Elamur Research
☰
home / papers / 2022 / FOLIO: Natural Language Reasoning with First-Order Logic

FOLIO: Natural Language Reasoning with First-Order Logic

Written for the Research library (claude-opus-5-5) from the paper text, in our own words: the license "arXiv — non-exclusive license to distribute" does not allow redistributing the text itself. Original — arxiv.org/pdf/2209.00840

Summary

Current benchmarks for logical reasoning in language models tend to be synthetic, use small vocabularies, involve shallow reasoning, or mix logic with other skills such as commonsense. FOLIO addresses this with an expert-written English dataset of deductive reasoning problems. Each problem gives a set of premises and asks whether a conclusion is True, False or Unknown. Every sentence is paired with a first-order logic (FOL) formula, and an FOL inference engine checks these formulas automatically, so the gold labels are logically sound. The annotators were students and researchers trained in FOL. The stories come in two subsets: WikiLogic, written from scratch using Wikipedia knowledge, and HybLogic, built from templates and then edited by humans. The NL–FOL pairs also form a new semantic-parsing task. The authors benchmark fine-tuned medium-sized models and few-shot LLMs. GPT-4 remains far below expert humans, especially on the deeper HybLogic stories. FOLIO is therefore a demanding, verifiable testbed for measuring progress in logical reasoning.

Key points

  • Size and structure: FOLIO has 1,430 conclusions spread over 487 premise sets. Reasoning depth ranges from 0 to 7. By comparison, RuleTaker and LogicNLI reach at most depth 5, have fewer than 50 distinct ASTs, and have vocabularies of 101 and 1077 words respectively.
  • Two subsets:
    • WikiLogic has more varied sentence-level logic, with 53 ASTs.
    • HybLogic has longer reasoning chains but uses only 33 ASTs.
  • Few-shot LLM results: GPT-4 scores only 53.1% on HybLogic, close to chance. GPT-3.5 and GPT-4 both do clearly better on WikiLogic.
  • Fine-tuned model results: fine-tuned RoBERTa-large does the opposite and scores higher on HybLogic, probably because it learns the template patterns.
  • Human baselines: experts reach 95.98% accuracy and non-experts 61.82%, which puts experts about 32 points ahead of GPT-4.
  • GPT-4 error analysis: among GPT-4's wrong answers, 65% follow a faulty reasoning path and 25% contain an incorrect derivation step. A further 5% misread complex syntax, and the remaining 5% take commonsense shortcuts.

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

Fields: Other

Cited by

187 papers of our library cite it (of the 140673 whose bibliographies we read); 7 of them have a page here, 180 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2209.00840 · arXiv 2209.00840

@misc{han2022folio,
  title = {{FOLIO: Natural Language Reasoning with First-Order Logic}},
  author = {Han, Simeng and Schoelkopf, Hailey and Zhao, Yilun and Qi, Zhenting and Riddell, Martin and Zhou, Wenfei and Coady, James and Peng, David and Qiao, Yujie and Benson, Luke and Sun, Lucy and Wardle-Solano, Alex and Szabo, Hannah and Zubova, Ekaterina and Burtell, Matthew and Fan, Jonathan and Liu, Yixin and Wong, Brian and Sailor, Malcolm and Ni, Ansong and Nan, Linyong and Kasai, Jungo and Yu, Tao and Zhang, Rui and Fabbri, Alexander R. and Kryscinski, Wojciech and Yavuz, Semih and Liu, Ye and Lin, Xi Victoria and Joty, Shafiq and Zhou, Yingbo and Xiong, Caiming and Ying, Rex and Cohan, Arman and Radev, Dragomir},
  year = {2022},
  doi = {10.48550/arxiv.2209.00840},
  eprint = {2209.00840},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2209.00840}
}

