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Register a new userNested Regular Path Queries in Description Logics
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Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Two-way regular path queries (2RPQs) have received increased attention recently due to their ability to relate pairs of objects by flexibly navigating graph-structured data. They are present in property paths in SPARQL 1.1, the new standard RDF query language, and in the XML query language XPath. In line with XPath, we consider the extension of 2RPQs with nesting, which allows one to require that objects along a path satisfy complex conditions, in turn expressed through (nested) 2RPQs. We study the computational complexity of answering nested 2RPQs and conjunctions thereof (CN2RPQs) in the presence of domain knowledge expressed in description logics (DLs). We establish tight complexity bounds in data and combined complexity for a variety of DLs, ranging from lightweight DLs (DL-Lite, EL) up to highly expressive ones. Interestingly, we are able to show that adding nesting to (C)2RPQs does not affect worst-case data complexity of query answering for any of the considered DLs. However, in the case of lightweight DLs, adding nesting to 2RPQs leads to a surprising jump in combined complexity, from P-complete to Exp-complete.
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We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NEXPTIME-completeness and extend this result to monadic disjunctive Datalog and to OMQs.
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a within modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.
In the last decade, substantial progress has been made towards standardizing the syntax of graph query languages, and towards understanding their semantics and complexity of evaluation. In this paper, we consider temporal property graphs (TPGs) and propose temporal regular path queries (TRPQ) that incorporate time into TPGs navigation. Starting with design principles, we propose a natural syntactic extension of the MATCH clause of popular graph query languages. We then formally present the semantics of TRPQs, and study the complexity of their evaluation. We show that TRPQs can be evaluated in polynomial time if TPGs are time-stamped with time points. We also identify fragments of the TRPQ language that admit efficient evaluation over a more succinct interval-annotated representation. Our work on the syntax, and the positive complexity results, pave the way to implementations of TRPQs that are both usable and practical.
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.
The Shapes Constraint Language (SHACL) allows for formalizing constraints over RDF data graphs. A shape groups a set of constraints that may be fulfilled by nodes in the RDF graph. We investigate the problem of containment between SHACL shapes. One shape is contained in a second shape if every graph node meeting the constraints of the first shape also meets the constraints of the second. To decide shape containment, we map SHACL shape graphs into description logic axioms such that shape containment can be answered by description logic reasoning. We identify several, increasingly tight syntactic restrictions of SHACL for which this approach becomes sound and complete.
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