Describing Structure and Semantics of Graphs Using an RDF Vocabulary
John R. Punin Mukkai Krishnamoorthy

Rensselaer Polytechnic Institute Department of Computer Science 2001

Outline

Introduction to Resource Description Framework (RDF)
RDF Graph Modeling Language (RGML)
WWWPal System
RGML Schema
RGML Examples
Notation 3 and Graph Rules
Conclusions

Resource Description Framework (RDF)

Resource Description Framework (RDF) Model and Syntax Specification
http://www.w3.org/TR/REC-rdf-syntax/
Resource Description Framework (RDF) Schema Specification 1.0
http://www.w3.org/TR/2000/CR-rdf-schema-20000327/

RDF Model and Syntax

Language to describe resources
Use metadata (data about data) to describe Web resources
Provides interoperability between applications that exchange machine-understandable information on the Web
Use XML as a syntax

Application Areas

Resource discovery - better search engine capabilities
Cataloging - describe content and content relationship (web pages)
Intelligent software agents - knowledge sharing
Content Rating - PICS
Collections of pages
Intellectual property rights
Privacy preferences and policies
Digital signatures - build the "Web of Trust"

Basic RDF Model

Three object types:

Resources - Things being described by RDF expressions. Resources are always named by URIs

HTML Document
Specific XML element within the document source.
Collection of pages
Book

Properties - Specific aspect, characteristic, attribute or relation used to describe a resource

Creator
Title
Name

Statements - Resource (Subject) +
Property (Predicate) +
Property Value (Object)

Statement Example

John Punin is the creator of the web page http://www.cs.rpi.edu/~puninj/XMLJ/

Subject (Resource) - http://www.cs.rpi.edu/~puninj/XMLJ/
Predicate (Property) - Creator
Object (Literal) - John Punin

RDF Property Elements

Property names must be associated with a schema.
Qualify property names with a namespace prefix
Production propertyElt : <PropertyName> Value </PropertyName>
Value - Description element or String

   <?xml version="1.0"?>
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
	    xmlns:dc="http://purl.org/dc/elements/1.1/">
     <rdf:Description rdf:about="http://www.cs.rpi.edu/~puninj/XMLJ/">
       <dc:creator>John Punin</dc:creator>
     </rdf:Description>
   </rdf:RDF>

Describing Multiple Properties

Describing creator, title and date of the resource http://www.cs.rpi.edu/~puninj/XMLJ/

   <?xml version="1.0"?>
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
	    xmlns:dc="http://purl.org/dc/elements/1.1/">
     <rdf:Description rdf:about="http://www.cs.rpi.edu/~puninj/XMLJ/">
       <dc:creator>John Punin</dc:creator>
       <dc:title>Programming XML in Java</dc:title>
       <dc:date>2001-04-10</dc:date>
     </rdf:Description>
   </rdf:RDF>

Using Abbreviated RDF Syntax

Third basic abbreviation syntax:

New fact: http://www.cs.rpi.edu/~puninj/XMLJ/ is an instance of a WebPage
rdf:type element adds this new fact
value of the rdf:type can be used directly as element name


   <?xml version="1.0"?>
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   	    xmlns:dc="http://purl.org/dc/elements/1.1/">
     <rdf:Description rdf:about="http://www.cs.rpi.edu/~puninj/XMLJ/">
       <rdf:type rdf:resource="http://www.schemas.org/www/Webpage"/>
       <dc:creator>John Punin</dc:creator>
       <dc:title>Programming XML in Java</dc:title>
       <dc:date>2001-04-10</dc:date>
     </rdf:Description>
   </rdf:RDF>

   <?xml version="1.0"?>
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
	    xmlns:dc="http://purl.org/dc/elements/1.1/"
	    xmlns:s="http://www.schemas.org/www/">
     <s:WebPage rdf:about="http://www.cs.rpi.edu/~puninj/XMLJ/">
       <dc:creator>John Punin</dc:creator>
       <dc:title>Programming XML in Java</dc:title>
       <dc:date>2001-04-10</dc:date>
     </s:WebPage>
   </rdf:RDF>

