LogicTree：面向大型语言模型连贯且严谨逻辑推理的结构化证明探索
LogicTree: Structured Proof Exploration for Coherent and Rigorous Logical Reasoning with Large Language Models
AI总结：
提出推理时框架LogicTree，通过算法引导的结构化证明探索、缓存机制与线性前提搜索，提升LLMs的逻辑连贯性，在五个数据集上超越CoT和ToT。
摘要：
大型语言模型（LLMs）在各种领域已具备卓越的多步推理能力。然而，LLMs在复杂逻辑推理中仍面临明显挑战，因为（1）证明寻找需要系统性的探索以及逻辑连贯性的维持，且（2）在具有大前提空间的任务中，在每个推理步骤搜索正确的前提组合本身极具挑战。为此，我们提出LogicTree，一个采用算法引导搜索的推理时模块化框架，以自动化结构化证明探索并确保逻辑连贯。超越思维树（ToT），我们将缓存机制引入LogicTree，以实现对历史知识的有效利用，防止推理停滞并最小化冗余。此外，我们通过将前提搜索分解为线性过程来解决其组合复杂性。改进后的前提选择将后续推理限制为每步最多一次推导，增强了推理粒度并强制执行严格的逐步推理。另外，我们引入两种无需LLM的启发式方法进行前提优先级排序，实现策略性证明搜索。在五个数据集上的实验结果表明，LogicTree最优地扩展了推理时计算以实现更高的证明准确率，在GPT-4o上分别超越思维链（CoT）和ToT，平均增益分别为23.6%和12.5%。此外，在LogicTree内部，GPT-4o平均比o3-mini高出7.6%。
英文摘要：
Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration and the maintenance of logical coherence and (2) searching the right combination of premises at each reasoning step is inherently challenging in tasks with large premise space. To address this, we propose LogicTree, an inference-time modular framework employing algorithm-guided search to automate structured proof exploration and ensure logical coherence. Advancing beyond tree-of-thought (ToT), we incorporate caching mechanism into LogicTree to enable effective utilization of historical knowledge, preventing reasoning stagnation and minimizing redundancy. Furthermore, we address the combinatorial complexity of premise search by decomposing it into a linear process. The refined premise selection restricts subsequent inference to at most one derivation per step, enhancing reasoning granularity and enforcing strict step-by-step reasoning. Additionally, we introduce two LLM-free heuristics for premise prioritization, enabling strategic proof search. Experimental results on five datasets demonstrate that LogicTree optimally scales inference-time computation to achieve higher proof accuracy, surpassing chain-of-thought (CoT) and ToT with average gains of 23.6% and 12.5%, respectively, on GPT-4o. Moreover, within LogicTree, GPT-4o outperforms o3-mini by 7.6% on average.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
