# Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2409.17539 · HTML: https://mlsanity.com/paper/2409.17539/

## Key facts

- Cited by 23 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 33 of its 36 references that are in the map.
- First posted on arXiv 26 Sep 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, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learning](https://mlsanity.com/paper/2010.15875/) (2020)
- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Automatic Prompt Augmentation and Selection with Chain-of-Thought from Labeled Data](https://mlsanity.com/paper/2302.12822/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)

## Built on by (most cited first, 23 of 23)

- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Learning to Reason via Mixture-of-Thought for Logical Reasoning](https://mlsanity.com/paper/2505.15817/) (2025)
- [DrugPilot: LLM-based Parameterized Reasoning Agent for Drug Discovery](https://mlsanity.com/paper/2505.13940/) (2025)
- [A Neurosymbolic Approach to Natural Language Formalization and Verification](https://mlsanity.com/paper/2511.09008/) (2025)
- [Faithful and Robust LLM-Driven Theorem Proving for NLI Explanations](https://mlsanity.com/paper/2505.24264/) (2025)
- [Blind Spot Navigation in Large Language Model Reasoning with Thought Space Explorer](https://mlsanity.com/paper/2410.24155/) (2024)
- [LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision](https://mlsanity.com/paper/2512.18196/) (2025)
- [Beyond Correctness: Exposing LLM-generated Logical Flaws in Reasoning via Multi-step Automated Theorem Proving](https://mlsanity.com/paper/2512.23511/) (2025)
- [RAVEN: Robust Advertisement Video Violation Temporal Grounding via Reinforcement Reasoning](https://mlsanity.com/paper/2510.16455/) (2025)
- [StaRPO: Stability-Augmented Reinforcement Policy Optimization](https://mlsanity.com/paper/2604.08905/) (2026)
- [Benchmarking Abstract and Reasoning Abilities Through A Theoretical Perspective](https://mlsanity.com/paper/2505.23833/) (2025)
- [ATA: A Neuro-Symbolic Approach to Implement Autonomous and Trustworthy Agents](https://mlsanity.com/paper/2510.16381/) (2025)
- [DFlow: Diverse Dialogue Flow Simulation with Large Language Models](https://mlsanity.com/paper/2410.14853/) (2024)
- [The promise and limits of LLMs in constructing proofs and hints for logic problems in intelligent tutoring systems](https://mlsanity.com/paper/2505.04736/) (2025)
- [SafePyramid: A Hierarchical Benchmark for In-context Policy Guardrailing](https://mlsanity.com/paper/2606.29887/) (2026)
- [BELL: Benchmarking the Explainability of Large Language Models](https://mlsanity.com/paper/2504.18572/) (2025)
- [Formal Reasoning for Intelligent QA Systems: A Case Study in the Educational Domain](https://mlsanity.com/paper/2509.11572/) (2025)
- [Automatic Prompt Generation via Adaptive Selection of Prompting Techniques](https://mlsanity.com/paper/2510.18162/) (2025)
- [IFDNS: An Iterative Feedback-Driven Neuro-Symbolic Method for Faithful Logical Reasoning](https://mlsanity.com/paper/2601.07464/) (2026)
- [FloCA: Towards Faithful and Logically Consistent Flowchart Reasoning](https://mlsanity.com/paper/2602.14035/) (2026)
- [Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning](https://mlsanity.com/paper/2603.12953/) (2026)
- [Quantifying Cross-Query Contradictions in Multi-Query LLM Reasoning](https://mlsanity.com/paper/2604.14525/) (2026)
- [Abductive Reasoning with Probabilistic Commonsense](https://mlsanity.com/paper/2605.08011/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information descriptions and utilizes them as an additional augmentation to original contexts, thereby ensuring information completeness and enhancing logical reasoning ability. LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%, improves Chain-of-Thought with Self-Consistency's performance on the RuleTaker dataset by +3.52%, and boosts performance of Tree-of-Thoughts on the ProofWriter dataset by +8%.