RDF Containers

Bag - An unordered list of resources or literals
Sequence - An ordered list of resources or literals
Alternative - A list of resources or literals that represent alternatives for the value of a property

Using the Bag Container

Statement: The authors of the book 0201000237 are Alfred, John and Jeffrey

Statement using Bag Container

   <?xml version="1.0"?>
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   	    xmlns:dc="http://purl.org/dc/elements/1.1/">
     <rdf:Description rdf:about="urn:ISBN:0-201-00023-7">
       <dc:creator>
           <rdf:Bag>
	      <rdf:li>Alfred</rdf:li>
	      <rdf:li>John</rdf:li>
	      <rdf:li>Jeffrey</rdf:li>
           </rdf:Bag>
       </dc:creator>
     </rdf:Description>
   </rdf:RDF>

RDF Schema

Basic vocabulary to describe RDF vocabularies
Defines properties of the resources (e.g., title, author, subject, etc)
Defines kinds of resources being describes (books, Web pages, people, etc)
XML Schema gives specific constraints on the structure of an XML document
RDF Schema provides information about the interpretation of the RDF statements

RDF Classes and Properties

Namespace prefix:'rdfs' URI:'http://www.w3.org/2000/01/rdf-schema#'
Resources may be instances of one or more classes
Indicated by rdf:type property
Resource http://www.cs.rpi.edu/students/puninj is rdf:type Student
Resource http://www.cs.rpi.edu/students/puninj is rdf:type Person
Student is rdfs:subClassOf Person
Property-centric approach

Define properties in terms of the classes of resource to which they apply

RDF Graph Modeling Language (RGML)

RDF Vocabulary to describe graph structures
Graphs, Nodes, Edges as Resources
Relationships between graphs, nodes and edges
- graph G1 has a node N1 and edge E1
- node N1 is the source node of edge E1
- graph G2 is subgraph of graph G1
Properties of graphs, nodes and edges
- graph G1 is an undirected graph
- node N1 has a weight of "300"
- edge E1 has a label "Table of Contents"

Graph XML vocabularies

GraphML
XGMML
GXL
GraphXML

   <graph>
      <node id="n1"/>
      <node id="n2"/>
      <edge source="n1" target="n2"/>
   </graph>

WWWPal System - Analysis and Organization of Web Sites

http://www.cs.rpi.edu/projects/pb/WWWPal/

Display of a Graph of a Web Site

WWWPal System (2)

Web site

WWWPal System (3)

IP network

WWWPal System (4)

Log Graphs

RGML Classes and Properties

RDF Classes
- rgml:Graph - Graph Class
- rgml:Node - Node Class
- rgml:Edge - Edge Class
RDF Properties
- rgml:directed - direction of the edges
- rgml:label - text representation of graph objects
- rgml:nodes - bag of node resources
- rgml:edges - bag of edge resources
- rgml:graphs - bag of graph resources
- rgml:weight - weight value of the node or edge
- rgml:source - source node of the edge
- rgml:target - target node of the edge

Objectives of RGML

Graph Structures
Hypergraphs
Mixed Graphs
Directed and Undirected Graphs
Subgraphs
Graph Rules

RGML Schema


<?xml version="1.0" ?> 
<!-- 
     RDF Schema declaration for RDF Graph Modeling Language (RGML) 1.0 
     <http://purl.org/puninj/2001/05/rgml-schema#>
     
     John Punin (puninj@cs.rpi.edu)
     05-26-2001
-->
<rdf:RDF 
     xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:rgml="http://purl.org/puninj/2001/05/rgml-schema#">

<!-- Class Declarations -->

<!-- Graph Class declaration -->

  <rdfs:Class rdf:ID="Graph" 
    rdfs:label="Graph"
    rdfs:comment="A Graph Description">
    <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/>
  </rdfs:Class>

<!-- Node Class declaration -->

  <rdfs:Class rdf:ID="Node" 
    rdfs:label="Node"
    rdfs:comment="A Node Description">
    <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/>
  </rdfs:Class>

<!-- Edge Class declaration -->

  <rdfs:Class rdf:ID="Edge" 
    rdfs:label="Edge"
    rdfs:comment="An Edge Description">
    <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/>
  </rdfs:Class>

