When is Ontology-Mediated Querying Efficient?

Barceló, Pablo; Feier, Cristina; Lutz, Carsten; Pieris, Andréas

doi:10.1109/lics.2019.8785823

Cited by 9 publications

(32 citation statements)

References 29 publications

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“…Here, OMQ evaluation is in FPT (assuming FPT W [1]) if and only if for some k ≥ 1, every OMQ in the class is equivalent to an OMQ of treewidth k, i.e., an OMQ such that the UCQ in it is of treewidth k. Note that the equivalence is now on the level of OMQs rather than on the level of UCQs. The same work [7] precisely characterizes the (recursively enumerable) classes of OMQs from (ELH ⊥ , UCQ), where ELH ⊥ is a key fragment of ELH I ⊥ that underpins the OWL 2 EL profile of the OWL 2 recommendation [32]. Here, evaluation is in PTime (again assuming FPT W [1]) if and only if for some k ≥ 1, every OMQ in the class is equivalent to an OMQ of treewidth k. This also shows that PTime and FPT coincide for evaluating classes of OMQs from (ELH ⊥ , UCQ).…”

Section: Introductionmentioning

confidence: 81%

“…The formal definition of Q a k can be found in the appendix. It is signficantly more involved than in the case of description logics [7] because there the chase only generates structures of treewidth one. Proposition 5.2.…”

Section: The Guarded Casementioning

confidence: 99%

“…Efficiency characterizations in the same spirit have been recently obtained for OMQ languages based on description logics (DLs). In particular, [7] precisely characterizes the (recursively enumerable) classes of OMQs from (ELH I ⊥ , UCQ), where ELH I ⊥ is an important DL, essentially a fragment of guarded TGDs. Here, OMQ evaluation is in FPT (assuming FPT W [1]) if and only if for some k ≥ 1, every OMQ in the class is equivalent to an OMQ of treewidth k, i.e., an OMQ such that the UCQ in it is of treewidth k. Note that the equivalence is now on the level of OMQs rather than on the level of UCQs.…”

Section: Introductionmentioning

confidence: 99%

“…(2) For a recursively enumerable class of CQSs from (G, UCQ) over a schema of bounded arity, evaluation is in PTime if and only if evaluation is in FPT if and only if there is k ≥ 1 such that each CQS in the class is equivalent to one from (G, UCQ k ) (Theorem 5. 7). It is not surprising that characterization (1) talks only about FPT and not PTime complexity since we know from [14] that the ExpTime-hardness of OMQ evaluation in (G, UCQ) in the case of schemas of bounded arity holds even if the actual query is an atomic query of the simplest form, i.e., a propositional atom.…”

Section: Introductionmentioning

confidence: 99%

“…For (1), the fact that the ontology can introduce additional relations beyond the data signature causes serious challenges. Moreover, unlike the characterizations of [7] for OMQs based on DLs, where only unary and binary relations are used, we need to deal with relations of arity beyond two, which also causes additional non-trivial complications that require novel ideas and techniques. For ( 3), unlike Grohe, we are more constrained in defining the right database as it must satisfy the given set of constraints.…”

Section: Introductionmentioning

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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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: Introductionmentioning

confidence: 81%

Section: The Guarded Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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Temporal Ontology-Mediated Queries and First-Order Rewritability: A Short Course

Ryzhikov

Wałęga

Zakharyaschev

2020

Lecture Notes in Computer Science

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We discuss recent attempts to extend the ontology-based data access (aka virtual knowledge graph) paradigm to the temporal setting. Our main aim is to understand when answering temporal ontologymediated queries can be reduced to evaluating standard first-order queries over timestamped data and what numeric predicates and operators are required in such reductions. We consider two ways of introducing a temporal dimension in ontologies and queries: using linear temporal logic LTL over discrete time and using metric temporal logic MTL over dense time.

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Semantic Optimization of Conjunctive Queries

Barceló

Figueira

Gottlob

et al. 2020

J. ACM

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This work deals with the problem of semantic optimization of the central class of conjunctive queries (CQs). Since CQ evaluation is NP-complete, a long line of research has focussed on identifying fragments of CQs that can be efficiently evaluated. One of the most general such restrictions corresponds to generalized hypetreewidth bounded by a fixed constant k ≥ 1; the associated fragment is denoted GHW k. A CQ is semantically in GHW k if it is equivalent to a CQ in GHW k. The problem of checking whether a CQ is semantically in GHW k has been studied in the constraint-free case, and it has been shown to be NP-complete. However, in case the database is subject to constraints such as tuple-generating dependencies (TGDs) that can express, e.g., inclusion dependencies, or equality-generating dependencies (EGDs) that capture, e.g., key dependencies, a CQ may turn out to be semantically in GHW k under the constraints, while not being semantically in GHW k without the constraints. This opens avenues to new query optimization techniques. In this paper, we initiate and develop the theory of semantic optimization of CQs under constraints. More precisely, we study the following natural problem: Given a CQ and a set of constraints, is the query semantically in GHW k , for a fixed k ≥ 1, under the constraints, or, in other words, is the query equivalent to one that belongs to GHW k over all those databases that satisfy the constraints? We show that, contrary to what one might expect, decidability of CQ containment is a necessary but not a sufficient condition for the decidability of the problem in question. In particular, we show that checking whether a CQ is semantically in GHW 1 is undecidable in the presence of full TGDs (i.e., Datalog rules) or EGDs. In view of the above negative results, we focus on the main classes of TGDs for which CQ containment is decidable, and that do not capture the class of full TGDs, i.e., guarded, non-recursive and sticky sets of TGDs, and show that the problem in question is decidable, while its complexity coincides with the complexity of CQ containment. We also consider key dependencies over unary and binary relations, and show that the problem in question is decidable in elementary time. Furthermore, we investigate whether being semantically in GHW k alleviates the cost of query evaluation. Finally, in case a CQ is not semantically in GHW k , we discuss how it can be approximated via a CQ that falls in GHW k in an optimal way. Such approximations might help finding "quick" answers to the input query when exact evaluation is intractable.

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When is Ontology-Mediated Querying Efficient?

Cited by 9 publications

References 29 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

Temporal Ontology-Mediated Queries and First-Order Rewritability: A Short Course

Semantic Optimization of Conjunctive Queries

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