---
title: "Terminological Cycles in a Description Logic with Existential Restrictions"
authors:
  - "Franz Baader"
doi: ""
url: "https://ijcai.org/proceedings/2003/48"
pdf: "https://ijcai.org/proceedings/2003/0048.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "325-329"
track: ""
keywords:
---

# Terminological Cycles in a Description Logic with Existential Restrictions

Franz Baader

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 325-329.

## Abstract

Cyclic definitions in description logics have until now been investigated only for description logics allowing for value restrictions. Even for the most basic language F £ 0 , which allows for conjunction and value restrictions only, deciding subsumption in the presence of terminological cycles is a PSPACE-complete problem. This paper investigates subsumption in the presence of terminological cycles for the language £ C, which allows for conjunction, existential restrictions, and the topconcept. In contrast to the results for F Co, subsumption in £C remains polynomial, independent of whether we use least fixpoint semantics, greatest fix point semantics, or descriptive semantics.