# Geometric Models for (Temporally) Attributed Description Logics

arXiv: https://arxiv.org/abs/2108.12239 · HTML: https://mlsanity.com/paper/2108.12239/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 27 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Embedding Models for Episodic Knowledge Graphs](https://mlsanity.com/paper/1807.00228/) (2018)
- [From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules](https://mlsanity.com/paper/1805.10461/) (2018)
- [Predicting the Co-Evolution of Event and Knowledge Graphs](https://mlsanity.com/paper/1512.06900/) (2015)

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

- [Generalizing to Unseen Elements: A Survey on Knowledge Extrapolation for Knowledge Graphs](https://mlsanity.com/paper/2302.01859/) (2023)
- [Knowledge Base Embeddings: Semantics and Theoretical Properties](https://mlsanity.com/paper/2408.04913/) (2024)
- [BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization](https://mlsanity.com/paper/2605.23937/) (2026)

## Abstract (arXiv)

In the search for knowledge graph embeddings that could capture ontological knowledge, geometric models of existential rules have been recently introduced. It has been shown that convex geometric regions capture the so-called quasi-chained rules. Attributed description logics (DL) have been defined to bridge the gap between DL languages and knowledge graphs, whose facts often come with various kinds of annotations that may need to be taken into account for reasoning. In particular, temporally attributed DLs are enriched by specific attributes whose semantics allows for some temporal reasoning. Considering that geometric models and (temporally) attributed DLs are promising tools designed for knowledge graphs, this paper investigates their compatibility, focusing on the attributed version of a Horn dialect of the DL-Lite family. We first adapt the definition of geometric models to attributed DLs and show that every satisfiable ontology has a convex geometric model. Our second contribution is a study of the impact of temporal attributes. We show that a temporally attributed DL may not have a convex geometric model in general but we can recover geometric satisfiability by imposing some restrictions on the use of the temporal attributes.