Combining Existential Rules and Description Logics

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; 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 aritytwo relations (e. g. GC2, ALCQIb) while retaining decidable query answering. Further, we provide conditions to add functionality constraints on the higher-arity relations.

Authors

• Antoine Amarilli
• Michael Benedikt

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