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ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language
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Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications.However, their ability to generate implications of a theory has not yet been demonstrated, and methods for reconstructing proofs of answers are imperfect.In this work we show that a generative model, called ProofWriter, can reliably generate both implications of a theory and the natural language proofs that support them.In particular, iterating a 1-step implication generator results in proofs that are highly reliable, and represent actual model decisions (rather than post-hoc rationalizations).On the RuleTaker dataset, the accuracy of ProofWriter's proofs exceed previous methods by +9% absolute, and in a way that generalizes to proof depths unseen in training and on out-of-domain problems.We also show that generative techniques can perform a type of abduction with high precision: Given a theory and an unprovable conclusion, identify a missing fact that allows the conclusion to be proved, along with a proof.These results significantly improve the viability of neural methods for systematically reasoning over natural language.1
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![Figure 4 [Task 1] All-At-Once proofs can be verified by checking each step as a separate QA query.](/paper-figures/063dd318c078425ab0814082c0fc932b/proofwriter-generating-implications-proofs-and-abductive-statements-over-natural-figure-4.png)
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“ProofWriter (Tafjord et al., 2021) is a synthetic dataset created to assess deductive reasoning abilities of LLMs.”
From OpenHands: An Open Platform for AI Software Developers as Generalist Agents (2024) · cites this paper as Tafjord et al., 2021
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“ProofWriter, meanwhile, is a synthetically generated dataset for logical reasoning over natural language.”
From LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers (2023) · cites this paper as Tafjord et al., 2021
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“Early work on deductive reasoning benchmarks such as RuleTaker (Clark et al., 2020) and ProofWriter (Tafjord et al., 2021) established the basic setup of query answering over sets of rules and facts, with ProofWriter reaching a maximum proof depth of five steps.ProntoQA (Saparov and He, 2023) introduces proof-structure controls and formal error attribution, also evaluated up to five hops.”
From Probing for Long-Horizon Deductive Reasoning Capabilities in Language Models with Prolog (2026) · cites this paper as Tafjord et al., 2021
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“These benchmarks revealed that models at the time struggle as proof depth increases, but the depths studied remain shallow.”
From Probing for Long-Horizon Deductive Reasoning Capabilities in Language Models with Prolog (2026) · cites this paper as Tafjord et al., 2021
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“This process is algorithmic; a model that has learned a robust implementation of this algorithm should, in principle, generalize beyond the shallow depths seen in previous benchmarks (Clark et al., 2020;Tafjord et al., 2021;Saparov and He, 2023).”
From Probing for Long-Horizon Deductive Reasoning Capabilities in Language Models with Prolog (2026) · cites this paper as Tafjord et al., 2021
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Porada, I., Sordoni, A., & Cheung, J. C. K. (2022) · Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT) · doi:10.18653/v1/2022.naacl-main.337 · Cited by 6
Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-hop Inference
Thayaparan, M., Valentino, M., Ferreira, D. M., Rozanova, J., & Freitas, A. (2022) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00508 · Cited by 3
DCoL-A: Agentic dual chain of thinking helps LLMs pretend logic solvers
Chen, M., Wu, L.-I., Liu, R., Chang, X., Xue, J., & Li, G. (2026) · Journal of Systems Architecture · doi:10.1016/j.sysarc.2026.103780 · Cited by 2
Betz, G., & Richardson, K. (2022) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2022.900943 · Cited by 2
Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models
Hou, Y., Li, J., Fei, Y., Stolfo, A., Zhou, W., Zeng, G., Bosselut, A., & Sachan, M. (2023) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2023.emnlp-main.299 · Cited by 42
Identifying the limits of transformers when performing model-checking with natural language
Madusanka, T., Batista-Navarro, R., & Pratt-Hartmann, I. E. (2023) · Conference of the European Chapter of the Association for Computational Linguistics · doi:10.18653/v1/2023.eacl-main.257 · Cited by 5
Madusanka, T., Zahid, I., Li, H., Pratt-Hartmann, I. E., & Batista-Navarro, R. (2023) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2023.emnlp-main.536 · Cited by 3
A Generative Symbolic Model for More General Natural Language Understanding and ReasoningPreprint
Saparov, A., & Mitchell, T. M. (2021) · arXiv (Cornell University) · Cited by 2
Large-Scale Commonsense Knowledge for Default Logic Reasoning
Järv, P., Tammet, T., Verrev, M., & Draheim, D. (2023) · SN Computer Science · doi:10.1007/s42979-023-01963-2 · Cited by 1
Can Language Models Pretend Solvers? Logic Code Simulation with LLMs
