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Register a new userFirst Order-Rewritability and Containment of Conjunctive Queries in Horn Description Logics
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Added by
Carsten Lutz
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study FO-rewritability of conjunctive queries in the presence of ontologies formulated in a description logic between EL and Horn-SHIF, along with related query containment problems. Apart from providing characterizations, we establish complexity results ranging from ExpTime via NExpTime to 2ExpTime, pointing out several interesting effects. In particular, FO-rewriting is more complex for conjunctive queries than for atomic queries when inverse roles are present, but not otherwise.
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Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every database, the result of one query is a subset of the result of another query. In this paper, we deal with unions of conjunctive queries, and we address query containment and query answering under Description Logic constraints. Every such constraint is essentially an inclusion dependencies between concepts and relations, and their expressive power is due to the possibility of using complex expressions, e.g., intersection and difference of relations, special forms of quantification, regular expressions over binary relations, in the specification of the dependencies. These types of constraints capture a great variety of data models, including the relational, the entity-relationship, and the object-oriented model, all extended with various forms of constraints, and also the basic features of the ontology languages used in the context of the Semantic Web. We present the following results on both query containment and query answering. We provide a method for query containment under Description Logic constraints, thus showing that the problem is decidable, and analyze its computational complexity. We prove that query containment is undecidable in the case where we allow inequalities in the right-hand side query, even for very simple constraints and queries. We show that query answering under Description Logic constraints can be reduced to query containment, and illustrate how such a reduction provides upper bound results with respect to both combined and data complexity.
We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We also give a tight complexity bound for the related problem of deciding whether a given MMSNP sentence is equivalent to a CSP.
We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.
We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree automata. Although it does not lead to a tight complexity bound, it provides a transparent solution based on widely known tools. The second approach relies on a sophisticated automata model, known as cost automata. This allows us to show that our problem is 2ExpTime-complete. In both approaches, we provide semantic characterizations of FO-rewritability that are of independent interest.
Single-round multiway join algorithms first reshuffle data over many servers and then evaluate the query at hand in a parallel and communication-free way. A key question is whether a given distribution policy for the reshuffle is adequate for computing a given query, also referred to as parallel-correctness. This paper extends the study of the complexity of parallel-correctness and its constituents, parallel-soundness and parallel-completeness, to unions of conjunctive queries with and without negation. As a by-product it is shown that the containment problem for conjunctive queries with negation is coNEXPTIME-complete.
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