Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models (2025)

Abstract: 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%.

## introduction in recent years, large language models (llms) have demonstrated excellent capabilities across var-* equal contributions. to tackle the challenge of the unfaithfulness in the reasoning process, researchers have proposed many neuro-symbolic methods that integrate llms with symbolic reasoning, such as faithful chain-of-thought @xcite , linc @xcite , logic-lm @xcite and satlm @xcite . these methods follow a similar process: initially, the problem and objectives are translated into symbolic expressions. subsequently, symbolic results are derived through external tools such as symbolic solvers. finally, it's optional to explain symbolic results using llms or interpreters. however, these existing neuro-symbolic methods inevitably suffer from the issue of information loss, which results from omissions in the figure 1 : comparison between linc and lot. the left part involves the workflow of linc, which converts problems into logical expressions and then derives results using prover9. however, linc loses fact information person(harry) and book(walden), leading to errors. on the right side, lot generates supplementary logical information "if a person reads a book, that person become smarter" that is seamlessly integrated into the original prompt, thereby enhancing the capability of llms to produce accurate results. to address the issue of information loss, in this paper, we propose a novel zero-shot prompting method named logic-of-thought (lot). specifically, lot first extracts propositions and logical expressions from the input context, expands these logical expressions according to logical reasoning laws, and converts the deduced logical expressions back into natural language form. then lot considers these extended logical descriptions as additional logical augmentation for llms and concatenates it with the original context, which not only encourages llms to utilize these new deduced logical information when answering the original question but also ensures information completeness through preserving full original contexts for llms reasoning, thereby enhancing logical reasoning ability. additionally, the lot prompting approach is compatible and orthogonal to existing prompting methods, enabling seamless integration of these methods. to validate the effectiveness of lot, we conduct extensive experiments to evaluate its capability in boosting various prompting methods such as cot, sc, cot-sc and tot across five logical reasoning datasets. experimental results demonstrate that lot prompting can seamlessly integrate with existing prompting methods and significantly boost their performance in logical reasoning. specifically, lot significantly enhances the performance of cot on the reclor dataset, achieving an improvement in accuracy up to +4.35%. furthermore, lot improves the sc's performance on the reclor dataset by a remarkable +6.52%. moreover, lot boost the accuracy of cot-sc on ruletaker by +3.52%. additionally, lot effectively elevates the performance of tot on the proofwriter dataset, resulting in a significant improvement of +8%. the main contributions of this paper are as follows: ## preliminary as this study focuses on logical reasoning tasks, we first provide some definitions and symbols about the propositional logic system, which will be used throughout the paper. although the presented logic system setting is straightforward, our paper primarily concentrates on introducing a new prompting paradigm to address information loss in existing neuro-symbolic methods. moreover, notable enhancements have already been achieved within this setting (see section 4.4). therefore, we leave the exploration of incorporating more diverse connectives and laws in our method to future work. ## conclusion in this paper, we introduce a zero-shot prompting approach logic-of-thought (lot), designed to address the challenge of information loss inherent in existing neuro-symbolic methods. lot leverages propositional logic to derive expanded logical information from input context, which serves as a supplementary augmentation to the original prompts, and can enhance logical reasoning capabilities of llms. lot exhibits compatibility with widely used prompting techniques. in the experiments, we demonstrate that lot significantly boosts the performance of various existing prompting methods across multiple logical reasoning datasets and can be seamlessly integrated with them. 7 limitations although our proposed lot has achieved excellent performance in various logical reasoning tasks, there are still some limitations in lot. firstly, current lot supports a limited set of connectives and logical reasoning laws. more connectives and logical reasoning laws in lot means more complex prompt design in the logic extraction and logic translation phase, and increased difficulty in logical deducing in the logic extension phase. in the future, we will try to include additional connectives and logical reasoning laws in lot to further enhance the logical reasoning capabilities. additionally, although lot preserve original question structures and utilizes extra deduced logical information as additional augmentation to mitigate information loss issue, hallucination issues inherent in llms can still lead to some failure in the logic extraction phase and need to be addressed, such as repetition of expressions, omission of logical relationships, and deviations in logical propositions and expressions.