Chen, M., Li, G., Wu, L.-I., Liu, R., Su, Y., Chang, X., & Xue, J. (2024) · Lecture notes in computer science · doi:10.1007/978-981-96-0602-3_6 · Cited by 6
Toward Enhancing Reasoning Capabilities of LLMs: An Approach via Synthetic Logic Corpus
Morishita, T., Morio, G., Yamaguchi, A., & Sogawa, Y. (2025) · Journal of Natural Language Processing · doi:10.5715/jnlp.32.520 · Cited by 1
Think straight or think again? Continual joint learning of deduction, abduction and induction
Xiong, K., Ding, X., Cao, Y., Zhao, Y., Liu, T., & Qin, B. (2025) · Neural Networks · doi:10.1016/j.neunet.2025.107768 · Cited by 1
Question Answering with LLMs and Learning from Answer Sets
Borroto, M., GALLAGHER, K., Ielo, A., KAREEM, I., Ricca, F., & Russo, A. (2025) · Theory and Practice of Logic Programming · doi:10.1017/s1471068425100343 · Cited by 5
EMRDCM : An experience-enhanced multi-role debate method based on compromise mechanisms
Zhang, Y., Feng, J., Yiming, X., Wang, Z., Yang, T., & Wang, X. (2026) · Journal of Intelligent Information Systems · doi:10.1007/s10844-026-01022-1 · Cited by 1
DL-ReasonSuite: A Benchmark for Evaluating Description Logic Reasoning in Large Language Models
Olucoglu, M., & Bursa, O. (2026) · Applied Sciences · doi:10.3390/app16041821 · Cited by 1
LogiCue: Targeted Prompting for Improved Modal and Conditional Reasoning in Large Language Models
Shahrokhshahi, F., Mohammadi, F., & Sönmez, F. (2026) · Procedia Computer Science · doi:10.1016/j.procs.2026.01.057 · Cited by 1
Large Language Model for OWL Proofs
Yang, H., Chen, J., & Sattler, U. (2026) · International World Wide Web Conference (WWW) · doi:10.1145/3774904.3792395 · Cited by 4
Neuro-symbolic NLP: taxonomy, assessment, and directions
Chatzikyriakidis, S., & Lappin, S. (2026) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2026.1797587 · Cited by 2
Investigating Transformer-Guided Chaining for Interpretable Natural Logic Reasoning
Kanagasabai, R., Rajamanickam, S., & Shi, W. (2023) · Findings of the Association for Computational Linguistics: ACL (Findings of ACL) · doi:10.18653/v1/2023.findings-acl.588 · Cited by 1
MTR: A Dataset Fusing Inductive, Deductive, and Defeasible Reasoning
Li, Y., Tian, J., Fan, C., Chen, W., He, H., & Jin, Y. (2023) · Findings of the Association for Computational Linguistics: ACL (Findings of ACL) · doi:10.18653/v1/2023.findings-acl.640 · Cited by 1
Transformers in the Service of Description Logic-Based Contexts
Poulis, A., Tsalapati, E., & Koubarakis, M. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-77792-9_20 · Cited by 1
Advances in reasoning by prompting large language models: A survey
Hong, R., Pang, X., & Zhang, C. (2026) · Cybernetics and Intelligence · doi:10.26599/cai.2024.9390004 · Cited by 3
Language-Based Syllogistic Reasoning Using Deep Neural Networks
Aghahadi, Z., & Talebpour, A. (2022) · Cognitive Semantics · doi:10.1163/23526416-bja10026 · Cited by 2
Empirical Investigation of Neural Symbolic Reasoning Strategies
Aoki, Y., Kudo, K., Kuribayashi, T., Brassard, A., Yoshikawa, M., Sakaguchi, K., & Inui, K. (2023) · Findings of the Association for Computational Linguistics: EACL · doi:10.18653/v1/2023.findings-eacl.86 · Cited by 1
Evaluating and Improving the Reasoning Abilities of Language Models
Helwe, C. (2024) · theses.fr (ABES) · doi:10.70675/7fc70e59zdd27z4b0fza38dz03a2c67cda50 · Cited by 1
Probing for Long-Horizon Deductive Reasoning Capabilities in Language Models with Prolog
Al-Negheimish, H., Ilieva, J., & Kim, Y. (2026) · arXiv · doi:10.48550/arxiv.2610.11592
“This process is algorithmic; a model that has learned a robust implementation of this algorithm should, in principle, generalize beyond the shallow depths seen in previous benchmarks (Clark et al., 2020; Tafjord et al., 2021; Saparov and He, 2023).”
Neural Unification for Logic Reasoning over Natural LanguagePreprint
Picco, G., Lam, H. T., Sbodio, M. L., & Garcia, V. L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.08460 · Cited by 1
ProofInfer: Generating Proof via Iterative Hierarchical Inference
Fei, Z., Zhang, Q., Zhou, X., Gui, T., & Huang, X. (2022) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2022.emnlp-main.747
Natural Language Annotations for Reasoning about Program Semantics
Zocca, M. (2023) · Findings of the Association for Computational Linguistics: EMNLP (Findings of EMNLP) · doi:10.18653/v1/2023.findings-emnlp.601
Zhang, Z., Storks, S., Hu, F., Sohn, S., Lee, M., Lee, H., & Chai, J. Y. (2023) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2023.emnlp-main.456 · Cited by 3
Metadata
- Authors
- Tafjord, O., Dalvi, B., & Clark, P.
- Affiliations
- Allen Institute for Artificial Intelligence (US)
- ORCID
- Clark, Peter
- Venue
- Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021
- Published
- 2021
- Pages
- 3621-3634
- OpenAlex
- W3115201256
- Cited by
- 122
- References
- 25
- Citations by year
- 2026: 22 · 2025: 18 · 2024: 14 · 2023: 32 · 2022: 27 · 2021: 9
- FWCI
- 9.47
- Type
- conference paper
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- Locations
- Findings of the Association for Computational Linguistics: ACL (Findings of ACL) (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Artificial Intelligence › Natural Language Processing Techniques
- Keywords
- proof generation, abductive reasoning, large language models, generative models
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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