Logic-Thinker: Teaching Large Language Models to Think more Logically. (2025)

Abstract: Recent Large Reasoning Models (LRMs) have demonstrated the ability to generate long chains of thought (LongCoT) before arriving at a final conclusion. Despite remarkable breakthroughs in complex reasoning capabilities, LongCoT still faces challenges such as redundancy and logical incoherence. To address these issues, we aim to equip large language models (LLMs) with rigorous and concise logical reasoning capabilities. In this work, we propose Logic-Thinker, a neural-symbolic reasoning framework that employs symbolic solvers to precisely solve problems and transforms their internal solving processes into concise and rigorous chains of thought, referred to as ThinkerCoT. Our experimental results demonstrate that Logic-Thinker achieves state-of-the-art performance in logical reasoning problems. Additionally, LLMs fine-tuned with ThinkerCoT outperform models distilled from QwQ32B on logic reasoning tasks, achieving an overall accuracy improvement of 3.6% while reducing token output by 73%-91%. Furthermore, ThinkerCoT enhances the comprehensive reasoning capabilities of LLMs, as evidenced by performance improvements on reasoning benchmarks such as GPQA and AIME.

## introduction large language models (llms), such as the gpt series @xcite and the qwen series @xcite , have demonstrated remarkable capabilities across a wide range of natural language understanding tasks @xcite @xcite . however, their performance in complex reasoning problems has remained suboptimal. to address this challenge, a new type of model has emerged in recent years: large reasoning models (lrms). by generating a long chain of thought (cot) @xcite before reaching the final conclusion, these models have achieved significant breakthroughs in many challenging reasoning tasks @xcite @xcite . this inference-time scaling paradigm was popularized by @xcite , deepseek-r1(deepseek-ai, 2025), and qwq @xcite , gaining significant traction in the industry. currently, a large number of studies are following this paradigm in an effort to enhance the upper limits of reasoning capabilities. however, recent studies have highlighted several issues with this longcot reasoning paradigm: 1) redundant content, including question restatements, verbose explanations and repetitive narratives @xcite , results in a large amount of unnecessary token completion. 2) overthinking, specifically manifested as the repeated verification of some straightforward and direct questions @xcite . 3) incoherent reasoning, when dealing with complex reasoning problems, lrms may superficially jump between approaches, leading to shallow, fragmented reasoning, rather than a deep, coherent analysis @xcite . to address these issues, many studies have proposed the idea of compressing longcot while retaining its critical reasoning steps. through supervised fine-tuning (sft), the refined cot enables llms to acquire the capability if concise reasoning. experiments have demonstrated that such methods can effectively reduce cot redundancy while maintaining reasoning accuracy. rather than postprocessing longcot, some research has delved deeper into the fundamental causes of these issues, finding that llms allocate a large portion of their output to text coherence rather than core reasoning advancement @xcite . on the other hand, the longcot capability of lrms originates from the exploration of the response space during the reinforcement learning (rl) @xcite stage, primarily aiming at obtaining accuracy at the solution level, while the consistency of the intermediate reasoning process has been overlooked @xcite . based on these conclusions, we propose that the redundancy, overthinking, and incoherent reasoning issues of llms are primarily caused by the inability of rigorous logic reasoning. such rigorous logic reasoning ability is particularly critical in many logical reasoning tasks, including deduction, induction and hypothesis testing. therefore, we focus on logical reasoning problems and aim to translate the inherent precise reasoning paths of neuro-symbolic solvers into concise and logically rigorous cots, thereby equipping llms with robust and concise reasoning capabilities. in this work, we introduce logic-thinker, a neuro-symbolic reasoning framework that integrates both logic problem-solving and reasoning cot generation capabilities. logic-thinker consists of three core modules: a formulator for converting logical reasoning problems into symbolic expressions, a logicsolver for executing symbolic expressions to solve problems, and a cot-generator for transforming the solver's internal execution process into cots, referred to as thinker-cot. we categorize common logical reasoning problems into two types: fol (first-order logic) and csp (constraint satisfaction problems), and implement them respectively in the three modules. the rest of this paper is organized as follows. section 2 presents related work. we present preliminaries in section 3. our approach is discussed in section 4. we conduct comprehensive experiments to evaluate the effectiveness of out proposed methods in section 5 and we conclude the paper in section 6. in summary, we make the following contributions in this paper. ## logic-thinker symbolic solvers possess an inherent capability for rigorous reasoning: 1) the symbolic system ensures that each step's conclusion is deterministic rather than probabilistic and is verifiable. 2) solvers follow a systematic search methodology, exploring the solution space exhaustively to ensure that no potential reasoning paths are overlooked. to enable llms to acquire such rigorous reasoning capabilities, we propose logic-thinker, which enables the transformation of the symbolic solver's internal execution process into concise and logically rigorous cot, named thinkercot. as shown in figure 1 , logic-thinker consists of three modules: a formulator that formalizes natural language problems into symbolic expressions, a log-icsolver that executes symbolic expressions and derives conclusions, and a cot generator that produce thinkercot based on reasoning processes. ## experiment to comprehensively evaluate the effectiveness of logic-thinker, we designed experiments from two perspectives: we first introduce the datasets of logical reasoning problems used in the two experiments, followed by a detailed description of the two experiments, including their settings, baselines, experimental results, and analysis. then, we conducted an experiment to verify whether applying thinkercot to real-world sft tasks could enhance the comprehensive reasoning capabilities of llms. finally, we conduct a detailed case study to analyze the effectiveness of thinkercot compared to longcot. if childlist ̸ = ∅ then 11: s.push(childlist) 12: return reverse(c) ## conclusion we introduce a novel neuro-symbolic logic reasoning framework, named logic-thinker, which can transform the reasoning process of solvers into a rigorous and concise cot, referred to as thinkercot. the proposed framework consists of three modules: formulator, logicsolver and cot-generator. we categorize logical reasoning problems into two types and implement them respectively in three modules. the experimental results demonstrated that logic-thinker outperforms other state-of-the-art frameworks in logical reasoning capability. additionally, thinkercot achieves a 3.6% improvement in accuracy while reducing token output by 73%-91% compaed to longcot. furthermore, the logical reasoning data synthesized through thinkercot can effectively enhance the overall reasoning ability of llms, such as in mathematics and scientific reasoning, which demonstrates the significant value of our methods in practical llm training tasks.