Combining Existential Rules and Description Logics (Extended Version)

TL;DR

This paper explores combining existential rules with description logics to achieve decidable query answering across arbitrary relation arities, introducing new rule classes and conditions for functionality constraints.

Contribution

It introduces a new class of existential rules compatible with description logics, enabling decidable query answering with rich constraints on arbitrary and binary relations.

Findings

Negative results on combining certain decidable languages.

A new class of frontier-one rules compatible with powerful constraints.

Conditions for adding functionality constraints on higher-arity relations.

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 [BLM10, BLMS11]. Query answering is also decidable for description logics [Baa03], 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. GC 2, ALCQIb) while retaining decidable query answering. Further, we provide conditions to add functionality constraints on the higher-arity relations.