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The Role of Deductive and Inductive Reasoning in Large Language Models

Paper · 2025 · Chengkun Cai, Xu Zhao, Haoliang Liu et al.

Summary

Prompting methods such as Tree of Thought improve LLM reasoning by exploring many output paths, but this is expensive, and fixed prompt templates adapt poorly to harder instances. The authors propose DID (De-In-Ductive), a prompting framework that puts its effort into structuring the input. It draws on cognitive-science accounts of how people combine two modes of reasoning. First, the model works inductively on simplified versions of the task, gradually raising their difficulty until it arrives at a general rule. Then it applies that rule deductively to the original problem.

Problem difficulty is scored with two measures:

  • Littlestone dimension, which captures structural complexity;
  • information entropy over the relevant numeric variables, which captures how hard a particular instance is.

These scores determine how finely the problem is decomposed and how long the reasoning chain should be. DID was tested on AIW, MR-GSM8K and a new Holiday Puzzle set using GPT-3.5 Turbo, GPT-4o and Claude 3.5 Sonnet. It reached 70.3% on AIW versus 62.2% for ToT, at a lower cost per case. This suggests that structuring the input can replace costly output search and requires no fine-tuning.

Key points

  • Instance entropy. It is computed as log₂ of the product of (1 + |xᵢ|) over the relevant variables. This explains why "Alice" problems with the same Littlestone dimension but larger numbers are harder for LLMs.
  • AIW accuracy and cost.
    • DID reaches 70.3% accuracy, compared with 62.2% for ToT.
    • Cost per case is $0.0031 for DID, $0.0038 for ToT and $0.0022 for CoT.
    • DID uses more input tokens than ToT (90 vs 56).
  • MR-GSM8K (meta-reasoning: finding errors in given solutions). DID performs on par with the baselines rather than clearly ahead, for example 87.7% on GPT-4o vs 89.1% for ToT. It is cheaper than ToT ($0.0128 vs $0.0194).
  • Holiday Puzzle (new set of 20 date and holiday calculation problems).
    • Absolute accuracy is low for all methods.
    • DID still scores highest on every model, for example 15.4% on GPT-4o vs 7.5% for ToT.
    • DID costs less than ToT ($0.0181 vs $0.0262).
  • Training and setup. DID works with one model instance through prompting alone, with no fine-tuning. This sets it apart from multi-agent or RL-trained approaches such as DeepSeek-R1.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of WashingtonSeattle · United States353 works · 200,043 citations🎓University of EdinburghEdinburgh · United Kingdom359 works · 77,352 citations🎓Tsinghua UniversityBeijing · China333 works · 87,019 citations🎓University of CopenhagenCopenhagen · Denmark115 works · 15,292 citations🎓University of ManchesterManchester · United Kingdom87 works · 44,938 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 works

Cite

Cite as Chengkun Cai, Xu Zhao, Haoliang Liu, Zhongyu Jiang, Tianfang Zhang, Zongkai Wu, Jenq-Neng Hwang and Lei Li. 2025. The Role of Deductive and Inductive Reasoning in Large Language Models. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.acl-long.820

@inproceedings{cai2025role,
  title = {{The Role of Deductive and Inductive Reasoning in Large Language Models}},
  author = {Chengkun Cai, Xu Zhao, Haoliang Liu, Zhongyu Jiang, Tianfang Zhang, Zongkai Wu, Jenq-Neng Hwang and Lei Li},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.820},
  url = {https://doi.org/10.18653/v1/2025.acl-long.820}
}

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