References

57 references, 20 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. David Arps, Jan Kels, Florian Krämer, Yunus Renz, Regina Stodden, and Wiebke Petersen. 2022. HHU-plexity at text complexity DE challenge 2022. In Proceedings of the GermEval 2022 Workshop on Text Complexity Assessment of German Text, pages 27–32, Potsdam, Germany. Association for Computational Lingu… find
  2. Sid Black, Stella Biderman, Eric Hallahan, Quentin Anthony, Leo Gao, Laurence Golding, Horace He, Connor Leahy, Kyle McDonell, Jason Phang, Michael Pieler, USVSN Sai Prashanth, Shivanshu Purohit, Laria Reynolds, Jonathan Tow, Ben Wang, and Samuel Weinbach. 2022. Gpt-neox-20b: An open-source autoregr… find our card
  3. Samuel R. Bowman, Gabor Angeli, Christopher Potts, and Christopher D. Manning. 2015. A large annotated corpus for learning natural language inference. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 632–642, Lisbon, Portugal. Association for Computati… find
  4. Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chri… find
  5. Wenhu Chen, Hanwen Zha, Zhiyu Chen, Wenhan Xiong, Hong Wang, and William Yang Wang. 2020. HybridQA: A dataset of multi-hop question answering over tabular and textual data. In Findings of the Association for Computational Linguistics: EMNLP 2020, pages 1026–1036, Online. Association for Computationa… find our card
  6. Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al. 2022. Palm: Scaling language modeling with pathways. arXiv preprint arXiv:2204.02311. find
  7. Peter Clark, Oyvind Tafjord, and Kyle Richardson. 2020. Transformers as soft reasoners over language. CoRR, abs/2002.05867. find our card
  8. Peter Clark, Oyvind Tafjord, and Kyle Richardson. 2021. Transformers as soft reasoners over language. In Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pages 3882–3890. find our card
  9. Robin Cooper, Dick Crouch, Jan Van Eijck, Chris Fox, Johan Van Genabith, Jan Jaspars, Hans Kamp, David Milward, Manfred Pinkal, Massimo Poesio, et al. 1996. Using the framework. Technical report, Technical Report LRE 62-051 D-16, The FraCaS Consortium. find
  10. Antonia Creswell, Murray Shanahan, and Irina Higgins. 2022. Selection-inference: Exploiting large language models for interpretable logical reasoning. arXiv preprint arXiv:2205.09712. find
  11. Edgar Dale and Jeanne S. Chall. 1948. A formula for predicting readability. Educational Research Bulletin, 27(1):11–28. find
  12. Edgar Dale and Jeanne S. Chall. 1995. Readability Revisited: The New Dale-Chall Readability Formula. Brookline Books. find
  13. Ishita Dasgupta, Andrew K Lampinen, Stephanie CY Chan, Antonia Creswell, Dharshan Kumaran, James L McClelland, and Felix Hill. 2022. Language models show human-like content effects on reasoning. arXiv preprint arXiv:2207.07051. find
  14. Donald Davidson. 2001. 105The Logical Form of Action Sentences. In Essays on Actions and Events. Oxford University Press. find
  15. Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies,… find
  16. David Dohan, Winnie Xu, Aitor Lewkowycz, Jacob Austin, David Bieber, Raphael Gontijo Lopes, Yuhuai Wu, Henryk Michalewski, Rif A. Saurous, Jascha Sohl-dickstein, Kevin Murphy, and Charles Sutton. 2022. Language model cascades. arXiv preprint. find
  17. Weinan He, Canming Huang, Yongmei Liu, and Xiaodan Zhu. 2021. WinoLogic: A zero-shot logic-based diagnostic dataset for Winograd Schema Challenge. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 3779–3789, Online and Punta Cana, Dominican Republic. As… find
  18. Akira Kawabata and Saku Sugawara. 2023. Evaluating the rationale understanding of critical reasoning in logical reading comprehension. Preprint, arXiv:2311.18353. find
  19. Mehran Kazemi, Quan Yuan, Deepti Bhatia, Najoung Kim, Xin Xu, Vaiva Imbrasaite, and Deepak Ramachandran. 2023. Boardgameqa: A dataset for natural language reasoning with contradictory information. Preprint, arXiv:2306.07934. — [arXiv:2306.07934](https://arxiv.org/abs/2306.07934) find
