The Role of Deductive and Inductive Reasoning in Large Language Models

Large Language Models (LLMs) have demonstrated impressive capabilities in reasoning tasks, yet their reliance on static prompt structures and limited adaptability to complex scenarios remains a significant challenge. In this paper, we propose the Deductive and InDuctive(DID) method, a novel framework that enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning approaches. Drawing from cognitive science principles, DID implements a dual-metric complexity evaluation system that combines Littlestone dimension and information entropy to precisely assess task difficulty and guide decomposition strategies. DID enables the model to progressively adapt its reasoning pathways based on problem complexity, mirroring human cognitive processes. We evaluate DID's effectiveness across multiple benchmarks, including the AIW and MR-GSM8K, as well as our custom Holiday Puzzle dataset for temporal reasoning. Our results demonstrate significant improvements in reasoning quality and solution accuracy - achieving 70.3% accuracy on AIW (compared to 62.2% for Tree of Thought) while maintaining lower computational costs. The success of DID in improving LLM performance while preserving computational efficiency suggests promising directions for developing more cognitively aligned and capable language models. Our work contributes a theoretically grounded, input-centric approach to enhancing LLM reasoning capabilities, offering an efficient alternative to traditional output-exploration methods.