---
title: "An Incomplete Loop — paper by Liu et al. (2024)"
description: "The authors treat these routes as deductive, inductive, and abductive reasoning, and test whether skill… 43 references, cited by 9 papers here."
authors: ["Emmy Liu", "Graham Neubig", "Jacob Andreas"]
year: 2024
venue: "arXiv:2404.03028"
source: "https://arxiv.org/abs/2404.03028"
doi: "10.48550/arxiv.2404.03028"
arxiv: "2404.03028"
licence: "CC BY-SA 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by-sa/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/liu-2024-incomplete-loop-deductive-inductive-abductive/"
---
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# An Incomplete Loop: Deductive, Inductive, and Abductive Reasoning in Language Models

**Authors:** [Emmy Liu](https://md.research.elamur.ai/free/en/authors/emmy-liu/), [Graham Neubig](https://md.research.elamur.ai/free/en/authors/graham-neubig/) and [Jacob Andreas](https://md.research.elamur.ai/free/en/authors/jacob-andreas/) · **Year:** 2024 · **Venue:** arXiv:2404.03028 · **Licence:** [CC BY-SA 4.0 (arXiv)](http://creativecommons.org/licenses/by-sa/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2404.03028) · [PDF](https://arxiv.org/pdf/2404.03028) · [DOI 10.48550/arxiv.2404.03028](https://doi.org/10.48550/arxiv.2404.03028) · [arXiv 2404.03028](https://arxiv.org/abs/2404.03028) · [OpenAlex](https://openalex.org/W4394007083)

**Citations:** 3 citations (OpenAlex, 2026-10-14) · [9](https://md.research.elamur.ai/free/en/papers/liu-2024-incomplete-loop-deductive-inductive-abductive/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Language models can acquire a new task in three ways: from an explicit instruction, from a few examples, or by first writing their own task description from examples and then following it. The authors treat these routes as deductive, inductive, and abductive reasoning, and test whether skill in one predicts skill in the others. Four gpt and llama chat models are evaluated on linear function learning, an artificial colour language, and English–Kalamang translation. For the abductive route, a model proposes five hypotheses, which are reranked by verbalized confidence, by LM likelihood, or, for functions, by an external validator that executes the rule. Self-generated instructions beat plain few-shot prompting and zero-shot chain-of-thought on the synthetic tasks. On low-resource Kalamang, however, wrong hypotheses undermine them. The three abilities turn out to be largely dissociated: a model may learn from examples yet fail to state the rule, or state a useful rule yet not benefit from it. Following a correct supplied instruction, by contrast, is reliably strong. Prompting methods that look similar can therefore engage quite different mechanisms.

## Key points
- Models tested: gpt-3.5-turbo, gpt-4-turbo (gpt-4-1106-preview), llama-2-7b-chat and llama-2-70b-chat. Code, data and generated hypotheses are released on GitHub (nightingal3, "rule induction" repo).
- Domains and data:
  - 40 linear functions (e.g. f(x) = 20x − 13).
  - A nonce-word colour language (e.g. "lug" → blue).
  - Kalamang vocabulary and typological grammar features (e.g. SV order), evaluated with chrF in both directions (ek, ke).
- Hypothesis scoring options (n = 5 hypotheses per task):
  - verbalized confidence;
  - P(data), the summed log-probabilities of the in-context examples, computed by a separate LM;
  - P(answer), which counts only the answer tokens;
  - a parsing-based external validator, used only for functions.
- Correlation between correct induced hypotheses and few-shot success is generally weak. This was measured with point-biserial correlation and FDR (Benjamini–Hochberg) correction. The only exception is a small positive link for gpt models on Kalamang vocabulary.
- The authors argue that pipelines which select among hypotheses are better described as abduction than induction. They suggest future work on hypothesis verification and correction, and on consistency-enforcing joint training.

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

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## Cite

Cite as: Emmy Liu, Graham Neubig and Jacob Andreas. 2024. An Incomplete Loop: Deductive, Inductive, and Abductive Reasoning in Language Models. arXiv:2404.03028.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{liu2024incomplete,
  title = {{An Incomplete Loop: Deductive, Inductive, and Abductive Reasoning in Language Models}},
  author = {Emmy Liu, Graham Neubig and Jacob Andreas},
  year = {2024},
  doi = {10.48550/arxiv.2404.03028},
  eprint = {2404.03028},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2404.03028}
}
```

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42. Ruiqi Zhong, Peter Zhang, Steve Li, Jinwoo Ahn, Dan Klein, and Jacob Steinhardt. [Goal driven discovery of distributional differences via language descriptions](https://md.research.elamur.ai/free/en/papers/zhong-2023-goal-driven-discovery-distributional-differences/). In Advances in Neural Information Processing Systems 36 (NeurIPS 2023), 2023.
43. Zhaocheng Zhu, Yuan Xue, Xinyun Chen, Denny Zhou, Jian Tang, Dale Schuurmans, and Hanjun Dai. Large language models can learn rules, 2023. [find](https://scholar.google.com/scholar?q=Zhaocheng+Zhu%2C+Yuan+Xue%2C+Xinyun+Chen%2C+Denny+Zhou%2C+Jian+Tang%2C+Dale+Schuurmans%2C+and+Hanjun+Dai%2E+Large+language+models+can+learn+rules%2C+2023%2E)

*Updated 30 October 2026*
