On Finite and Unrestricted Query Entailment beyond SQ with Number Restrictions on Transitive Roles

Abstract

We study the description logic SQ with number restrictions applicable to transitive roles, extended with either nominals or inverse roles. We show tight 2EXPTIME upper bounds for unrestricted entailment of regular path queries for both extensions and finite entailment of positive existential queries for nominals. For inverses, we establish 2EXPTIME-completeness for unrestricted and finite entailment of instance queries (the latter under restriction to a single, transitive role).

Finite Controllability for Ontology-Mediated Query Answering of CRPQ

“…Without transitivity, Rudolph (2016) shows that FOMQA for 2RPQ under ALCOIF is undecidable. Gogacz et al (2019) have studied a related problem, the finite query entailment for positive existential queries under SQ ontologies, possibly extended with nominals (O) and inverse roles (I).…”

“…Finitely controllability was later studied in (Bárány, Gottlob, and Otto 2014), generalising Rosati's finite chase to show finite controllability of ontologies in guarded firstorder and UCQs. For Datalog ± , finite controllability holds for several fragments (Gogacz and Marcinkowski 2013;Amendola, Leone, and Manna 2018;Baget et al 2011a; Gottlob, Manna, and Pieris 2018; Civili and Rosati 2012).…”

On Finite Entailment of Non-Local Queries in Description Logics

“…Prior work on finite entailment in DLs has focused on local queries, UCQs in particular (Rosati 2008;Ibáñez-García, Lutz, and Schneider 2014;Amarilli and Benedikt 2015;Gogacz, Ibáñez-García, and Murlak 2018;Danielski and Kieronski 2019;Gogacz et al 2019). The single work studying extensions of UCQs (Rudolph 2016), brings only undecidability results for navigational queries and various expressive DLs.…”

“…The single work studying extensions of UCQs (Rudolph 2016), brings only undecidability results for navigational queries and various expressive DLs. In contrast, for unrestricted entailment a large body of literature is available, providing multiple positive results for navigational queries and both expressive and lightweight DLs (Calvanese, Eiter, and Ortiz 2014;Stefanoni et al 2014;Bienvenu, Ortiz, and Simkus 2015;Jung et al 2017;Gutiérrez-Basulto, Ibáñez-García, and Jung 2018;Gogacz et al 2019;Bednarczyk and Rudolph 2019). The lack of research on finite entailment of non-local queries (e.g.…”

“…While there are positive results on finite entailment in expressive DLs related to ALCOI + or ALCOQ + , they all concern local queries. For example, the 2EXPTIME algorithms for finite entailment of UCQs in SOI, SIF, and SOQ (Gogacz, Ibáñez-García, and Murlak 2018;Gogacz et al 2019) are considerably easier to obtain owing to the relatively simple structure of transitive roles. For the more expressive SHOIF, the problem is undecidable (Rudolph 2016).…”