  20. Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa. 2022. Large language models are zero-shot reasoners. arXiv preprint arXiv:2205.11916. find our card
  21. Anne Lehman. 1973. Two sets of perfect syllogisms. Notre Dame Journal of Formal Logic, 14(3):425 – 429. find
  22. Sarah-Jane Leslie. 2008. Generics: Cognition and Acquisition. The Philosophical Review, 117(1):1–47. find
  23. Yifei Li, Zeqi Lin, Shizhuo Zhang, Qiang Fu, Bei Chen, Jian-Guang Lou, and Weizhu Chen. 2022. On the advance of making language models better reasoners. arXiv preprint arXiv:2206.02336. — [arXiv:2206.02336](https://arxiv.org/abs/2206.02336) find
  24. Jian Liu, Leyang Cui, Hanmeng Liu, Dandan Huang, Yile Wang, and Yue Zhang. 2021. Logiqa: a challenge dataset for machine reading comprehension with logical reasoning. In Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pages 3622… find our card
  25. Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2020. Ro{bert}a: A robustly optimized {bert} pretraining approach. arXiv preprint arXiv:1907.11692. find
  26. W. McCune. 2005–2010. Prover9 and mace4. http: //www.cs.unm.edu/~mccune/prover9/ . find
  27. Ansong Ni, Pengcheng Yin, Yilun Zhao, Martin Riddell, Troy Feng, Rui Shen, Stephen Yin, Ye Liu, Semih Yavuz, Caiming Xiong, Shafiq Joty, Yingbo Zhou, Dragomir Radev, and Arman Cohan. 2023. L2ceval: Evaluating language-to-code generation capabilities of large language models. Preprint, arXiv:2309.174… find
  28. Tobias Nipkow, Lawrence C. Paulson, and Markus Wenzel. 2002. Isabelle/Hol a Proof Assistant for Higher-Order Logic. Springer. find
  29. Theo Olausson, Alex Gu, Ben Lipkin, Cedegao Zhang, Armando Solar-Lezama, Joshua Tenenbaum, and Roger Levy. 2023. LINC: A neurosymbolic approach for logical reasoning by combining language models with first-order logic provers. In Proceedings of the 2023 Conference on Empirical Methods in Natural Lan… find our card
  30. OpenAI, Josh Achiam, and Others. 2023. Gpt-4 technical report. Preprint, arXiv:2303.08774. find our card
  31. Liangming Pan, Alon Albalak, Xinyi Wang, and William Wang. 2023. Logic-LM: Empowering large language models with symbolic solvers for faithful logical reasoning. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 3806–3824, Singapore. Association for Computational Lingui… find our card
  32. Terence Parsons. 1990. Events in the Semantics of English. MIT Press, Cambridge, MA, USA. find
  33. Stuart Russell and Peter Norvig. 2010. Artificial Intelligence: A Modern Approach, 3 edition. Prentice Hall. find
  34. Mohammed Saeed, Naser Ahmadi, Preslav Nakov, and Paolo Papotti. 2021. RuleBERT: Teaching soft rules to pre-trained language models. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 1460–1476, Online and Punta Cana, Dominican Republic. Association for C… find
  35. Abulhair Saparov and He He. 2023. Language models can (kind of) reason: A systematic formal analysis of chain-of-thought. In International Conference on Learning Representations. find
  36. Hrituraj Singh, Milan Aggrawal, and Balaji Krishnamurthy. 2020. Exploring neural models for parsing natural language into first-order logic. arXiv preprint arXiv:2002.06544. — [arXiv:2002.06544](https://arxiv.org/abs/2002.06544) find
  37. Pranaydeep Singh, Luna De Bruyne, Orphée De Clercq, and Els Lefever. 2023. Misery loves complexity: Exploring linguistic complexity in the context of emotion detection. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 12871–12880, Singapore. Association for Computation… find
  38. Koustuv Sinha, Shagun Sodhani, Jin Dong, Joelle Pineau, and William L. Hamilton. 2019. CLUTRR: A diagnostic benchmark for inductive reasoning from text. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Lan… find
  39. Aarohi Srivastava, Abhinav Rastogi, and +447 Authors. 2023. Beyond the imitation game: Quantifying and extrapolating the capabilities of language models. Preprint, arXiv:2206.04615. find our card
