Languages and Reasoning for the Semantic Web

1
Languages and Reasoning for the Semantic Web

• Grigoris Antoniou
• FORTH-ICS, Greece

2
Course Outline (1)

• Part I Semantic Web Overview
• The Semantic Web Vision
• Describing Web Resources in RDF
• Web Ontology Language OWL
• Current Trends

3
Course Outline (2)

• Part II Rule-Based Systems
• Comparing the Expressive power of OWL and Horn
  Logic
• Defeasible Reasoning
• Defeasible Reasoning System DR-DEVICE
• Semantic Web Enabled e-Commerce Applications of
  Defeasible Reasoning

4
A Note on chapters 1-4

• Chapters 1-4 are heavily based on
• G. Antoniou and F. van Harmelen. A Semantic Web
  Primer. MIT Press 2004
• Slides based on presentations associated with the
  book
• More complete set of slides and other links are
  found at www.semanticwebprimer.org

5
Chapter 1The Semantic Web Vision

6
Todays Web

• Most of todays Web content is suitable for human
  consumption
• Even Web content that is generated automatically
  from databases is usually presented without the
  original structural information found in
  databases
• Typical Web uses today peoples
• seeking and making use of information, searching
  for and getting in touch with other people,
  reviewing catalogs of online stores and ordering
  products by filling out forms

7
Keyword-Based Search Engines

• Current Web activities are not particularly well
  supported by software tools
• Except for keyword-based search engines (e.g.
  Google, AltaVista, Yahoo)
• The Web would not have been the huge success it
  was, were it not for search engines

8
Problems of Keyword-Based Search Engines

• High recall, low precision.
• Low or no recall
• Results are highly sensitive to vocabulary
• Results are single Web pages
• Human involvement is necessary to interpret and
  combine results
• Results of Web searches are not readily
  accessible by other software tools

9
The Key Problem of Todays Web

• The meaning of Web content is not
  machine-accessible lack of semantics
• It is simply difficult to distinguish the meaning
  between these two sentences
• I am a professor of computer science.
• I am a professor of computer science,
• you may think. Well, . . .

10
The Semantic Web Approach

• Represent Web content in a form that is more
  easily machine-processable.
• Use intelligent techniques to take advantage of
  these representations.
• The Semantic Web will gradually evolve out of the
  existing Web, it is not a competition to the
  current WWW

11
Semantic Web Technologies

• Explicit Metadata
• Ontologies
• Logic and Inference
• Agents

12
On HTML

• Web content is currently formatted for human
  readers rather than programs
• HTML is the predominant language in which Web
  pages are written (directly or using tools)
• Vocabulary describes presentation

13
An HTML Example

• lth1gtAgilitas Physiotherapy Centrelt/h1gt
• Welcome to the home page of the Agilitas
  Physiotherapy Centre. Do
• you feel pain? Have you had an injury? Let our
  staff Lisa Davenport,
• Kelly Townsend (our lovely secretary) and Steve
  Matthews take care
• of your body and soul.
• lth2gtConsultation hourslt/h2gt
• Mon 11am - 7pmltbrgt
• Tue 11am - 7pmltbrgt
• Wed 3pm - 7pmltbrgt
• Thu 11am - 7pmltbrgt
• Fri 11am - 3pmltpgt
• But note that we do not offer consultation during
  the weeks of the
• lta href". . ."gtState Of Originlt/agt games.

14
Problems with HTML

• Humans have no problem with this
• Machines (software agents) do
• How distinguish therapists from the secretary,
• How determine exact consultation hours
• They would have to follow the link to the State
  Of Origin games to find when they take place.

