# Convergence Laws for Extensions of First-Order Logic with Averaging

arXiv: https://arxiv.org/abs/2504.14270 · HTML: https://mlsanity.com/paper/2504.14270/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2025.

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

- [Domain size asymptotics for Markov logic networks](https://mlsanity.com/paper/2509.04192/) (2025)

## Abstract (arXiv)

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of first-order sentences converge to 0 or 1. In other cases, such as certain ``sparse random graph'' models, the probabilities of sentences converge, although not necessarily to 0 or 1. In this work we deal with extensions of first-order logic with aggregate operators, variations of averaging. These logics will consist of real-valued terms, and we allow arbitrary Lipschitz functions to be used as ``connectives''. We show that some of the well-known convergence laws extend to this setting.