# Description Logics with Abstraction and Refinement

arXiv: https://arxiv.org/abs/2306.03717 · HTML: https://mlsanity.com/paper/2306.03717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 69 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 5 of 5)

- [Ontology-based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP](https://mlsanity.com/paper/1301.6479/) (2013)
- [A Single-Exponential Time 2-Approximation Algorithm for Treewidth](https://mlsanity.com/paper/2104.07463/) (2021)
- [An Experimental Study of the Treewidth of Real-World Graph Data (Extended Version)](https://mlsanity.com/paper/1901.06862/) (2019)
- [Unary negation](https://mlsanity.com/paper/1309.2069/) (2013)
- [How to Approximate Ontology-Mediated Queries](https://mlsanity.com/paper/2107.05369/) (2021)

## Abstract (arXiv)

Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens and which provides explicit operators for the abstraction and refinement of concepts and roles across multiple abstraction levels, based on conjunctive queries. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable. We also pinpoint the precise complexity of our logics and several relevant fragments.