# Integrating Learning and Reasoning with Deep Logic Models

arXiv: https://arxiv.org/abs/1901.04195 · HTML: https://mlsanity.com/paper/1901.04195/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2019.

## Built on by (most cited first, 21 of 21)

- [ChemCrow: Augmenting large-language models with chemistry tools](https://mlsanity.com/paper/2304.05376/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2308.12595/) (2023)
- [Greybox XAI: a Neural-Symbolic learning framework to produce interpretable predictions for image classification](https://mlsanity.com/paper/2209.14974/) (2022)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Understanding the Logic of Direct Preference Alignment through Logic](https://mlsanity.com/paper/2412.17696/) (2024)
- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [DeepPSL: End-to-end perception and reasoning](https://mlsanity.com/paper/2109.13662/) (2021)
- [Knowledge-enhanced Neural Machine Reasoning: A Review](https://mlsanity.com/paper/2302.02093/) (2023)
- [Improving Neural-based Classification with Logical Background Knowledge](https://mlsanity.com/paper/2402.13019/) (2024)
- [DANA: Domain-Aware Neurosymbolic Agents for Consistency and Accuracy](https://mlsanity.com/paper/2410.02823/) (2024)
- [Logic Rules Meet Deep Learning: A Novel Approach for Ship Type Classification](https://mlsanity.com/paper/2111.01042/) (2021)
- [sLTN: Structural Logic Tensor Networks](https://mlsanity.com/paper/2608.11136/) (2026)
- [NUTS, NARS, and Speech](https://mlsanity.com/paper/2405.17874/) (2024)
- [Neurosymbolic Deep Learning Semantics](https://mlsanity.com/paper/2511.02825/) (2025)
- [Is Code Better Than Language for Algorithmic Reasoning](https://mlsanity.com/paper/2606.15589/) (2026)

## Abstract (arXiv)

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learning and logic reasoning is still an open-research problem and it is considered to be the key for the development of real intelligent agents. This paper presents Deep Logic Models, which are deep graphical models integrating deep learning and logic reasoning both for learning and inference. Deep Logic Models create an end-to-end differentiable architecture, where deep learners are embedded into a network implementing a continuous relaxation of the logic knowledge. The learning process allows to jointly learn the weights of the deep learners and the meta-parameters controlling the high-level reasoning. The experimental results show that the proposed methodology overtakes the limitations of the other approaches that have been proposed to bridge deep learning and reasoning.