# Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)

arXiv: https://arxiv.org/abs/1706.03207 · HTML: https://mlsanity.com/paper/1706.03207/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings](https://mlsanity.com/paper/2407.11821/) (2024)
- [Scalable Uncertainty Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2605.16568/) (2026)

## Abstract (arXiv)

We present a probabilistic extension of the description logic ALC for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical consequences of these proportions. After introducing some general reasoning problems and analyzing their properties, we present first algorithms and complexity results for reasoning in some fragments of Statistical ALC.