# On the uniform one-dimensional fragment

arXiv: https://arxiv.org/abs/1604.01673 · HTML: https://mlsanity.com/paper/1604.01673/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2016.

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

- [Weighted Model Counting in FO2 with Cardinality Constraints and Counting Quantifiers: A Closed Form Formula](https://mlsanity.com/paper/2110.05992/) (2021)

## Abstract (arXiv)

The uniform one-dimensional fragment of first-order logic, U1, is a formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to description logics designed to accommodate higher arity relations, with particular attention given to DLR_reg. We also define a description logic version of a variant of U1 and prove a range of new results concerning the expressivity of U1 and related logics.