15
A Better Representation

• ltcompanygt
• lttreatmentOfferedgtPhysiotherapylt/treatmentOffered
  gt
• ltcompanyNamegtAgilitas Physiotherapy
  Centrelt/companyNamegt
• ltstaffgt
• lttherapistgtLisa Davenportlt/therapistgt
• lttherapistgtSteve Matthewslt/therapistgt
• ltsecretarygtKelly Townsendlt/secretarygt
• lt/staffgt
• lt/companygt

16
Explicit Metadata

• This representation is far more easily
  processable by machines
• Metadata data about data
• Metadata capture part of the meaning of data
• Semantic Web does not rely on text-based
  manipulation, but rather on machine-processable
  metadata

17
Ontologies

• The term ontology originates from philosophy
• The study of the nature of existence
• Different meaning from computer science
• An ontology is an explicit and formal
  specification of a conceptualization

18
Typical Components of Ontologies

• Terms denote important concepts (classes of
  objects) of the domain
• e.g. professors, staff, students, courses,
  departments
• Relationships between these terms typically
  class hierarchies
• a class C to be a subclass of another class C' if
  every object in C is also included in C'
• e.g. all professors are staff members
• Value restrictions
• e.g. only faculty members can teach courses

19
Example of a Class Hierarchy

20
The Role of Ontologies on the Web

• Ontologies provide a shared understanding of a
  domain semantic interoperability
• overcome differences in terminology
• mappings between ontologies
• Ontologies are useful for the organization and
  navigation of Web sites

21
Logic and Inference

• Logic is the discipline that studies the
  principles of reasoning
• Formal languages for expressing knowledge
• Well-understood formal semantics
• Declarative knowledge we describe what holds
  without caring about how it can be deduced
• Automated reasoners can deduce (infer)
  conclusions from the given knowledge

22
An Inference Example

• prof(X) ? faculty(X)
• faculty(X) ? staff(X)
• prof(michael)
• We can deduce the following conclusions
• faculty(michael)
• staff(michael)
• prof(X) ? staff(X)

23
Logic versus Ontologies

• The previous example involves knowledge typically
  found in ontologies
• Logic can be used to uncover ontological
  knowledge that is implicitly given
• It can also help uncover unexpected relationships
  and inconsistencies
• Logic is more general than ontologies
• It can also be used by intelligent agents for
  making decisions and selecting courses of action

24
Inference and Explanations

• Explanations the series of inference steps can
  be retraced
• They increase users confidence in Semantic Web
  agents Oh yeah? button
• Activities between agents create or validate
  proofs

25
A Layered Approach

• The development of the Semantic Web proceeds in
  steps
• Each step building a layer on top of another
• Principles
• Downward compatibility
• Upward partial understanding

26
The Semantic Web Layer Tower
27
Semantic Web Layers

• XML layer
• Syntactic basis
• RDF layer
• RDF basic data model for facts
• RDF Schema simple ontology language
• Ontology layer
• More expressive languages than RDF Schema
• Current Web standard OWL

28
Semantic Web Layers (2)

• Logic layer
• enhance ontology languages further
• application-specific declarative knowledge
• Proof layer
• Proof generation, exchange, validation
• Trust layer
• Digital signatures
• recommendations, rating agencies .

29
Chapter 2Describing Web Resources in RDF

30
Chapter Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

31
Basic Ideas of RDF

• Basic building block object-attribute-value
  triple
• It is called a statement
• Sentence about Billington is such a statement
• RDF has been given a syntax in XML
• This syntax inherits the benefits of XML
• Other syntactic representations of RDF possible

32
Basic Ideas of RDF (2)

• The fundamental concepts of RDF are
• resources
• properties
• statements

33
Resources

• We can think of a resource as an object, a
  thing we want to talk about
• E.g. authors, books, publishers, places, people,
  hotels
• Every resource has a URI, a Universal Resource
  Identifier
• A URI can be
• a URL (Web address) or
• some other kind of unique identifier

34
Properties

• Properties are a special kind of resources
• They describe relations between resources
• E.g. written by, age, title, etc.
• Properties are also identified by URIs
• Advantages of using URIs
• ? global, worldwide, unique naming scheme
• Reduces the homonym problem of distributed data
  representation

35
Statements

• Statements assert the properties of resources
• A statement is an object-attribute-value triple
• It consists of a resource, a property, and a
  value
• Values can be resources or literals
• Literals are atomic values (strings)

36
Three Views of a Statement

• A triple
• A piece of a graph
• A piece of XML code
• Thus an RDF document can be viewed as
• A set of triples
• A graph (semantic net)
• An XML document