<!-- Property declarations -->

<!-- Global Properties -->

 <rdf:Property rdf:ID="label"
    rdfs:label="label"
    rdfs:comment="Text representation of the graph elements">
   <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/> 
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Graph"/>
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Node"/>
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/>
 </rdf:Property>

<!-- Graph Properties -->

 <rdf:Property rdf:ID="directed"
    rdfs:label="directed"
    rdfs:comment="Boolean value to indicate whether the Graph is directed or not">
   <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/> 
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Graph"/>
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
 </rdf:Property>

 <rdf:Property rdf:ID="nodes"
   rdfs:label="Nodes"
   rdfs:comment="List of the nodes belong to the graph">
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Graph"/>
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Resource"/>
 </rdf:Property>

 <rdf:Property rdf:ID="edges"
   rdfs:label="Edges"
   rdfs:comment="List of the edges belong to the graph">
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Graph"/>
   <rdfs:range rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/>
 </rdf:Property>

 <rdf:Property rdf:ID="graphs"
   rdfs:label="Subgraphs"
   rdfs:comment="List of subgraphs belong to the graph">
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Graph"/>
   <rdfs:range rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/>
 </rdf:Property>

<!-- Node Properties -->

 <rdf:Property rdf:ID="weight"
    rdfs:label="weight"
    rdfs:comment="Value (usually numerical) to show the node or edge weight">
   <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/> 
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Node"/>
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/>
 </rdf:Property>

<!-- Edge Properties -->

 <rdf:Property rdf:ID="source"
    rdfs:label="source"
    rdfs:comment="The source node of the edge">
   <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/> 
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/2000/01/rdf-schema#Resource"/>
 </rdf:Property>

 <rdf:Property rdf:ID="target"
    rdfs:label="target"
    rdfs:comment="The target node of the edge">
   <rdfs:isDefinedBy rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#"/> 
   <rdfs:domain rdf:resource="http://purl.org/puninj/2001/05/rgml-schema#Edge"/>
   <rdfs:range rdf:resource="http://www.w3.org/2000/01/rdf-schema#Resource"/>
 </rdf:Property>

</rdf:RDF>

RGML Schema (Graph Visualization using FRODO RDFSViz)

Simple Graph

RGML file:

<?xml version="1.0" encoding="utf-8"?> 

<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 
  xmlns="http://purl.org/puninj/2001/05/rgml-schema#"
  xmlns:rgml="http://purl.org/puninj/2001/05/rgml-schema#"
> 

<Graph rdf:ID="g1" rgml:directed="#true">
   <nodes>
      <rdf:Bag>
         <rdf:li rdf:resource="#n1"/>
         <rdf:li rdf:resource="#n2"/>
         <rdf:li rdf:resource="#n3"/>
      </rdf:Bag>
   </nodes>

   <edges>
      <rdf:Bag>
         <rdf:li rdf:resource="#e1"/>
         <rdf:li rdf:resource="#e2"/>
      </rdf:Bag>
   </edges>
</Graph>

<Node rdf:ID="n1"/>
<Node rdf:ID="n2"/>
<Node rdf:ID="n3"/>

<Edge rdf:ID="e1">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n2"/>
</Edge>
<Edge rdf:ID="e2">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n3"/>
</Edge>

</rdf:RDF>

Webgraph Example

RGML file:

<?xml version="1.0" encoding="utf-8"?> 

<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 
  xmlns="http://purl.org/puninj/2001/05/rgml-schema#"
  xmlns:rgml="http://purl.org/puninj/2001/05/rgml-schema#"
  xmlns:dc="http://purl.org/dc/elements/1.1/"> 

<Graph rdf:ID="g1" rgml:directed="true">
   <nodes>
      <rdf:Bag>
         <rdf:li rdf:resource="#n1"/>
         <rdf:li rdf:resource="#n2"/>
         <rdf:li rdf:resource="#n3"/>
      </rdf:Bag>
   </nodes>

   <edges>
      <rdf:Bag>
         <rdf:li rdf:resource="#e1"/>
         <rdf:li rdf:resource="#e2"/>
      </rdf:Bag>
   </edges>
</Graph>

