# Fuzzy Datalog^exists over Arbitrary t-Norms

arXiv: https://arxiv.org/abs/2403.02933 · HTML: https://mlsanity.com/paper/2403.02933/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 7 of 7)

- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Anatomy of the chase](https://mlsanity.com/paper/1303.6682/) (2013)
- [The Space-Efficient Core of Vadalog](https://mlsanity.com/paper/1809.05951/) (2018)
- [From Shallow to Deep Interactions Between Knowledge Representation, Reasoning and Machine Learning (Kay R. Amel group)](https://mlsanity.com/paper/1912.06612/) (2019)
- [Generative Datalog with Stable Negation](https://mlsanity.com/paper/2206.12247/) (2022)

## Built on by (most cited first, 1 of 1)

- [Applying Answer Set Programming with Fuzzy Membership Functions: a Case Study](https://mlsanity.com/paper/2607.03550/) (2026)

## Abstract (arXiv)

One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential rules (commonly referred to as tuple-generating dependencies) to the fuzzy setting, by allowing for arbitrary t-norms in the place of classical conjunctions in rule bodies. The resulting formalism allows us to perform reasoning about data associated with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for the standard Datalog setting. In particular, we provide fuzzy extensions of Datalog chases which produce fuzzy universal models and we exploit them to show that in important fragments of the language, reasoning has the same complexity as in the classical setting.