Containment for Rule-Based Ontology-Mediated Queries

Barceló, Pablo; Berger, Gérald; Pieris, Andréas

doi:10.1145/3196959.3196963

Cited by 6 publications

(35 citation statements)

References 57 publications

(116 reference statements)

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“…Note that Proposition 5.2 also provides an approach to deciding UCQ k -equivalence, and thus to establishing Theorem 5.1: compute the UCQ k -approximation Q a k of Q and accept if Q ⊆ Q a k (note that Q a k ⊆ Q holds always); otherwise, reject. We can show that Q a k can be computed in double exponential time and it is known that OMQ containment for (G, UCQ) can be decided in double exponential time [6]. A naive use of these observations yields only a 4ExpTime upper bound, but we show in the appendix how to improve this to 2ExpTime.…”

Section: The Guarded Casementioning

confidence: 90%

“…Containment between OMQs from (G, UCQ) can be decided in 2ExpTime [6]. Since, however, q a k may consists of double exponentially many CQs, it is not clear how to implement step (2) above in 2ExpTime and how to obtain the 2ExpTime upper bound in Theorem 5.1 by a direct implementation of the above procedure.…”

Section: B Proof Of Theorem 51mentioning

confidence: 99%

“…that is equivalent to Q a k , and such that q ′ k contains only single exponentially many CQs, each of polynomial size. And second, we modify the containment check from [6] in a mild way.…”

Section: B Proof Of Theorem 51mentioning

confidence: 99%

“…The non-trivial task is to check whether Q ⊆ Q ′ k . We know from [6] that checking containment among OMQs from (G, UCQ) is in 2ExpTime. In fact, [6] first provides a polynomial time reduction from containment among OMQs from (G, UCQ), denoted Cont(G, UCQ), to containment among OMQs from (G, CQ), denoted Cont(G, CQ), and then devises an automata-based procedure for Cont(G, CQ) that runs in double exponential time in the combined size of the OMQs.…”

Section: B2 Checking Equivalencementioning

confidence: 99%

See 3 more Smart Citations

The Limits of Efficiency for Open- and Closed-World Query Evaluation Under Guarded TGDs

Barceló¹,

Dalmau

Feier

et al. 2020

Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Ontology-mediated querying and querying in the presence of constraints are two key database problems where tuple-generating dependencies (TGDs) play a central role. In ontology-mediated querying, TGDs can formalize the ontology and thus derive additional facts from the given data, while in querying in the presence of constraints, they restrict the set of admissible databases. In this work, we study the limits of efficient query evaluation in the context of the above two problems, focussing on guarded and frontier-guarded TGDs and on UCQs as the actual queries. We show that a class of ontology-mediated queries (OMQs) based on guarded TGDs can be evaluated in FPT iff the OMQs in the class are equivalent to OMQs in which the actual query has bounded treewidth, up to some reasonable assumptions. For querying in the presence of constraints, we consider classes of constraint-query specifications (CQSs) that bundle a set of constraints with an actual query. We show a dichotomy result for CQSs based on guarded TGDs that parallels the one for OMQs except that, additionally, FPT coincides with PTime combined complexity. The proof is based on a novel connection between OMQ and CQS evaluation. Using a direct proof, we also show a similar dichotomy result, again up to some reasonable assumptions, for CQSs based on frontier-guarded TGDs with a bounded number of atoms in TGD heads. Our results on CQSs can be viewed as extensions of Grohe's well-known characterization of the tractable classes of CQs (without constraints). Like Grohe's characterization, all the above results assume that the arity of relation symbols is bounded by a constant. We also study the associated meta problems, i.e., whether a given OMQ or CQS is equivalent to one in which the actual query has bounded treewidth.