37
Statements as Triples

• (David Billington,
• http//www.mydomain.org/site-owner,
• http//www.cit.gu.edu.au/db)
• The triple (x,P,y) can be considered as a logical
  formula P(x,y)
• Binary predicate P relates object x to object y
• RDF offers only binary predicates (properties)

38
XML Vocabularies

• A directed graph with labeled nodes and arcs
• from the resource (the subject of the statement)
• to the value (the object of the statement)
• Known in AI as a semantic net
• The value of a statement may be a resource
• ?t may be linked to other resources

39
A Set of Triples as a Semantic Net
40
Statements in XML Syntax

• Graphs are a powerful tool for human
  understanding but
• The Semantic Web vision requires
  machine-accessible and machine-processable
  representations
• There is a 3rd representation based on XML
• But XML is not a part of the RDF data model
• E.g. serialisation of XML is irrelevant for RDF

41
A Critical View of RDF Binary Predicates

• RDF uses only binary properties
• This is a restriction because often we use
  predicates with more than 2 arguments
• But binary predicates can simulate these
• Example referee(X,Y,Z)
• X is the referee in a chess game between players
  Y and Z

42
A Critical View of RDF Binary Predicates (2)

• We introduce
• a new auxiliary resource chessGame
• the binary predicates ref, player1, and player2
• We can represent referee(X,Y,Z) as

43
A Critical View of RDF Properties

• Properties are special kinds of resources
• Properties can be used as the object in an
  object-attribute-value triple (statement)
• They are defined independent of resources
• This possibility offers flexibility
• But it is unusual for modelling languages and OO
  programming languages
• It can be confusing for modellers

44
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

45
XML-Based Syntax of RDF

• An RDF document consists of an rdfRDF element
• The content of that element is a number of
  descriptions
• A namespace mechanism is used
• Disambiguation
• Namespaces are expected to be RDF documents
  defining resources that can be reused
• Large, distributed collections of knowledge

46
Example of University Courses

• ltrdfRDF
• xmlnsrdf"http//www.w3.org/1999/02/22-rdf-synta
  x-ns"
• xmlnsxsd"http//www.w3.org/2001/XLMSchema"
• xmlnsuni"http//www.mydomain.org/uni-ns"gt
• ltrdfDescription rdfabout"949318"gt
• ltuninamegtDavid Billingtonlt/uninamegt
• ltunititlegtAssociate Professorlt/unititlegt
• ltuniage rdfdatatype"xsdinteger"gt27ltuniagegt
  
• lt/rdfDescriptiongt

47
Example of University Courses (2)

• ltrdfDescription rdfabout"CIT1111"gt
• ltunicourseNamegtDiscrete Mathslt/unicourseNamegt
• ltuniisTaughtBygtDavid Billingtonlt/uniisTaughtBy
  gt
• lt/rdfDescriptiongt
• ltrdfDescription rdfabout"CIT2112"gt
• ltunicourseNamegtProgramming IIIlt/unicourseNamegt
  
• ltuniisTaughtBygtMichael Maherlt/uniisTaughtBygt
• lt/rdfDescriptiongt
• lt/rdfRDFgt

48
rdfabout versus rdfID

• An element rdfDescription has
• an rdfabout attribute indicating that the
  resource has been defined elsewhere
• An rdfID attribute indicating that the resource
  is defined
• Formally, there is no such thing as defining an
  object in one place and referring to it elsewhere
  
• Sometimes is useful (for human readability) to
  have a defining location, while other locations
  state additional properties

49
Property Elements

• Content of rdfDescription elements
• ltrdfDescription rdfabout"CIT3116"gt
• ltunicourseNamegtKnowledge Representationlt/unic
  ourseNamegt
• ltuniisTaughtBygtGrigoris Antonioult/uniisTaughtB
  ygt
• lt/rdfDescriptiongt
• unicourseName and uniisTaughtBy define two
  property-value pairs for CIT3116 (two RDF
  statements)
• read conjunctively

