# Statistical relational learning and neuro-symbolic AI: what does first-order logic offer?

arXiv: https://arxiv.org/abs/2306.13660 · HTML: https://mlsanity.com/paper/2306.13660/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 10 of 10)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Analyzing Differentiable Fuzzy Implications](https://mlsanity.com/paper/2006.03472/) (2020)
- [Explanations for Occluded Images](https://mlsanity.com/paper/2103.03622/) (2021)
- [Challenges of Human-Aware AI Systems](https://mlsanity.com/paper/1910.07089/) (2019)
- [Learning Chordal Markov Networks by Constraint Satisfaction](https://mlsanity.com/paper/1310.0927/) (2013)
- [Implicitly Learning to Reason in First-Order Logic](https://mlsanity.com/paper/1906.10106/) (2019)

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

- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)

## Abstract (arXiv)

In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for machine learning researchers unaware of why the research community cares about relational representations, this article can serve as a gentle introduction. Second, for logical experts who are newcomers to the learning area, such an article can help in navigating the differences between finite vs infinite, and subjective probabilities vs random-world semantics. Finally, for researchers from statistical relational learning and neuro-symbolic AI, who are usually embedded in finite worlds with subjective probabilities, appreciating what infinite domains and random-world semantics brings to the table is of utmost theoretical import.