On Finite Entailment of Non-Local Queries in Description Logics

Abstract

We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard

Static Analysis of Graph Database Transformations

“…To the best of our knowledge this is the first result on finite containment of C2RPQs in the context of description logics. A related problem of finite entailment has been studied for various logics [27][28][29]31], but while for conjunctive queries the solutions carry over to finite containment, for C(2)RPQs these logics are too weak to allow this. Unrestricted containment of C2RPQs modulo ALCIF TBoxes is known to be in 2EXPTIME [16], but passing from unrestricted to finite structures is typically challenging for such problems.…”

Finite Entailment of Local Queries in the Z Family of Description Logics

“…In the last few years the field of logic-based knowledge representation took a lot of inspiration from database theory. In particular, finite model semantics in description logics (DLs) is reconsidered as a desirable alternative to classical one and query entailment has replaced knowledge base satisfiability checking as the key inference problem (Gogacz et al 2020). Under classical semantics, that is when arbitrary models are admitted, the conjunctive query (CQ) entailment problem for DLs is already quite well understood (Glimm et al 2008).…”

“…On the positive side, the decidability of finite CQ entailment in Horn DLs was shown in (Ibáñez-García, Lutz, and Schneider 2014). Another positive example is the series of papers on CQ entailment for the S family of logics (Gogacz, Ibáñez-García, and Murlak 2018;Gogacz et al 2019;Danielski and Kieronski 2019). On the negative side (Rudolph 2016) proves undecidability of finite querying in SHOIQ.…”