50
The rdfresource Attribute

• The relationships between courses and lecturers
  (in the example) were not formally defined but
  existed implicitly through the use of the same
  name
• The use of the same name may just be a
  coincidence for a machine
• We can denote that two entities are the same
  using the rdfresource attribute

51
The rdfresource Attribute (2)

• ltrdfDescription rdfabout"CIT1111"gt
• ltunicourseNamegtDiscrete Mathematicslt/unicourse
  Namegt
• ltuniisTaughtBy rdfresource"949318"/gt
• lt/rdfDescriptiongt
• ltrdfDescription rdfabout"949318"gt
• ltuninamegtDavid Billingtonlt/uninamegt
• ltunititlegtAssociate Professorlt/unititlegt
• lt/rdfDescriptiongt

52
Referencing Externally Defined Resources

• E.g., to refer the externally defined resource
  CIT1111
• http//www.mydomain.org/uni-nsCIT1111
• as the value of rdfabout
• www.mydomain.org/uni-ns is the URI where the
  definition of CIT1111 is found
• A description with an ID defines a fragment URI,
  which can be used to reference the defined
  description

53
Nested Descriptions Example

• ltrdfDescription rdfabout"CIT1111"gt
• ltunicourseNamegtDiscrete Mathslt/unicourseNamegt
• ltuniisTaughtBygt
• ltrdfDescription rdfID"949318"gt
• ltuninamegtDavid Billingtonlt/uninamegt
• ltunititlegtAssociate Professorlt/unititlegt
• lt/rdfDescriptiongt
• lt/uniisTaughtBygt
• lt/rdfDescriptiongt

54
Nested Descriptions

• Descriptions may be defined within other
  descriptions
• Other courses, such as CIT3112, can still refer
  to the new resource with ID 949318
• Although a description may be defined within
  another description, its scope is global

55
Introducing some Structure to RDF Documents using
the rdftype Element

• ltrdfDescription rdfID"CIT1111"gt
• ltrdftype rdfresource"http//www.mydomain.org/
  uni- nscourse"/gt
• ltunicourseNamegtDiscrete Mathslt/unicourseNamegt
• ltuniisTaughtBy rdfresource"949318"/gt
• lt/rdfDescriptiongt
• ltrdfDescription rdfID"949318"gt
• ltrdftype rdfresource"http//www.mydomain.org/
  uni- nslecturer"/gt
• ltuninamegtDavid Billingtonlt/uninamegt
• ltunititlegtAssociate Professorlt/unititlegt
• lt/rdfDescriptiongt

56
Abbreviated Syntax

• Simplification rules
• Childless property elements within description
  elements may be replaced by XML attributes
• For description elements with a typing element we
  can use the name specified in the rdftype
  element instead of rdfDescription
• These rules create syntactic variations of the
  same RDF statement
• They are equivalent according to the RDF data
  model, although they have different XML syntax

57
Abbreviated Syntax Example

• ltrdfDescription rdfID"CIT1111"gt
• ltrdftype rdfresource"http//www.mydomain.org/
  uni- nscourse"/gt
• ltunicourseNamegtDiscrete Mathslt/unicourseNamegt
• ltuniisTaughtBy rdfresource"949318"/gt
• lt/rdfDescriptiongt

58
Application of First Simplification Rule

• ltrdfDescription rdfID"CIT1111"
• unicourseName"Discrete Maths"gt
• ltrdftype rdfresource"http//www.mydomain.org/
  uni- nscourse"/gt
• ltuniisTaughtBy rdfresource"949318"/gt
• lt/rdfDescriptiongt

59
Application of 2nd Simplification Rule

• ltunicourse rdfID"CIT1111"
• unicourseName"Discrete Maths"gt
• ltuniisTaughtBy rdfresource"949318"/gt
• lt/unicoursegt

60
Container Elements

• Collect a number of resources or attributes about
  which we want to make statements as a whole
• E.g., we may wish to talk about the courses given
  by a particular lecturer
• The content of container elements are named
  rdf_1, rdf_2, etc.
• Alternatively rdfli