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Section: The Guarded Casementioning

confidence: 90%

Section: B Proof Of Theorem 51mentioning

confidence: 99%

Section: B Proof Of Theorem 51mentioning

confidence: 99%

Section: B2 Checking Equivalencementioning

confidence: 99%

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The Limits of Efficiency for Open- and Closed-World Query Evaluation Under Guarded TGDs

Barceló¹,

Dalmau

Feier

et al. 2020

Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…One of the most important tools in ontology-mediated querying is query rewriting: reformulate a given ontology-mediated query (OMQ) in an equivalencepreserving way in a query language that is supported by a database system used to store the data. Since SQL is the dominating query language in conventional database systems, rewriting into SQL and into first-order logic (FO) as its logical core has attracted particularly much attention [3,4,5,6,7,10,12,15]. In fact, the DL-Lite family of description logics (DLs) was invented specifically with the aim to guarantee that FO-rewritings of OMQs (whose ontology is formulated in DL-Lite) always exist [1,7], but is rather restricted in expressive power.…”

Section: Introductionmentioning

confidence: 99%

The Semantic Web – ISWC 2017

2017

Lecture Notes in Computer Science

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A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the description logic EL and the actual query is a conjunctive query and show that rewritings of such OMQs can be efficiently computed in practice, in a sound and complete way. Our approach combines a reduction with a decomposed backwards chaining algorithm for OMQs that are based on the simpler atomic queries, also illuminating the relationship between first-order rewritings of OMQs based on conjunctive and on atomic queries. Experiments with real-world ontologies show promising results. ⋆ This is a pre-print of an article published in ISWC2018. The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-68288-4 21 natural in the context of backwards chaining and satisfied by the decomposed algorithm.We then move to rooted CQs (rCQs) in which every quantified variable must be reachable from some answer variable (in an undirected sense, in the query graph). We consider this a mild restriction and expect that almost all queries in practical applications will be rCQs. In the rCQ case, we do not achieve a 'black box' reduction. Instead, we assume that FO-rewritings of the constructed OMQs from (EL, AQ) are obtained from a certain straightforward backwards chaining algorithm or a refinement thereof as implemented in the Grind system. We then show how to combine the construction of (several) OMQs from (EL, AQ), similar to those constructed in the tqCQ case, with a modification of the assumed algorithm to decide FO-rewritability in (EL, rCQ) and to construct actual rewritings. The approach involves exponential blowups, but only in parameters that we expect to be very small in practical cases and that, in particular, only depend on the actual query contained in the OMQ but not on the ontology.We have implemented our approach in the Grind system and carried out experiments on five real-world ontologies with 10 hand-crafted CQs for each. The average runtimes are between 0.5 and 19 seconds (depending on the ontology), which we consider very reasonable given that we are dealing with a complex static analysis problem.Proofs are deferred to the appendix, which is made available at http://www.cs.uni-bremen.de/tdki/research/ Related Work. We directly build on our prior work in [12] as discussed above, and to a lesser degree also on [5,6]. The latter line of work has recently been picked up in the context of existential rules [3]. The distinguishing features of our work are that (1) our algorithms are sound, complete, and terminating, that is, they find an FO-rewriting if there is one and report failure otherwise, and (2) we rely on the decomposed calculus from [12] that implements structure sharing for constructing small rewritings and achieving practical feasibility. We are not aware of other work that combines features (1) and (2) and is applicable to OMQs based on EL....

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Guarded Ontology-Mediated Queries

Barceló

Berger

Gottlob

et al. 2021

Hajnal Andréka and István Németi on Unity of Science

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We concentrate on ontology-mediated queries (OMQs) expressed using guarded Datalog ∃ and conjunctive queries. Guarded Datalog ∃ is a rule-based knowledge representation formalism inspired by the guarded fragment of first-order logic, while conjunctive queries represent a prominent database query language that lies at the core of relational calculus (i.e., first-order queries). For such guarded OMQs we discuss three main algorithmic tasks: query evaluation, query containment, and first-order rewritability. The first one is the task of computing the answer to an OMQ over an input database. The second one is the task of checking whether the answer to an OMQ is contained in the answer of some other OMQ on every input database. The third one asks whether an OMQ can be equivalently rewritten as a first-order query. For query evaluation, we explain how classical results on the satisfiability problem for the guarded fragment of first-order logic can be applied. For query containment, we discuss how tree automata techniques can be used. Finally, for first-order rewritability, we explain how techniques based on a more sophisticated automata model, known as cost automata, can be exploited.

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Containment for Rule-Based Ontology-Mediated Queries

Cited by 6 publications

References 57 publications

The Limits of Efficiency for Open- and Closed-World Query Evaluation Under Guarded TGDs

The Limits of Efficiency for Open- and Closed-World Query Evaluation Under Guarded TGDs

The Semantic Web – ISWC 2017

Guarded Ontology-Mediated Queries

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