# Semirings for Probabilistic and Neuro-Symbolic Logic Programming

arXiv: https://arxiv.org/abs/2402.13782 · HTML: https://mlsanity.com/paper/2402.13782/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 88 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Builds on (most cited first, 11 of 11)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Semantic Relational Object Tracking](https://mlsanity.com/paper/1902.09937/) (2019)
- [SMProbLog: Stable Model Semantics in ProbLog and its Applications in Argumentation](https://mlsanity.com/paper/2110.01990/) (2021)
- [Simply Logical -- Intelligent Reasoning by Example (Fully Interactive Online Edition)](https://mlsanity.com/paper/2208.06823/) (2022)
- [Declarative Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2302.10674/) (2023)
- [Forward- or Reverse-Mode Automatic Differentiation: What's the Difference?](https://mlsanity.com/paper/2212.11088/) (2022)
- [Symbolic Learning and Reasoning with Noisy Data for Probabilistic Anchoring](https://mlsanity.com/paper/2002.10373/) (2020)
- [Measure Theoretic Weighted Model Integration](https://mlsanity.com/paper/2103.13901/) (2021)

## Built on by (most cited first, 6 of 6)

- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [On the Hardness of Probabilistic Neurosymbolic Learning](https://mlsanity.com/paper/2406.04472/) (2024)
- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [Neurosymbolic Inference On Foundation Models For Remote Sensing Text-to-image Retrieval With Complex Queries](https://mlsanity.com/paper/2512.14102/) (2025)
- [Pruning Boolean d-DNNF Circuits Through Tseitin-Awareness](https://mlsanity.com/paper/2407.17951/) (2024)
- [A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)](https://mlsanity.com/paper/2507.16067/) (2025)

## Abstract (arXiv)

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference and learning in probabilistic logic programs. While originally PLP focused on discrete probability, more recent approaches have incorporated continuous distributions as well as neural networks, effectively yielding neural-symbolic methods. We provide a unified algebraic perspective on PLP, showing that many if not most of the extensions of PLP can be cast within a common algebraic logic programming framework, in which facts are labeled with elements of a semiring and disjunction and conjunction are replaced by addition and multiplication. This does not only hold for the PLP variations itself but also for the underlying execution mechanism that is based on (algebraic) model counting.