# RuleBert: Teaching Soft Rules to Pre-trained Language Models

arXiv: https://arxiv.org/abs/2109.13006 · HTML: https://mlsanity.com/paper/2109.13006/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 55 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [The Woman Worked as a Babysitter: On Biases in Language Generation](https://mlsanity.com/paper/1909.01326/) (2019)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [Towards Understanding and Mitigating Social Biases in Language Models](https://mlsanity.com/paper/2106.13219/) (2021)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [On the Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Baselines](https://mlsanity.com/paper/2006.04884/) (2020)
- [Negated and Misprimed Probes for Pretrained Language Models: Birds Can Talk, But Cannot Fly](https://mlsanity.com/paper/1911.03343/) (2019)
- [Towards Debiasing Sentence Representations](https://mlsanity.com/paper/2007.08100/) (2020)
- [oLMpics -- On what Language Model Pre-training Captures](https://mlsanity.com/paper/1912.13283/) (2019)
- [Continual Lifelong Learning in Natural Language Processing: A Survey](https://mlsanity.com/paper/2012.09823/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Evaluating Commonsense in Pre-trained Language Models](https://mlsanity.com/paper/1911.11931/) (2019)
- [Hurtful Words: Quantifying Biases in Clinical Contextual Word Embeddings](https://mlsanity.com/paper/2003.11515/) (2020)
- [Clingo = ASP + Control: Preliminary Report](https://mlsanity.com/paper/1405.3694/) (2014)
- [What Do Position Embeddings Learn? An Empirical Study of Pre-Trained Language Model Positional Encoding](https://mlsanity.com/paper/2010.04903/) (2020)
- [Differentiable Reasoning on Large Knowledge Bases and Natural Language](https://mlsanity.com/paper/1912.10824/) (2019)

## Built on by (most cited first, 25 of 25)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [A Survey of Knowledge Enhanced Pre-trained Language Models](https://mlsanity.com/paper/2211.05994/) (2022)
- [LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2404.15522/) (2024)
- [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022)
- [BoardgameQA: A Dataset for Natural Language Reasoning with Contradictory Information](https://mlsanity.com/paper/2306.07934/) (2023)
- [Transfer Learning with Synthetic Corpora for Spatial Role Labeling and Reasoning](https://mlsanity.com/paper/2210.16952/) (2022)
- [Chain of Thought Imitation with Procedure Cloning](https://mlsanity.com/paper/2205.10816/) (2022)
- [Enhancing Reasoning Capabilities of LLMs via Principled Synthetic Logic Corpus](https://mlsanity.com/paper/2411.12498/) (2024)
- [Improved Logical Reasoning of Language Models via Differentiable Symbolic Programming](https://mlsanity.com/paper/2305.03742/) (2023)
- [RECKONING: Reasoning through Dynamic Knowledge Encoding](https://mlsanity.com/paper/2305.06349/) (2023)
- [Large language models for artificial general intelligence (AGI): A survey of foundational principles and approaches](https://mlsanity.com/paper/2501.03151/) (2025)
- [Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization](https://mlsanity.com/paper/2505.15918/) (2025)
- [LogicPro: Improving Complex Logical Reasoning via Program-Guided Learning](https://mlsanity.com/paper/2409.12929/) (2024)
- [RFEval: Benchmarking Reasoning Faithfulness under Counterfactual Reasoning Intervention in Large Reasoning Models](https://mlsanity.com/paper/2602.17053/) (2026)
- [GLUECons: A Generic Benchmark for Learning Under Constraints](https://mlsanity.com/paper/2302.10914/) (2023)
- [A Survey on Symbolic Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2408.10210/) (2024)
- [Leveraging Large Language Models for Bengali Math Word Problem Solving with Chain of Thought Reasoning](https://mlsanity.com/paper/2505.21354/) (2025)
- [Teaching Probabilistic Logical Reasoning to Transformers](https://mlsanity.com/paper/2305.13179/) (2023)
- [Automatic Rule Induction for Interpretable Semi-Supervised Learning](https://mlsanity.com/paper/2205.09067/) (2022)
- [A Survey of Knowledge Enhanced Pre-trained Models](https://mlsanity.com/paper/2110.00269/) (2021)
- [Reasoning over Logically Interacted Conditions for Question Answering](https://mlsanity.com/paper/2205.12898/) (2022)
- [Dynamic MOdularized Reasoning for Compositional Structured Explanation Generation](https://mlsanity.com/paper/2309.07624/) (2023)
- [Where Reasoning Breaks: Logic-Aware Path Selection by Controlling Logical Connectives in LLMs Reasoning Chains](https://mlsanity.com/paper/2604.20564/) (2026)
- [MIH-TCCT: Mitigating Inconsistent Hallucinations in LLMs via Event-Driven Text-Code Cyclic Training](https://mlsanity.com/paper/2502.08904/) (2025)

## Abstract (arXiv)

While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction with a probability for a given hypothesis. We release the first dataset for this task, and we propose a revised loss function that enables the PLM to learn how to predict precise probabilities for the task. Our evaluation results show that the resulting fine-tuned models achieve very high performance, even on logical rules that were unseen at training. Moreover, we demonstrate that logical notions expressed by the rules are transferred to the fine-tuned model, yielding state-of-the-art results on external datasets.