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RAL: an R DF Al gebra

Explore the RAL (RDF Algebra) framework for querying RDF data models, operators, and optimization in web information systems. Understand the Semantic Web architecture and RDF query languages.

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RAL: an R DF Al gebra

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  1. RAL: an RDF Algebra Flavius Frasincar Geert-Jan Houben Richard Vdovjak Peter Barna WISE 2002

  2. Contents • Introduction • RAL Goals • RAL Data Model • RAL Operators • Conclusion WISE 2002

  3. 1. Introduction • Metadata is machine understandable information about web resources or other things [Source: Tim Berners-Lee, “Metadata Architecture”] • RDF (Resource Description Framework) is the Web metadata language for the Web • RDF extends the syntactic interoperability of XML to semantic interoperability being the foundation for the Semantic Web WISE 2002

  4. Semantic Web Architecture “Layer Cake” [Source: Tim Berners-Lee Director W3C Keynote speech at XML2000 “RDF and the Semantic Web” (Washington DC, 6 Dec. 2000)] WISE 2002

  5. Hera • Hera research project: Web Information Systems (WIS) and web (hypermedia) generation in WIS • WIS use RDF to represent and query application data for: • Semantic integration of data coming from heterogeneous sources • Semantic information presentation • Semantic querying • Huge quantities of data and metadata need to be processed in real-time: optimization is crucial WISE 2002

  6. Hera Methodology/Suite WISE 2002

  7. Rembrandt painted_by http://example.com/sb.jpg RDF Representations Primitive semantics: Subject Predicate Object Three alternative notations: • Triple (http://example.com/sb.jpg, painted_by, “Rembrandt”) • RDF/XML<rdf:Description rdf:ID=http://example.com/sb.jpg> <painted_by> Rembrandt </painted_by> </rdf:Description> • Graph WISE 2002

  8. RDF Query Languages • Triple-based: • Triple [successor of SiLRI] (Horn logic) • Metalog (Datalog) • XML-based: • RDF Query • RQuery (XQuery) • Graph-based (but not graphical): • RQL (OQL) WISE 2002

  9. 2. RAL Goals • Support the formal specification of RDF query languages • Provide a reference framework to compare different RDF query languages • Consider the result construction phase • presently neglected by RDF query languages which focus only on extraction • Enable algebraic query optimization WISE 2002

  10. RAL • RAL Data Model: specify what information is accessible (for RAL operators) in an RDF graph • Nodes: Resources and Literals • Edges: Properties • RAL Operators: define operators working on collections of nodes from the RAL Data Model • Extraction Operators • Loop Operators • Construction Operators WISE 2002

  11. rdf:Property rdf:type 3. RAL Data Model • R is the set of resources R = U  B • U is the set of URI references rdf:Property U • B is the set of blank nodes • L is the set of literals U, B, L are disjoint • P is the set of properties P  R, rdf:type P R L U B P WISE 2002

  12. An RDF model M is a finite set of triples(statements) M  R  U  (R  L) • The set of properties of an RDF model M PM = {p| (s, p, o)  M  (p, rdf:type, rdf:Property)  M} • The RDF graph model is similar to a directed labeled graph (DLG) • It is not a DLG since it allows for multiple edges between two nodes • It is not a general multigraph because different edges between two nodes cannot share the same label WISE 2002

  13. The RDFgraph model corresponding to an RDF model M is defined by • GM= (N, E, lN , lE), lN: N  R L, lE: E P • using the following construction mechanism: • for each (s, p, o)  M • add nodes ns, no to N (different only if s  o) • assign lN (ns) = s, lN (no) = o • add ep to E as a directed edge between ns and no • assign lE (ep ) = p • Observations: • lN (.) is an injective partial function • lE (.) is a total function WISE 2002

  14. Basic Properties Edges Nodes • Two non-blank nodes are equal if they have the same id • Twoblank nodes are equal if they have the same properties • and the corresponding property values are equal WISE 2002

  15. RDF(S)-Closure • RDF Model Theory defines the RDF-closure and RDFS-closure of an RDF Model M by proposing a set of rules for generating new triples • Extensional data: the original model M triples • Intensional data: the new triples generated by the RDF(S)-closure • RAL operators work on extensional+intensional data • Variants of the operators can be defined to neglect the intensional data (similar to the RQL strict interpretation) WISE 2002

