# Teaching Probabilistic Logical Reasoning to Transformers

arXiv: https://arxiv.org/abs/2305.13179 · HTML: https://mlsanity.com/paper/2305.13179/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 22 May 2023.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [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)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Large Language Models are few(1)-shot Table Reasoners](https://mlsanity.com/paper/2210.06710/) (2022)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [QuaRTz: An Open-Domain Dataset of Qualitative Relationship Questions](https://mlsanity.com/paper/1909.03553/) (2019)
- [Reasoning Over Paragraph Effects in Situations](https://mlsanity.com/paper/1908.05852/) (2019)
- [Logic-Guided Data Augmentation and Regularization for Consistent Question Answering](https://mlsanity.com/paper/2004.10157/) (2020)
- [WIQA: A dataset for "What if..." reasoning over procedural text](https://mlsanity.com/paper/1909.04739/) (2019)
- [StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts](https://mlsanity.com/paper/2204.08292/) (2022)
- [A Logic-Driven Framework for Consistency of Neural Models](https://mlsanity.com/paper/1909.00126/) (2019)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [PRover: Proof Generation for Interpretable Reasoning over Rules](https://mlsanity.com/paper/2010.02830/) (2020)
- [Learning to Prove Theorems by Learning to Generate Theorems](https://mlsanity.com/paper/2002.07019/) (2020)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [Measuring Sentence-Level and Aspect-Level (Un)certainty in Science Communications](https://mlsanity.com/paper/2109.14776/) (2021)
- [RuleBert: Teaching Soft Rules to Pre-trained Language Models](https://mlsanity.com/paper/2109.13006/) (2021)
- [Improved Logical Reasoning of Language Models via Differentiable Symbolic Programming](https://mlsanity.com/paper/2305.03742/) (2023)
- [GLUECons: A Generic Benchmark for Learning Under Constraints](https://mlsanity.com/paper/2302.10914/) (2023)

## Built on by (most cited first, 7 of 7)

- [Enhancing Reasoning Capabilities of LLMs via Principled Synthetic Logic Corpus](https://mlsanity.com/paper/2411.12498/) (2024)
- [A Survey on Compositional Learning of AI Models: Theoretical and Experimental Practices](https://mlsanity.com/paper/2406.08787/) (2024)
- [Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization](https://mlsanity.com/paper/2505.15918/) (2025)
- [Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2509.10739/) (2025)
- [Bayesian Network Structure Discovery Using Large Language Models](https://mlsanity.com/paper/2511.00574/) (2025)
- [Federated Neuro-Symbolic Learning](https://mlsanity.com/paper/2308.15324/) (2023)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)

## Abstract (arXiv)

In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large Language Models (LLMs). Our evaluation results show that both generations of language models struggle with reasoning over uncertain text. We propose a novel end-to-end fine-tuning approach, Probabilistic Constraint Training (PCT), that utilizes probabilistic logical rules as constraints in the fine-tuning phase without relying on these rules in the inference stage. To assess the effectiveness of PCT, we utilize the related corpora and, additionally, create a new and more challenging benchmark that, unlike the previous ones, uses instance-specific rules. Our study demonstrates that PCT improves the transformer-based language model's intrinsic reasoning and makes their probabilistic logical reasoning process more explicit and explainable. Furthermore, PCT equips these models to effectively handle novel situations, including higher reasoning depth, new domains, and complex probabilistic structures.