# Exploring End-to-End Differentiable Natural Logic Modeling

arXiv: https://arxiv.org/abs/2011.04044 · HTML: https://mlsanity.com/paper/2011.04044/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 10 of 10)

- [Automated Fact-Checking: A Survey](https://mlsanity.com/paper/2109.11427/) (2021)
- [ProoFVer: Natural Logic Theorem Proving for Fact Verification](https://mlsanity.com/paper/2108.11357/) (2021)
- [Logical Reasoning with Span-Level Predictions for Interpretable and Robust NLI Models](https://mlsanity.com/paper/2205.11432/) (2022)
- [Weakly Supervised Explainable Phrasal Reasoning with Neural Fuzzy Logic](https://mlsanity.com/paper/2109.08927/) (2021)
- [Neuro-symbolic Natural Logic with Introspective Revision for Natural Language Inference](https://mlsanity.com/paper/2203.04857/) (2022)
- [QA-NatVer: Question Answering for Natural Logic-based Fact Verification](https://mlsanity.com/paper/2310.14198/) (2023)
- [NatLogAttack: A Framework for Attacking Natural Language Inference Models with Natural Logic](https://mlsanity.com/paper/2307.02849/) (2023)
- [Modeling Low-Resource Health Coaching Dialogues via Neuro-Symbolic Goal Summarization and Text-Units-Text Generation](https://mlsanity.com/paper/2404.10268/) (2024)
- [Neuro-Symbolic Contrastive Learning for Cross-domain Inference](https://mlsanity.com/paper/2502.09213/) (2025)
- [Learning Proposition-Level Links from Sentence-Level Supervision for Neuro-Symbolic NLI](https://mlsanity.com/paper/2610.15158/) (2026)

## Abstract (arXiv)

We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector representations and neural components. The proposed model adapts module networks to model natural logic operations, which is enhanced with a memory component to model contextual information. Experiments show that the proposed framework can effectively model monotonicity-based reasoning, compared to the baseline neural network models without built-in inductive bias for monotonicity-based reasoning. Our proposed model shows to be robust when transferred from upward to downward inference. We perform further analyses on the performance of the proposed model on aggregation, showing the effectiveness of the proposed subcomponents on helping achieve better intermediate aggregation performance.