Abstract. This article is firstly an introduction into query languages for the Semantic Web, secondly an in-depth comparison of the languages introduced. Only RDF query languages are considered because, as of the writing of this paper, query languages for other Semantic Web data modeling formalisms, especially OWL, are still an open research issue, and only a very small number of, furthermore incomplete, proposals for querying Semantic Web data modeled after other formalisms than RDF exist. The limitation to a few RDF query languages is motivated both by the objective of an in-depth comparison of the languages addressed and by space limitations. During the three years before the writing of this article, more than three dozen proposals for RDF query languages have been published! Not only such a large number, but also the often immature nature of the proposals makes the focus on few, but representative languages a necessary condition for a non-trivial comparison.For this article, the following RDF query languages have been, admittedly subjectively, selected: Firstly, the "relational" or "pattern-based" query languages SPARQL, RQL, TRIPLE, and Xcerpt; secondly the reactive rule query language Algae; thirdly and last the "navigational access" query language Versa. Although subjective, this choice is arguably a good coverage of the diverse language paradigms considered for querying RDF data. It is the authors' hope and expectation, that this comparison will motivate and trigger further similar studies, thus completing the present article and overcoming its limitation.

This survey article introduces into the essential concepts and methods underlying rule-based query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundation-oriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the "Rule Interchange Framework (RIF)" currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in F-Logic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed.

N -ary conjunctive queries, i.e., queries with any number of answer variables, are the formal core of many Web query languages including XSLT, XQuery, SPARQL, and Xcerpt. Despite a considerable body of research on the optimization of such queries over tree-shaped XML data, little attention has been paid so far to efficient access to graph-shaped XML, RDF, or Topic Maps. We propose the first evaluation technique for n-ary conjunctive queries that applies to both tree-and graph-shaped data and retains the same complexity as the best known approaches that are restricted to tree-shaped data only. Furthermore, the approach treats tree and graph-shaped queries uniformly without sacrificing evaluation complexity on the restricted query class. The core of the evaluation technique is based on dynamic programming using a memoization data structure, called "memoization matrix". It can be populated and consumed in different ways. For each of population and consumption, we propose two resp. three algorithms each having their own advantages. The complexity of the algorithms is compared analytically and experimentally.

Abstract. RPL (pronounced "ripple") is the most expressive path language for navigating in RDF graphs proposed to date that can still be evaluated with polynomial combined complexity. RPL is a lean language well-suited for integration into RDF rule languages. This integration enables a limited form of recursion for traversing RDF paths of unknown length at almost no additional cost over conjunctive triple patterns. We demonstrate the power, ease, and efficiency of RPL with two applications on top of the RPL Web interface. The demonstrator implements RPL by transformation to extended nested regular expressions (NREs). For these extended NREs we have implemented an evaluation algorithm with polynomial data complexity. To the best of our knowledge, this demo is the first implementation of NREs (or similarly expressive RDF path languages) with this complexity. MotivationWith the promise of exciting "new kinds of usage scenarios", you finally got your boss at company C to embrace linked data and connect your community forum and contact database to other online communities and FOAF profiles of your contacts. Your boss now wants to put that technology to use: "I want to cooperate with X on topic Y ! Can you get me the name of any person that works at X and that's connected to us via people that are also interested in Y (so that they have an interest in connecting us). Oh, and none of the intermediates should be our competitor Z."Though the linked data movement and related initiatives like FOAF or SIOC provide specifically for this kind of scenario, most current analysis and query tools for RDF are not up to this task: SPARQL can only compute persons connected via fixed length paths due to the lack of any form of recursion. Under an (e.g., OWL-based) entailment regime that treats foaf:knows (the FOAF property used to build social networks) as a transitive property, SPARQL can compute all connected persons, but can not ensure that all intermediate persons share the same interest. The recent extension of SPARQL with property paths (to be incorporated into SPARQL 1.1) also fails at this task, as it only allows local restrictions on the traversed edges, but not on the traversed nodes, and no repetition ( * ) over paths with restrictions on nodes and edges.

SPARQL has become the gold-standard for RDF query languages. Nevertheless, we believe there is further room for improving RDF query languages. In this chapter, we investigate the addition of rules and quantifier alternation to SPARQL. That extension, called SPARQLog, extends previous RDF query languages by arbitrary quantifier alternation: blank nodes may occur in the scope of all, some, or none of the universal variables of a rule. In addition SPARQLog is aware of important RDF features such as the distinction between blank nodes, literals and IRIs or the RDFS vocabulary. The semantics of SPARQLog is closed (every answer is an RDF graph), but lifts RDF's restrictions on literal and blank node occurrences for intermediary data. We show how to define a sound and complete operational semantics that can be implemented using existing logic programming techniques. While SPARQLog is Turing complete, we identify a decidable (in fact, polynomial time) fragment SwARQLog ensuring polynomial data-complexity inspired from the notion of super-weak acyclicity in data exchange. Furthermore, we prove that SPARQLog with no universal quantifiers in the scope of existential ones (∀∃ fragment) is equivalent to full SPARQLog in presence of graph projection. Thus, the convenience of arbitrary quantifier alternation comes, in fact, for free. These results, though here presented in the context of RDF querying, apply similarly also in the more general setting of data exchange.