# ULLER: A Unified Language for Learning and Reasoning

arXiv: https://arxiv.org/abs/2405.00532 · HTML: https://mlsanity.com/paper/2405.00532/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 58 references that are in the map.
- First posted on arXiv 1 May 2024.

## Builds on (most cited first, 30 of 32)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [DiCE: The Infinitely Differentiable Monte-Carlo Estimator](https://mlsanity.com/paper/1802.05098/) (2018)
- [Adversarially Regularising Neural NLI Models to Integrate Logical Background Knowledge](https://mlsanity.com/paper/1808.08609/) (2018)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [TensorLog: A Differentiable Deductive Database](https://mlsanity.com/paper/1605.06523/) (2016)
- [Neural Markov Logic Networks](https://mlsanity.com/paper/1905.13462/) (2019)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (2020)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [A Boxology of Design Patterns for Hybrid Learning and Reasoning Systems](https://mlsanity.com/paper/1905.12389/) (2019)
- [Logic of Differentiable Logics: Towards a Uniform Semantics of DL](https://mlsanity.com/paper/2303.10650/) (2023)
- [Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trick](https://mlsanity.com/paper/2311.12569/) (2023)
- [Storchastic: A Framework for General Stochastic Automatic Differentiation](https://mlsanity.com/paper/2104.00428/) (2021)
- [Refining neural network predictions using background knowledge](https://mlsanity.com/paper/2206.04976/) (2022)
- [SLASH: Embracing Probabilistic Circuits into Neural Answer Set Programming](https://mlsanity.com/paper/2110.03395/) (2021)
- [Semirings for Probabilistic and Neuro-Symbolic Logic Programming](https://mlsanity.com/paper/2402.13782/) (2024)
- [TAR: Neural Logical Reasoning across TBox and ABox](https://mlsanity.com/paper/2205.14591/) (2022)

## Built on by (most cited first, 9 of 9)

- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (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)
- [DeepLog: A Software Framework for Modular Neurosymbolic AI](https://mlsanity.com/paper/2605.10279/) (2026)
- [A General Framework for Property-Driven Machine Learning](https://mlsanity.com/paper/2505.00466/) (2025)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning](https://mlsanity.com/paper/2606.19279/) (2026)
- [Think-Verify-Revise: Neuro-Symbolic Visual Reasoning with Vision-Language Models and Dynamic Logic Tensor Networks](https://mlsanity.com/paper/2609.05388/) (2026)

## Abstract (arXiv)

The field of neuro-symbolic artificial intelligence (NeSy), which combines learning and reasoning, has recently experienced significant growth. There now are a wide variety of NeSy frameworks, each with its own specific language for expressing background knowledge and how to relate it to neural networks. This heterogeneity hinders accessibility for newcomers and makes comparing different NeSy frameworks challenging. We propose a unified language for NeSy, which we call ULLER, a Unified Language for LEarning and Reasoning. ULLER encompasses a wide variety of settings, while ensuring that knowledge described in it can be used in existing NeSy systems. ULLER has a neuro-symbolic first-order syntax for which we provide example semantics including classical, fuzzy, and probabilistic logics. We believe ULLER is a first step towards making NeSy research more accessible and comparable, paving the way for libraries that streamline training and evaluation across a multitude of semantics, knowledge bases, and NeSy systems.