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Relative Expressive Power of Navigational Querying on Graphs
"... Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operato ..."
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Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; transitive closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular, the Hasse diagram for boolean queries contains nontrivial separations and a few surprising collapses.
TriAL for RDF: Adapting Graph Query Languages for RDF Data
"... Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natu ..."
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Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose somefunctionalitywhenused inconjunctionwith graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graphdatabasecontext(e.g., reachability)losetheir natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, ratherthan graphs. Our basiclanguageis called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion, and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by lowdegree polynomials. We compare our languages with relational languages, such as finitevariable logics, and previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide examples of the usefulness of TriAL in querying graph, RDF, and social networks data.
Containment of Data Graph Queries
"... The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and ..."
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The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and there are several fundamental issues regarding graph databases that are not fully understood. Indeed, while graph query languages that concentrate on topological properties are now well developed, not much is known about languages that can query both the topology of graphs and their underlying data. Our goal is to conduct a detailed study of static analysis problems for such languages. In this paper we consider the containment problem for several recently proposed classes of queries that manipulate both topology and data: regular queries with memory, regular queries with data tests, and graph XPath. Our results show that the problem is in general undecidable for all of these classes. However, by allowing only positive data comparisons we find natural fragments that enjoy much better static analysis properties: the containment problem is decidable, and its computational complexity ranges from PSPACEcomplete to EXPSPACEcomplete. We also propose extensions of regular queries with an inverse operator, and study query evaluation and query containment for them.
Beyond graph search: Exploring and exploiting rich connected data sets
 In ICWE’15: Engineering the Web in the Big Data Era, volume 9114 of LNCS
, 2015
"... Abstract. Modern Web data is highly structured in terms of entities and relations from large knowledge resources, geotemporal references and social network structures, resulting in a massive multidimensional graph. This graph essentially unifies both the searcher and the information resources that ..."
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Abstract. Modern Web data is highly structured in terms of entities and relations from large knowledge resources, geotemporal references and social network structures, resulting in a massive multidimensional graph. This graph essentially unifies both the searcher and the information resources that played a fundamentally different role in traditional information retrieval. Graph searchbased systems offer major new ways to access relevant information. Graph search affects both query formulation (complex queries about entities and relations building on the searcher’s context) as well as result exploration and discovery (slicing and dicing the information using the graph structure) in a completely novel way. This new graph based approach introduces great opportunities, but also great challenges, in terms of data quality and data integration, user interface design, and privacy. 1
XPath for DLLite Ontologies
"... Applications of description logics (DLs) such as OWL 2 and ontologybased data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their exte ..."
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Applications of description logics (DLs) such as OWL 2 and ontologybased data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their extensions, little attention has been paid to graph database queries, despite the fact that graph databases share the structure of interpretations with DLs; that is they describe essentially the same objects. In particular, not much is known about the interplay between DLs and XPath. The last is a powerful formalism for querying semistructured data: it is in the core of most practical query languages for XML trees, and it is also gaining popularity in theory and practice of graph databases. In this paper we make a step towards coupling knowledge bases and graph databases by studying how to answer powerful XPathstyle queries over DLLite. We start with adapting the definition of XPath to the DL context, and then proceed to study the complexity of evaluating XPath queries over knowledge bases. Results show that, while query answering is undecidable for the full XPath, by carefully tuning the amount of negation allowed in the queries we can arrive to XPath fragments that have a potential to be used in practical applications.
XPath for DL Ontologies
, 2015
"... Applications of description logics (DLs) such as ontologybased data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their extensions, li ..."
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Applications of description logics (DLs) such as ontologybased data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their extensions, little attention has been paid to graph database queries, despite the fact that graph databases have essentially the same structure as knowledge bases. In particular, not much is known about the interplay between DLs and XPath. The latter is a powerful formalism for querying semistructured data: it is in the core of most practical query languages for XML trees, and it is also gaining popularity in theory and practice of graph databases. In this paper we make a step towards coupling knowledge bases and graph databases by studying how to answer powerful XPathstyle queries over simple DLs like DLLite and EL. We start with adapting the definition of XPath to the DL context, and then proceed to study the complexity of evaluating XPath queries over knowledge bases. Results show that, while query answering is undecidable for the full XPath, by carefully tuning the shape of negation allowed in the queries we can arrive at XPath fragments that have a potential to be used in practice.
The Complexity of Regular Expressions and Property Paths in SPARQL
"... The World Wide Web Consortium (W3C) recently introduced property paths in SPARQL 1.1, a query language for RDF data. Property paths allow SPARQL queries to evaluate regular expressions over graphstructured data. However, they differ from standard regular expressions in several notable aspects. For ..."
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The World Wide Web Consortium (W3C) recently introduced property paths in SPARQL 1.1, a query language for RDF data. Property paths allow SPARQL queries to evaluate regular expressions over graphstructured data. However, they differ from standard regular expressions in several notable aspects. For example, they have a limited form of negation, they have numerical occurrence indicators as syntactic sugar, and their semantics on graphs is defined in a nonstandard manner. We formalize the W3C semantics of property paths and investigate various query evaluation problems on graphs. More specifically, let x and y be two nodes in an edgelabeled graph and r be an expression. We study the complexities of (1) deciding whether there exists a path from x to y that matches r and (2) counting how many paths from x to y match r. Our main results show that, compared to an alternative semantics of regular expressions on graphs, the complexity of (1) and (2) under W3C semantics is significantly higher. Whereas the alternative semantics remains in polynomial time for large fragments of expressions, the W3C semantics makes problems (1) and (2) intractable almost immediately. As a sideresult, we prove that the membership problem for regular expressions with numerical occurrence indicators and negation is in polynomial time.
Logics with rigidly guarded data sets
, 2014
"... The notion of orbit finite data monoid was recently introduced by Bojańczyk as an algebraic object for defining recognizable languages of data words. Following Büchi’s approach, we introduce a variant of monadic secondorder logic with data equality tests that captures precisely the data language ..."
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The notion of orbit finite data monoid was recently introduced by Bojańczyk as an algebraic object for defining recognizable languages of data words. Following Büchi’s approach, we introduce a variant of monadic secondorder logic with data equality tests that captures precisely the data languages recognizable by orbit finite data monoids. We also establish, following this time the approach of Schützenberger, McNaughton and Papert, that the firstorder fragment of this logic defines exactly the data languages recognizable by aperiodic orbit finite data monoids. Finally, we consider another variant of the logic that can be interpreted over generic structures with data. The data languages defined in this variant are also recognized by unambiguous finite memory automata.
On the Power of SPARQL in Expressing Navigational Queries
"... Navigational queries on graph databases return binary relations over the nodes of the graph. The calculus of relations, popularized by Tarski, serves as a natural benchmark for firstorder navigational querying. Recently, nested regular expressions have been proposed to extend navigational querying ..."
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Navigational queries on graph databases return binary relations over the nodes of the graph. The calculus of relations, popularized by Tarski, serves as a natural benchmark for firstorder navigational querying. Recently, nested regular expressions have been proposed to extend navigational querying to RDF graphs, i.e., ternary relations. In this paper we investigate a notion of “starfree ” nested regular expressions, obtained by removing the Kleene star (transitive closure) operator, but adding in the set difference operator. We claim this obtains the natural generalization of the Tarski algebra to RDF graphs. We then proceed to point out that the resulting navigational queries are already expressible in SPARQL proper, and we delineate a fragment of SPARQL, called TarskiSPARQL, that is precisely equivalent with the starfree nested regular expressions.