Finite Controllability for Ontology-Mediated Query Answering of CRPQ

Abstract

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

Finite Entailment of UCRPQs over ALC Ontologies

“…Beyond DLs, there have been several works on UCQ-finite controllability: for the guarded fragment of FOL (Bárány, Gottlob, and Otto 2014) or for various fragments of existential rules (Civili and Rosati 2012;Gogacz and Marcinkowski 2013;Baget et al 2011;Amendola, Leone, and Manna 2018;Gottlob, Manna, and Pieris 2018). Closer to our study, is the work by Figueira, Figueira, and Baque (2020) on the classification of finitely and nonfinitely controllable subclasses of CRPQs over ontologies formulated in the guarded-negation fragment of FOL or in the frontier fragment of existential rules. However, no complexity results or algorithms for finite entailment are provided for the non-finitely controllable cases.…”