<Node rdf:ID="n1" rgml:label="http://www.cs.rpi.edu/" 
      rgml:weight="3678">
  <dc:title>Rensselaer Computer Science Department</dc:title>
  <dc:date>2001-03-01</dc:date>
  <dc:format>text/html</dc:format>
</Node>
<Node rdf:ID="n2" rgml:label="http://www.cs.rpi.edu/people/" 
      rgml:weight="10611">
  <dc:title>People at Rensselaer Computer Science Department</dc:title>
  <dc:date>2001-02-26</dc:date>
  <dc:format>text/html</dc:format>
</Node>
<Node rdf:ID="n3" rgml:label="http://www.cs.rpi.edu/courses/"
      rgml:weight="6968">
  <dc:title>Courses at Rensselaer Computer Science Department</dc:title>
  <dc:date>2001-01-25</dc:date>
  <dc:format>text/html</dc:format>
</Node>

<Edge rdf:ID="e1" rgml:label="Courses">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n2"/>
</Edge>
<Edge rdf:ID="e2" rgml:label="People">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n3"/>
</Edge>

</rdf:RDF>

Hypergraph Example

Set of Nodes and Hyperedges
Hyperedge subset of set of Nodes
Directed Hypergraph - Ordered set of Nodes
Undirected Hypergraph - Unordered set of Nodes

RGML file:

<?xml version="1.0" encoding="utf-8"?> 

<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 
  xmlns="http://purl.org/puninj/2001/05/rgml-schema#"
  xmlns:rgml="http://purl.org/puninj/2001/05/rgml-schema#"
> 

<Graph rdf:ID="g1" rgml:directed="true">
   <nodes>
      <rdf:Bag>
         <rdf:li rdf:resource="#n1"/>
         <rdf:li rdf:resource="#n2"/>
         <rdf:li rdf:resource="#n3"/>
         <rdf:li rdf:resource="#n4"/>
      </rdf:Bag>
   </nodes>

   <edges>
      <rdf:Bag>
         <rdf:li rdf:resource="#e1"/>
         <rdf:li rdf:resource="#e2"/>
      </rdf:Bag>
   </edges>
</Graph>

<Node rdf:ID="n1"/>
<Node rdf:ID="n2"/>
<Node rdf:ID="n3"/>
<Node rdf:ID="n4"/>


<Edge rdf:ID="e1">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n2"/>
</Edge>

<Edge rdf:ID="e2">
   <nodes>
      <rdf:Seq>
         <rdf:li rdf:resource="#n2"/>
         <rdf:li rdf:resource="#n3"/>
         <rdf:li rdf:resource="#n4"/>
      </rdf:Seq>
   </nodes>
</Edge>

</rdf:RDF>

Subgraph Example

RGML file:

<?xml version="1.0" encoding="utf-8"?> 

<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" 
  xmlns="http://purl.org/puninj/2001/05/rgml-schema#"
  xmlns:rgml="http://purl.org/puninj/2001/05/rgml-schema#">

<Graph rdf:ID="g1" rgml:directed="true">
   <graphs>
      <rdf:Bag>
         <rdf:li rdf:resource="#g2"/>
         <rdf:li rdf:resource="#g3"/>
      </rdf:Bag>
   </graphs>
</Graph>

<Graph rdf:ID="g2" rgml:directed="true">
   <nodes>
      <rdf:Bag>
         <rdf:li rdf:resource="#n1"/>
         <rdf:li rdf:resource="#n2"/>
      </rdf:Bag>
   </nodes>

   <edges>
      <rdf:Bag>
         <rdf:li rdf:resource="#e1"/>
      </rdf:Bag>
   </edges>
</Graph>

<Graph rdf:ID="g3" rgml:directed="true">
   <nodes>
      <rdf:Bag>
         <rdf:li rdf:resource="#n3"/>
         <rdf:li rdf:resource="#n4"/>
      </rdf:Bag>
   </nodes>

   <edges>
      <rdf:Bag>
         <rdf:li rdf:resource="#e2"/>
      </rdf:Bag>
   </edges>
</Graph>

<Node rdf:ID="n1"/>
<Node rdf:ID="n2"/> 
<Node rdf:ID="n3"/>
<Node rdf:ID="n4"/>

<Edge rdf:ID="e1">
    <source rdf:resource="#n1"/>
    <target rdf:resource="#n2"/>
</Edge>
<Edge rdf:ID="e2">
    <source rdf:resource="#n3"/>
    <target rdf:resource="#n4"/>
</Edge>

</rdf:RDF>

Notation 3

RDF triples: Subject, Predicate, Object

   <#pat> <#child>  <#al>, <#chaz>, <#mo> ;
          <#age>    "24" ;
          <#eyecolor> "blue" .

