---
title: "Reasoning with Concrete Domains"
authors:
  - "Carsten Lutz"
doi: ""
url: "https://ijcai.org/proceedings/1999/14"
pdf: "https://ijcai.org/proceedings/1999/0014.pdf"
venue: "Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence"
year: 1999
pages: "90-94"
track: "Automated Reasoning"
keywords:
---

# Reasoning with Concrete Domains

Carsten Lutz

*Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence*, pages 90-94.

## Abstract

Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building real-world applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms.