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

Abstract

In the last few years the field of logic-based knowledge representation took a lot of inspiration from database theory. A vital example is that the finite model semantics in description logics (DLs) is reconsidered as a desirable alternative to the classical one and that query entailment has replaced knowledge-base satisfiability (KBSat) checking as the key inference problem. However, despite the considerable effort, the overall picture concerning finite query answering in DLs is still incomplete. In this work we study the complexity of finite entailment of local queries (conjunctive queries and positive boolean combinations thereof) in the Z family of DLs, one of the most powerful KR formalisms, lying on the verge of decidability. Our main result is that the DLs ZOQ and ZOI are finitely controllable, i.e. that their finite and unrestricted entailment problems for local queries coincide. This allows us to reuse recently established upper bounds on querying these logics under the classical semantics. While we will not solve finite query entailment for the third main logic in the Z family, ZIQ, we provide a generic reduction from the finite entail- ment problem to the finite KBSat problem, working for ZIQ and some of its sublogics. Our proofs unify and solidify previously established results on finite satisfiability and finite query entailment for many known DLs.

How to Tell Easy from Hard: Complexities of Conjunctive Query Entailment in Extensions of ALC

“…This work is a revised version of our existing papers extended with some new results. Section 3 extends the unpublished results from an arXiV note by the first author (Bednarczyk, 2021b). Some results from Section 4 were first presented as part of joint work with F. Baader (2020) published at ECAI'2020; except a few ideas 5 , this material has been completely reworked here.…”

A categorical account of composition methods in logic

“…In general, similar translations can be used for other logic extensions. For example, in [46] a translation is used to obtain description logics using M k . Nevertheless, the above technique applies verbatim to varying translations, operations and logics.…”

Finite Entailment of UCRPQs over ALC Ontologies

“…There have been also a few works on finite controllability in the context of DLs. For instance, Bednarczyk and Kieroński (2022) recently showed that the ZOI and ZOQ members of the Z family are finitely controllable for UCQs. 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).…”

“…In contrast, for the finite OMQE problem, where one is interested in reasoning over finite models only, the overall landscape is rather incomplete. However, in recent years, the study of finite OMQE has been gaining traction, considering both lightweight and expressive DLs and (mostly) unions of conjunctive queries (Rosati 2008;Ibáñez-García, Lutz, and Schneider 2014;Rudolph 2016;Gogacz, Ibáñez-García, and Murlak 2018;Gogacz et al 2019;Danielski and Kieronski 2019;Gogacz et al 2020;Bednarczyk and Kieroński 2022).…”