Making Vocabularies

   @prefix rdf:  <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
   @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .

   :Person a rdfs:Class.
   :Pat a :Person.
   :Woman a rdfs:Class; subClassOf :Person .
   :sister rdfs:domain :Person; rdfs:range :Woman.

RGML using Notation 3

Simple Graph

@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix rgml: <http://purl.org/puninj/2001/05/rgml-schema#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix : <simple_graph#> .

:g1 a rgml:Graph; 
    rgml:directed "true";
    rgml:nodes :n1;
    rgml:nodes :n2;
    rgml:nodes :n3;
    rgml:edges :e1;
    rgml:edges :e2 .

:n1 a rgml:Node .
:n2 a rgml:Node .
:n3 a rgml:Node .

:e1 a rgml:Edge ;
    rgml:source :n1;
    rgml:target :n2 .

:e2 a rgml:Edge ;
    rgml:source :n1;
    rgml:target :n3 .

#ends

RGML Graph rules

forall (e, u, v) : source(e,u) and target(e,v) -> adjacent(u,v)
forall (u,v) : adjacent(u,v) -> adjacent(v,u)

Using Notation 3 :

  @prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
  @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
  @prefix rgml: <http://purl.org/puninj/2001/05/rgml-schema#> .
  @prefix log: <http://www.w3.org/2000/10/swap/log#> .
  @prefix : <rgml_rules#> .

  :adjacent  rdfs:domain rgml:Node; rdfs:range rgml:Node.

  {{:e rgml:source :u. :e rgml:target :v.} log:implies { :u :adjacent :v } } 
      a log:Truth; log:forAll :e, :u, :v.
  {{ :u :adjacent :v. } log:implies { :v :adjacent :u. }; } 
     a log:Truth; log:forAll :u, :v.

Proof Engines

CWM - Closed World Machine (Python) - Tim Berners Lee
http://www.w3.org/2000/10/swap/Overview.html
Euler Proof Mechanism (Java) - Jos De Roo
http://www.agfa.com/w3c/euler/

Graph Path

Path - sequence of consecutive nodes

This example is a modification of Jos De Roo's graph example

forall (g,e,u,v) : g is directed and source(e,u) and target(e,v) -> parent(u,v)
forall (g,u,v) : g is directed and parent(u,v) -> path(u,v)
forall (g,u,v,w) : g is directed and parent(u,v) and path(v,w) -> path(u,w)

Notation 3 :

   @prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
   @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
   @prefix rgml: <http://purl.org/puninj/2001/05/rgml-schema#> .
   @prefix log: <http://www.w3.org/2000/10/swap/log#> .
   @prefix : <rgml_rules#> .

   :parent  rdfs:domain rgml:Node; rdfs:range rgml:Node.
   :path  rdfs:domain rgml:Node; rdfs:range rgml:Node.

   {{ :g rgml:directed "true". :e rgml:source :u. :e rgml:target :v.} 
      log:implies { :u :parent :v. }; } 
      a log:Truth; log:forAll :e, :u, :v , :g.

   {{ :g rgml:directed "true". :u :parent :v} 
      log:implies {:u :path :v}} 
      a log:Truth; log:forAll :g, :u, :v.

   {{ :g rgml:directed "true". :u :parent :v. :v :path :w} 
      log:implies {:u :path :w}} 
      a log:Truth; log:forAll :g, :u, :v, :w.

Conclusions

RDF vocabulary (RGML) to describe the structure and semantics of graphs
Combine RDF vocabularies
Logic rules to express graph properties.
Semantic Portals