# Quantified Markov Logic Networks

arXiv: https://arxiv.org/abs/1807.01183 · HTML: https://mlsanity.com/paper/1807.01183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2018.

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

- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)

## Abstract (arXiv)

Markov Logic Networks (MLNs) are well-suited for expressing statistics such as "with high probability a smoker knows another smoker" but not for expressing statements such as "there is a smoker who knows most other smokers", which is necessary for modeling, e.g. influencers in social networks. To overcome this shortcoming, we study quantified MLNs which generalize MLNs by introducing statistical universal quantifiers, allowing to express also the latter type of statistics in a principled way. Our main technical contribution is to show that the standard reasoning tasks in quantified MLNs, maximum a posteriori and marginal inference, can be reduced to their respective MLN counterparts in polynomial time.