---
title: "Combining Existential Rules and Description Logics"
authors:
  - "Antoine Amarilli"
  - "Michael Benedikt"
doi: ""
url: "https://ijcai.org/proceedings/2015/381"
pdf: "https://ijcai.org/proceedings/2015/0381.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "2691-2696"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# Combining Existential Rules and Description Logics

Antoine Amarilli, Michael Benedikt

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 2691-2696.

## Abstract

Query answering under existential rules — implications with existential quantifiers in the head — is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [Baget et al., 2010; Baget et al., 2011a]. Query answering is also decidable for description logics [Baader, 2003], which further allow disjunction and functionality constraints (assert that certain relations are functions); however, they are focused on ER-type schemas, where relations have arity two. This work investigates how to get the best of both worlds: having decidable existential rules on arbitrary arity relations, while allowing rich description logics, including functionality constraints, on arity-two relations. We first show negative results on combining such decidable languages. Second, we introduce an expressive set of existential rules (frontier-one rules with a certain restriction) which can be combined with powerful constraints on arity-two relations (e.g. GC2, ALCQIb) while retaining decidable query answering. Further, we provide conditions to add functionality constraints on the higher-arity relations.