By: Boanerges AlemanMeza

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Paper ReviewRAL An Algebra for Querying RDF
Citation Flavius Frasincar, Geert-Jan Houben,
Richard Vdovjak, Peter Barna. RAL An Algebra for
Querying RDF. World Wide Web Internet and Web
Information Systems, 7(1), pp. 83-109, 2004

• By Boanerges Aleman-Meza
• CSCI-8380 Advanced Topics in Information Systems
• Computer Science, University of Georgia
• February 19, 2004

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RAL An Algebra for Querying RDF
Alternative version of the paper (9 pages)
Flavius Frasincar, Geert-Jan Houben, Richard
Vdovjak, Peter Barna. RAL An Algebra for
Querying RDF. Proceedings of the Third
International Conference on Web Information
Systems Engineering (WISE'02), Singapure,
December 12-14, 2002. pp. 173-181
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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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RAL data model
Review of RAL An Algebra for RDF

• Where's the contribution in the data model?
• What's the value of defining sets U (uri), B
  (blank nodes), L (literals), R (resources), ?
• Are two blank nodes really 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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RDF(S) Closure Example
Review of RAL An Algebra for RDF
rdfssubClassOf
rdfssubClassOf
DOMAIN
RANGE
assistant_professor_at
schema/vocabulary
instances
assistant_professor_at
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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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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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Equivalents in RQL ?
Review of RAL An Algebra for RDF

• Selection, Projection
• Blank nodes in cartesian product, join
• Union, Difference, Intersection
• Map, Kleene Star

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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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RAL optimization options
Review of RAL An Algebra for Querying RDF

• Push selections down
• Law 9 - commutativity of ? with ?
• ?cond(e1 ? e2) ?cond(e1) ? e2

? ?rdftypePainter ?rdftypeTechnique
(x, y)
?
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RAL optimization options

• Law 15 - 19 ? Will consider ...?
• "sets" of nodes, with their neighboring nodes
• classes/properties hierarchy
• changing focus from datatypes to relations

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Conclusions (my review)

• Will RAL Algebra be used?
• Compare with RQL queries
• Compare with relational algebra
• W3C endorsed? Mentioned? Linked to?
• Remaining work
• develop a query optimization algorithm
• compare RAL expressive power with RQL, and other
  query languages

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Conclusions (my review)
Review of RAL An Algebra for Querying RDF

• (Possible) Misleading treatment/mention of
  "domain" and "range" restrictions
• RDF data with zero to many schemas, but does
  not have to comply with them !
• Why do they give examples using literals ?

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Comments, Questions