61
Three Types of Container Elements

• rdfBag an unordered container, allowing multiple
  occurrences
• E.g. members of the faculty board, documents in a
  folder
• rdfSeq an ordered container, which may contain
  multiple occurrences
• E.g. modules of a course, items on an agenda, an
  alphabetized list of staff members (order is
  imposed)
• rdfAlt a set of alternatives
• E.g. the document home and mirrors, translations
  of a document in various languages

62
Example for a Bag

• ltunilecturer rdfID"949352" uniname"Grigoris
  Antoniou"
• unititle"Professor"gt
• ltunicoursesTaughtgt
• ltrdfBaggt
• ltrdf_1 rdfresource"CIT1112"/gt
• ltrdf_2 rdfresource"CIT3116"/gt
• lt/rdfBaggt
• lt/unicoursesTaughtgt
• lt/unilecturergt

63
RDF Collections

• A limitation of these containers is that there is
  no way to close them
• these are all the members of the container
• RDF provides support for describing groups
  containing only the specified members, in the
  form of RDF collections
• list structure in the RDF graph
• constructed using a predefined collection
  vocabulary rdfList, rdffirst, rdfrest and
  rdfnil

64
RDF Collections (2)

• Shorthand syntax
• "Collection" value for the rdfparseType
  attribute
• ltrdfDescription rdfabout"CIT2112"gt
• ltuniisTaughtBy rdfparseType"Collection"gt
• ltrdfDescription rdfabout"949111"/gt
• ltrdfDescription rdfabout"949352"/gt
• ltrdfDescription rdfabout"949318"/gt
• lt/uniisTaughtBygt
• lt/rdfDescriptiongt

65
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

66
Basic Ideas of RDF Schema

• RDF is a universal language that lets users
  describe resources in their own vocabularies
• RDF does not assume, nor does it define semantics
  of any particular application domain
• The user can do so in RDF Schema using
• Classes and Properties
• Class Hierarchies and Inheritance
• Property Hierarchies

67
Classes and their Instances

• We must distinguish between
• Concrete things (individual objects) in the
  domain Discrete Maths, David Billington etc.
• Sets of individuals sharing properties called
  classes lecturers, students, courses etc.
• Individual objects that belong to a class are
  referred to as instances of that class
• The relationship between instances and classes in
  RDF is through rdftype

68
Why Classes are Useful

• Impose restrictions on what can be stated in an
  RDF document using the schema
• As in programming languages
• E.g. A1, where A is an array
• Disallow nonsense from being stated

69
Nonsensical Statements disallowed through the Use
of Classes

• Discrete Maths is taught by Concrete Maths
• We want courses to be taught by lecturers only
• Restriction on values of the property is taught
  by (range restriction)
• Room MZH5760 is taught by David Billington
• Only courses can be taught
• This imposes a restriction on the objects to
  which the property can be applied (domain
  restriction)

70
Class Hierarchies

• Classes can be organised in hierarchies
• A is a subclass of B if every instance of A is
  also an instance of B
• Then B is a superclass of A
• A subclass graph need not be a tree
• A class may have multiple superclasses

71
Class Hierarchy Example
72
Inheritance in Class Hierarchies

• Range restriction Courses must be taught by
  academic staff members only
• Michael Maher is a professor
• He inherits the ability to teach from the class
  of academic staff members
• This is done in RDF Schema by fixing the
  semantics of is a subclass of
• It is not up to an application (RDF processing
  software) to interpret is a subclass of

73
Property Hierarchies

• Hierarchical relationships for properties
• E.g., is taught by is a subproperty of
  involves
• If a course C is taught by an academic staff
  member A, then C also involves ?
• The converse is not necessarily true
• E.g., A may be the teacher of the course C, or
• a tutor who marks student homework but does not
  teach C
• P is a subproperty of Q, if Q(x,y) is true
  whenever P(x,y) is true

74
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

75
Core Classes

• rdfsResource, the class of all resources
• rdfsClass, the class of all classes
• rdfsLiteral, the class of all literals (strings)
  
• rdfProperty, the class of all properties.
• rdfStatement, the class of all reified
  statements

