Large language models (LLMs) such as ChatGPT have recently demonstrated significant potential in mathematical abilities, providing valuable reasoning paradigm consistent with human natural language. However, LLMs currently have difficulty in bridging perception, language understanding and reasoning capabilities due to incompatibility of the underlying information flow among them, making it challenging to accomplish tasks autonomously. On the other hand, abductive learning (ABL) frameworks for integrating the two abilities of perception and reasoning has seen significant success in inverse decipherment of incomplete facts, but it is limited by the lack of semantic understanding of logical reasoning rules and the dependence on complicated domain knowledge representation. This paper presents a novel method (ChatABL) for integrating LLMs into the ABL framework, aiming at unifying the three abilities in a more user-friendly and understandable manner. The proposed method uses the strengths of LLMs' understanding and logical reasoning to correct the incomplete logical facts for optimizing the performance of perceptual module, by summarizing and reorganizing reasoning rules represented in natural language format. Similarly, perceptual module provides necessary reasoning examples for LLMs in natural language format. The variable-length handwritten equation deciphering task, an abstract expression of the Mayan calendar decoding, is used as a testbed to demonstrate that ChatABL has reasoning ability beyond most existing state-of-the-art methods, which has been well supported by comparative studies. To our best knowledge, the proposed ChatABL is the first attempt to explore a new pattern for further approaching human-level cognitive ability via natural language interaction with ChatGPT.

翻译：近期，ChatGPT等大型语言模型在数学能力方面展现出巨大潜力，提供了与人类自然语言一致的宝贵推理范式。然而，由于感知、语言理解和推理能力之间的底层信息流不兼容，大型语言模型目前难以弥合三者之间的鸿沟，导致其难以自主完成任务。另一方面，用于整合感知与推理两种能力的溯因学习框架在逆推不完全事实方面取得了显著成功，但受限于对逻辑推理规则缺乏语义理解以及依赖复杂的领域知识表示。本文提出一种将大型语言模型集成到溯因学习框架中的新方法（ChatABL），旨在以更用户友好且易理解的方式统合三种能力。所提方法利用大型语言模型在理解与逻辑推理方面的优势，通过总结和重组以自然语言格式呈现的推理规则，修正不完整的逻辑事实，以优化感知模块的性能。同时，感知模块以自然语言格式为大型语言模型提供必要的推理示例。本文采用变长手写方程破译任务（玛雅历法解码的抽象表达）作为测试平台，结果表明ChatABL的推理能力超越了大多数现有最优方法，对比研究也充分支持了这一结论。据我们所知，所提出的ChatABL是首次尝试探索通过与ChatGPT进行自然语言交互来进一步接近人类水平认知能力的新模式。