Capturing Homomorphism-Closed Decidable Queries with Existential Rules

Camille Bourgaux (1) , David Carral (2, 3, 4, 5, 6) , Markus Krötzsch (7) , Sebastian Rudolph (7) , Michaël Thomazo (1)

1 VALDA - Value from Data
2 GRAPHIK - Graphs for Inferences on Knowledge
3 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
4 CRISAM - Inria Sophia Antipolis - Méditerranée
5 UM - Université de Montpellier
6 CNRS - Centre National de la Recherche Scientifique
7 TU Dresden - Technische Universität Dresden = Dresden University of Technology

Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.

Domaines: Informatique [cs]; Base de données [cs.DB]; Logique en informatique [cs.LO]

Camille Bourgaux, David Carral, Markus Krötzsch, Sebastian Rudolph, Michaël Thomazo. Capturing Homomorphism-Closed Decidable Queries with Existential Rules. KR 2021 - 18th International Conference on Principles of Knowledge Representation and Reasoning, Nov 2021, Virtual, Vietnam. pp.141-150, ⟨10.24963/kr.2021/14⟩. ⟨lirmm-03345614⟩