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

**Authors:** Tongxuan Liu, Wenjiang Xu, Weizhe Huang, Xingyu Wang, Jiaxing Wang, Hailong Yang, Jing Li  
**arXiv:** [2409.17539](https://arxiv.org/abs/2409.17539)  
**Date:** 2024-09-26  
**Summary page:** https://www.summarizepaper.com/en/paper/2409.17539v1/

## Key points

- Large Language Models (LLMs) excel in NLP tasks but struggle with complex logical reasoning.
- Chain-of-Thought (CoT) prompting introduces intermediate steps for logical reasoning enhancement.
- Existing methods like CoT may suffer from unfaithful reasoning, leading to misaligned conclusions.
- Some studies integrate propositional logic to improve LLMs' logical reasoning abilities.
- Logic-of-Thought (LoT) prompting proposes using propositional logic to extract expanded logical information and augment input prompts for LLMs.
- LoT aims to enhance logical reasoning while preserving the original input prompt and can be seamlessly integrated with existing methods.
- Extensive experiments show that LoT significantly improves performance across various logical reasoning tasks:
- Enhances Chain-of-Thought's performance on ReClor dataset by +4.35%
- Improves Chain-of-Thought with Self-Consistency on LogiQA by +5%
- Boosts Tree-of-Thoughts on ProofWriter dataset by +8%
- LoT guides LLMs to produce more accurate and reliable results in logical reasoning tasks compared to traditional prompting methods.

## Summary

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In recent years, Large Language Models (LLMs) have shown impressive capabilities in various NLP tasks. However, they still struggle with complex logical reasoning tasks. To enhance their logical reasoning abilities, Chain-of-Thought (CoT) prompting has been introduced as a method to add intermediate steps in the reasoning process. While this has shown promise, existing methods like CoT suffer from unfaithful reasoning where derived conclusions may not align with the generated chain of thought. To address this challenge, some studies have integrated propositional logic to improve LLMs' logical reasoning abilities. However, there are potential omissions in extracting logical expressions that can lead to information loss and incorrect results. To overcome these limitations, a new approach called Logic-of-Thought (LoT) prompting is proposed in this paper. LoT utilizes propositional logic to extract expanded logical information from the input context and integrates it as additional augmentation to the input prompts for LLMs. The LoT approach aims to enhance the capability of logical reasoning while preserving the original input prompt. It is complementary to existing prompting methods and can be seamlessly integrated with them. Extensive experiments have demonstrated that LoT significantly boosts the performance of various prompting methods across five logical reasoning tasks. For instance, it enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%, improves Chain-of-Thought with Self-Consistency on LogiQA by +5%, and boosts Tree-of-Thoughts on ProofWriter dataset by +8%. By incorporating expanded logical information into the input prompts, LoT effectively guides LLMs in producing more accurate and reliable results in logical reasoning tasks compared to traditional prompting methods.