  16. 4. RAL Operators • All operators have the following form o[f](x1, x2, … xn: expression) wherean expression is a collection of nodes and f is a function having as input/output collection of nodes • Extraction Operators: retrieve the needed information from an RDF graph • Loop Operators: control the repetitive application of certain operators • Construction Operators: build new RDF graphs from the extracted data WISE 2002

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  18. 4.1 Extraction Operators Projection [re_name](e: expression) computes the values of the properties with a name given by the regular expression re_name over strings on the input collection given by e Example [(P|p)aint[s]#](r4) returns the resources painted by r4 WISE 2002

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  20. Selection [condition](e: expression) selects input collection nodes fulfilling the given condition Example [[tname] = “Chiaroscuro”](c) where c is the collection of input resourcesr1, r2, r3, and r4, returns the resources representing the painting technique with the name“Chiaroscuro” WISE 2002

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  22. Cartesian Product • (x: expression)  (y: expression) • for each element in the Cartesian product of the input collections, a blank node that has all properties of both originating nodes is added to the result • Example • [[rdf:type] = Technique](c)[[rdf:type] = Painter](c) • returns a collection of blank nodes, each blank node having all the properties of the corresponding pair from the Cartesian product(the new nodes have both types Technique and Painter) WISE 2002

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  24. Join (x: expression) ⋈[condition] (y: expression)  [condition](x  y) is a Cartesian product followed by a selection Example (x:[[rdf:type] = Technique](c)) ⋈[[exemplified_by](x) = [paints](y)] (y: [[rdf:type] = Painter](c)) returns a collection of blank nodes, each blank node having all the properties of the corresponding pair from the Cartesian productthat satisfies the given condition WISE 2002

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  26. Union, Difference, Intersection (x: expression)  (y: expression) where  {, , } defined as in set theory Example [[rdf:type] = Technique](c)[[rdf:type] = Painter](c), returns the collection of resources obtained by combining the two collections (these two collections are obtained using two selections) WISE 2002

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  28. 4.2 Loop Operators Map map[f](e: expression) applies the function f to each element of the input collection; the function results are added in the output collection Example map[[rdfs:subClassOf]](Painting, Painter) computes the parent classes using the property rdfs:subClassOf for the collection consisting of Painting and Painter WISE 2002

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  31. Kleene Star [f](e: expression) repeats the function f possibly infinite times starting with the given input collection; at each iteration the results of the function are added to the next function input Example [[rdfs:subClassOf]](Painting)) computes the transitive closure of the property rdfs:subClassOf starting from Painting, i.e. Painting and all its superclasses WISE 2002

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  33. 4.3 Construction Operators Create Node node[type, id]() adds a new node to the graph with the given type and id (id is missing for blank nodes) and returns this node; if a resource is created, an rdf:type edge is added between the resource and the node representing rdfs:Resource The Create Node operator assigns a unique (in the resulted RDF graph) internal identifier for each created node WISE 2002

  34. Caravagio rdfs:Resource rdf:type Example node[Resource]() and node[Literal,“Caravagio”]() create a Resource representing a blank node and a Literal representing the string “Caravagio” WISE 2002

  35. Create Edge edge[name, subject](object: expression) adds edges between the subject node and each of the nodes in the object collection, and returns the subject node; the label of the edges is given by name which is the id of a property resource The Create Node and Create Edge operators abort if the “well-formed RDF(S) graph” conditions (e.g. rdf:type cannot refer to a literal, literals cannot have properties etc.) are not met after construction WISE 2002

  36. Caravagio rdfs:Resource rdf:type name Example edge[name, node[Resource]()](node[Literal, ”Caravagio”]()) creates an edge labeled with name between the nodes defined in the previous example WISE 2002

  37. 5. Conclusion • The RAL algebra is developed from a DB perspective and proposes a set of operators similar to their relational algebra counterparts: • Extraction Operators: Projection, Selection, Cartesian Product, Join, Union, Difference, Intersection • Similar to the existing semi-structured query languages RAL considers powerful repetition operators: • Loop Operators: Map, Kleene Star • As opposed to present RDF query languages RAL supports result construction: • Construction Operators: Create Node, Create Edge WISE 2002

  38. Future Work • Analyze the power of expression of RAL compared to RQL, a popular RDF query language at present time (build a translation scheme from RQL to RAL) • Formally specify the semantics of other RDF query languages in terms of RAL • Compare the power of expression of different RDF query languages using RAL as reference language • Explore equivalence rules for RAL expressions to be used in query optimization • Develop an RDF query optimization algorithm on RAL WISE 2002

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