  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.
