first, 30 of 100)

- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Multimodal Chain-of-Thought Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2503.12605/) (2025)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [CoT Red-Handed: Stress Testing Chain-of-Thought Monitoring](https://mlsanity.com/paper/2505.23575/) (2025)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [Unveiling the Key Factors for Distilling Chain-of-Thought Reasoning](https://mlsanity.com/paper/2502.18001/) (2025)
- [Semantic-Aware Logical Reasoning via a Semiotic Framework](https://mlsanity.com/paper/2509.24765/) (2025)
- [CoMT: A Novel Benchmark for Chain of Multi-modal Thought on Large Vision-Language Models](https://mlsanity.com/paper/2412.12932/) (2024)
- [Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning](https://mlsanity.com/paper/2410.08047/) (2024)
- [Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning](https://mlsanity.com/paper/2601.02902/) (2026)
- [Reason4Rec: Deliberative User Preference Alignment of Large Language Models for Recommendation](https://mlsanity.com/paper/2502.02061/) (2025)
- [Learning to Reason via Mixture-of-Thought for Logical Reasoning](https://mlsanity.com/paper/2505.15817/) (2025)
- [How does Chain of Thought Think? Mechanistic Interpretability of Chain-of-Thought Reasoning with Sparse Autoencoding](https://mlsanity.com/paper/2507.22928/) (2025)
- [Symbolic Working Memory Enhances Language Models for Complex Rule Application](https://mlsanity.com/paper/2408.13654/) (2024)
- [Improving Chain-of-Thought Reasoning via Quasi-Symbolic Abstractions](https://mlsanity.com/paper/2502.12616/) (2025)
- [Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study](https://mlsanity.com/paper/2506.04810/) (2025)
- [Think Clearly: Improving Reasoning via Redundant Token Pruning](https://mlsanity.com/paper/2507.08806/) (2025)
- [Can Transformers Reason Logically? A Study in SAT Solving](https://mlsanity.com/paper/2410.07432/) (2024)
- [CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning](https://mlsanity.com/paper/2410.10336/) (2024)
- [Can Compressed LLMs Truly Act? An Empirical Evaluation of Agentic Capabilities in LLM Compression](https://mlsanity.com/paper/2505.19433/) (2025)
- [NeSyC: A Neuro-symbolic Continual Learner For Complex Embodied Tasks In Open Domains](https://mlsanity.com/paper/2503.00870/) (2025)
- [Don't Let It Hallucinate: Premise Verification via Retrieval-Augmented Logical Reasoning](https://mlsanity.com/paper/2504.06438/) (2025)
- [Theorem Prover as a Judge for Synthetic Data Generation](https://mlsanity.com/paper/2502.13137/) (2025)
- [Divide-Then-Align: Honest Alignment based on the Knowledge Boundary of RAG](https://mlsanity.com/paper/2505.20871/) (2025)
- [VERUS-LM: a Versatile Framework for Combining LLMs with Symbolic Reasoning](https://mlsanity.com/paper/2501.14540/) (2025)
- [DecisionFlow: Advancing Large Language Model as Principled Decision Maker](https://mlsanity.com/paper/2505.21397/) (2025)
- [Blueprint First, Model Second: A Framework for Deterministic LLM Workflow](https://mlsanity.com/paper/2508.02721/) (2025)
- [HYBRIDMIND: Meta Selection of Natural Language and Symbolic Language for Enhanced LLM Reasoning](https://mlsanity.com/paper/2409.19381/) (2024)
- [Towards Reliable Code-as-Policies: A Neuro-Symbolic Framework for Embodied Task Planning](https://mlsanity.com/paper/2510.21302/) (2025)

## Abstract (arXiv)

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.