department of mathematics and computer science TU/e technische universiteit eindhoven WISE 2002December 12, 20021 RAL: an RDF Algebra Flavius Frasincar

WISE 2002

/department of mathematics and computer science

TU/e technische universiteit eindhoven

December 12, 2002 1

RAL: an RDF Algebra

Flavius Frasincar

Geert-Jan Houben

Richard Vdovjak

Peter Barna

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December 12, 2002 2

Contents

1. Introduction

2. RAL Goals

3. RAL Data Model

4. RAL Operators

5. Conclusion

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December 12, 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

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December 12, 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)]

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December 12, 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

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December 12, 2002 6

Hera Methodology/Suite

ConceptualDesign

IntegrationDesign

ApplicationDesign

AdaptationDesign

(Search)Agent

inforequest

(meta) data

ConceptualModel

ApplicationModel

inforequest

(slice)presentation

End User

RQL / RDF XML

UserModel

PresentationEngine

ApplicationEngine

IntegrationEngine

CuypersEngine

AdaptationEngine

inforequest

HTML/WML/SMIL

IntegrationModel

Semantic Layer Application Layer Presentation Layer

Presentation Templates(XSLT)

PresentationDesign

User/PlatformProfile

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December 12, 2002 7

RDF Representations

Primitive semantics: Subject Predicate ObjectThree 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 painted_byhttp://example.com/sb.jpg Rembrandt

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December 12, 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)

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December 12, 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

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December 12, 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

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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

rdf:type

rdf:PropertyU 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, 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

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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

Basic Property

Result for resources

Result for literals

id lN(u), u U lN(s), s L

type Resource Literal

Basic Property

Result

name lE(p), p P

subject r, r R

object o, o R L

• 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

Nodes Edges

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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 extensional+intensional 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

o[f](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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r2 r3

r1 r4

exemplified_by exemplified_by paints paints

Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by

1638 Self Portrait 1628

http://example.com/sb.jpg http://example.com/sp.jpg image

name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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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

4.1 Extraction Operators

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r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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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 name“Chiaroscuro”

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r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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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

[[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




r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

exemplified_by paints


tname cname

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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 product that satisfies the given condition

WISE 2002




r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance



tname cname

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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




r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique Artifact

Painter

Creator

Painting

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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4.2 Loop Operators

Mapmap[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

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Creator

Painter

Artifact

Painting

r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

WISE 2002




Creator

Painter

Artifact

Painting

r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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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

[[rdfs:subClassOf]](Painting))

computes the transitive closure of the property rdfs:subClassOf starting from Painting, i.e. Painting and all its superclasses

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Artifact

Painting

r2 r3

r1 r4


Stone Bridge

Rembrandt tname

image name

cname

Technique

Painter

Creator

Image

Literal

Literal Literal

Literal tname

exemplified_by

exemplifies creates

created_by

name year

cname

image

paints

painted_by



name year year name

Chiaroscuro

inferred rdf:type

rdf:type

rdfs:subClassOf

rdfs:subPropertyOf

Legend

schema

instance

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4.3 Construction Operators

Create Nodenode[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

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Caravagio

rdfs:Resource

rdf:type

Examplenode[Resource]() and node[Literal,“Caravagio”]()

create a Resource representing a blank node and a Literal representing the string “Caravagio”

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Create Edgeedge[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

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nameCaravagio

rdfs:Resource

rdf:type

Example edge[name, node[Resource]()](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

Documents

department of mathematics and computer science TU/e technische universiteit eindhoven WISE 2002December 12, 20021 RAL: an RDF Algebra Flavius Frasincar