RAL: an RDF Algebra

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RAL an RDF Algebra

• Flavius Frasincar
• Geert-Jan Houben
• Richard Vdovjak
• Peter Barna

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Contents

• Introduction
• RAL Goals
• RAL Data Model
• RAL Operators
• Conclusion

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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

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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)
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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

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Hera Methodology/Suite
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RDF Representations

• Primitive semantics Subject Predicate Object
• Three alternative notations
• Triple (http//example.com/sb.jpg,
  painted_by, Rembrandt)
• RDF/XML ltrdfDescription rdfIDhttp//examp
  le.com/sb.jpggt
• 
  ltpainted_bygt
• 
  Rembrandt
• 
  lt/painted_bygt
• 
  lt/rdfDescriptiongt
• Graph

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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)

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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

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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

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3. RAL Data Model

• R is the set of resources R U ? B
• U is the set of URI references rdfProperty ?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,
  rdftype ?P

R
L
U
B
P
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• 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, rdftype,
  rdfProperty) ? 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

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• The RDF graph 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

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Basic Properties
Edges
Nodes

• Two non-blank nodes are equal if they have the
  same id
• Two blank nodes are equal if they have the same
  properties
• and the corresponding property values are
  equal

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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 extensionalintensional
  data
• Variants of the operators can be defined to
  neglect the intensional data (similar to the RQL
  strict interpretation)

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4. RAL Operators

• All operators have the following form
• of(x1, x2, xn expression)
• where an 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

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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
• ?(Pp)aints(r4)
• returns the resources painted by r4

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• Selection
• ?condition(e expression)
• selects input collection nodes fulfilling the
  given condition
• Example
• ??tname Chiaroscuro(c)
• where c is the collection of input resources
  r1, r2, r3, and r4, returns the resources
  representing the painting technique with the
  nameChiaroscuro

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• 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
• ??rdftype Technique(c) ? ??rdftype
  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)

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Join (x expression) ?condition (y
expression) ? ?condition(x ? y) is a
Cartesian product followed by a selection
Example (x ??rdftype
Technique(c))
??exemplified_by(x) ? paints(y)
(y ??rdftype Painter(c))
returns a collection of blank nodes, each blank
node having all the properties of the
corresponding pair from the Cartesian product
that satisfies the given condition
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Union, Difference, Intersection (x expression)
? (y expression) where ? ??, ?,
? defined as in set theory Example
??rdftype Technique(c) ? ??rdftype
Painter(c), returns the collection of resources
obtained by combining the two collections (these
two collections are obtained using two selections)
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4.2 Loop Operators

• Map
• mapf(e expression)
• applies the function f to each element of the
  input collection the function results are added
  in the output collection
• Example
• map? rdfssubClassOf(Painting, Painter)
• computes the parent classes using the
  property rdfssubClassOf for the collection
  consisting of Painting and Painter

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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 ??rdfssubClassOf
(Painting)) computes the transitive closure
of the property rdfssubClassOf starting from
Painting, i.e. Painting and all its superclasses
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4.3 Construction Operators

• Create Node
• nodetype, 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
  rdftype edge is added between the resource and
  the node representing rdfsResource
• The Create Node operator assigns a unique (in
  the resulted RDF graph) internal identifier for
  each created node

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Example nodeResource() and
nodeLiteral,Caravagio() create a
Resource representing a blank node and a Literal
representing the string Caravagio
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Create Edge edgename, 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. rdftype cannot refer to
a literal, literals cannot have properties etc.)
are not met after construction
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Example edgename, nodeResource()(node
Literal, Caravagio()) creates an edge
labeled with name between the nodes defined
in the previous example
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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

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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