  40. Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao, Abu Awal Md Shoeb, Abubakar Abid, Adam Fisch, Adam R Brown, Adam Santoro, Aditya Gupta, Adrià Garriga-Alonso, et al. 2022. Beyond the imitation game: Quantifying and extrapolating the capabilities of language models. arXiv preprint arXiv:2206.04615. find our card
  41. Hongda Sun, Weikai Xu, Wei Liu, Jian Luan, Bin Wang, Shuo Shang, Ji-Rong Wen, and Rui Yan. 2023. From indeterminacy to determinacy: Augmenting logical reasoning capabilities with large language models. Preprint, arXiv:2310.18659. — [arXiv:2310.18659](https://arxiv.org/abs/2310.18659) find
  42. G. Sutcliffe. 2017. The TPTP Problem Library and Associated Infrastructure. From CNF to TH0, TPTP v6.4.0. Journal of Automated Reasoning, 59(4):483– 502. find
  43. Oyvind Tafjord, Bhavana Dalvi, and Peter Clark. 2021. ProofWriter: Generating implications, proofs, and abductive statements over natural language. In Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021, pages 3621–3634, Online. Association for Computational Linguistics. find our card
  44. Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. 2019. CommonsenseQA: A question answering challenge targeting commonsense knowledge. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies,… find
  45. Alon Talmor, Oyvind Tafjord, Peter Clark, Yoav Goldberg, and Jonathan Berant. 2020. Leap-of-thought: Teaching pre-trained models to systematically reason over implicit knowledge. Advances in Neural Information Processing Systems, 33:20227–20237. find
  46. Jidong Tian, Yitian Li, Wenqing Chen, Liqiang Xiao, Hao He, and Yaohui Jin. 2021. Diagnosing the first-order logical reasoning ability through LogicNLI. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 3738–3747, Online and Punta Cana, Dominican Republ… find
  47. Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, Aurelien Rodriguez, Armand Joulin, Edouard Grave, and Guillaume Lample. 2023. Llama: Open and efficient foundation language models. Preprint… find
  48. Alex Wang, Yada Pruksachatkun, Nikita Nangia, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel Bowman. 2019a. Superglue: A stickier benchmark for general-purpose language understanding systems. In Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc. find our card
  49. Alex Wang, Yada Pruksachatkun, Nikita Nangia, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel Bowman. 2019b. Superglue: A stickier benchmark for general-purpose language understanding systems. Advances in neural information processing systems, 32. find our card
  50. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations. find our card
  51. Jason Wei, Kelly Finn, Emma Templeton, Thalia Wheatley, and Soroush Vosoughi. 2021. Linguistic complexity loss in text-based therapy. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 4450–4459, On… find
  52. Jason Wei, Yi Tay, Rishi Bommasani, Colin Raffel, Barret Zoph, Sebastian Borgeaud, Dani Yogatama, Maarten Bosma, Denny Zhou, Donald Metzler, et al. 2022a. Emergent abilities of large language models. arXiv preprint arXiv:2206.07682. find our card
  53. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Ed Chi, Quoc Le, and Denny Zhou. 2022b. Chain of thought prompting elicits reasoning in large language models. arXiv preprint arXiv:2201.11903. find our card
  54. Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christopher D. Manning. 2018. HotpotQA: A dataset for diverse, explainable multi-hop question answering. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 2369… find our card
  55. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik R Narasimhan. 2023. Tree of thoughts: Deliberate problem solving with large language models. In Thirty-seventh Conference on Neural Information Processing Systems. find
  56. Weihao Yu, Zihang Jiang, Yanfei Dong, and Jiashi Feng. 2020. Reclor: A reading comprehension dataset requiring logical reasoning. In International Conference on Learning Representations. find our card
  57. Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah D. Goodman. 2022. Star: Bootstrapping reasoning with reasoning. arXiv preprint. find our card