76
Core Properties

• rdftype, which relates a resource to its class
• The resource is declared to be an instance of
  that class
• rdfssubClassOf, which relates a class to one of
  its superclasses
• All instances of a class are instances of its
  superclass
• rdfssubPropertyOf, relates a property to one of
  its superproperties

77
Core Properties (2)

• rdfsdomain, which specifies the domain of a
  property P
• The class of those resources that may appear as
  subjects in a triple with predicate P
• If the domain is not specified, then any resource
  can be the subject
• rdfsrange, which specifies the range of a
  property P
• The class of those resources that may appear as
  values in a triple with predicate P

78
Examples

• ltrdfsClass rdfabout"lecturer"gt
• ltrdfssubClassOf rdfresource"staffMember"/gt
• lt/rdfsClassgt
• ltrdfProperty rdfID"phone"gt
• ltrdfsdomain rdfresource"staffMember"/gt
• ltrdfsrange rdfresource"http//www.w3.org/
• 2000/01/rdf-schemaLiteral"/gt
• lt/rdfPropertygt

79
Utility Properties

• rdfsseeAlso relates a resource to another
  resource that explains it
• rdfsisDefinedBy is a subproperty of rdfsseeAlso
  and relates a resource to the place where its
  definition, typically an RDF schema, is found
• rfdscomment. Comments, typically longer text,
  can be associated with a resource
• rdfslabel. A human-friendly label (name) is
  associated with a resource

80
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

81
Axiomatic Semantics

• We formalize the meaning of the modeling
  primitives of RDF and RDF Schema
• By translating into first-order logic
• We make the semantics unambiguous and machine
  accessible
• We provide a basis for reasoning support by
  automated reasoners manipulating logical formulas

82
Basic Predicates

• PropVal(P,R,V)
• A predicate with 3 arguments, which is used to
  represent an RDF statement with resource R,
  property P and value V
• An RDF statement (triple) (P,R,V) is represented
  as PropVal(P,R,V).
• Type(R,T)
• Short for PropVal(type,R,T)
• Specifies that the resource R has the type T
• Type(?r,?t) ? PropVal(type,?r,?t)

83
RDF Classes

• Constants Class, Resource, Property, Literal
• All classes are instances of Class
• Type(Class,Class)
• Type(Resource,Class)
• Type(Property,Class)
• Type(Literal,Class)

84
RDF Classes (2)

• Resource is the most general class every class
  and every property is a resource
• Type(?p,Property) ? Type(?p,Resource)
• Type(?c,Class) ? Type(?c,Resource)
• The predicate in an RDF statement must be a
  property
• PropVal(?p,?r,?v) ? Type(?p,Property)

85
The type Property

• type is a property
• PropVal(type,type,Property)
• type can be applied to resources (domain) and has
  a class as its value (range)
• Type(?r,?c) ? (Type(?r,Resource) ? Type(?c,Class))

86
Subclass

• subClassOf is a property
• Type(subClassOf,Property)
• If a class C is a subclass of a class C', then
  all instances of C are also instances of C'
• PropVal(subClassOf,?c,?c') ?
• (Type(?c,Class) ? Type(?c',Class) ?
• ??x (Type(?x,?c) ? Type(?x,?c')))

87
Domain and Range

• If the domain of P is D, then for every P(x,y),
  x?D
• PropVal(domain,?p,?d) ?
• ??x ??y (PropVal(?p,?x,?y) ? Type(?x,?d))
• If the range of P is R, then for every P(x,y),
  y?R
• PropVal(range,?p,?r) ?
• ??x ??y (PropVal(?p,?x,?y) ? Type(?y,?r))

88
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

89
Semantics based on Inference Rules

• Semantics in terms of RDF triples instead of
  restating RDF in terms of first-order logic
• and sound and complete inference systems
• This inference system consists of inference rules
  of the form
• IF E contains certain triples
• THEN add to E certain additional triples
• where E is an arbitrary set of RDF triples

90
Examples of Inference Rules

• IF E contains the triple (?x,?p,?y)
• THEN E also contains (?p,rdftype,rdfproperty)
• IF E contains the triples (?u,rdfssubClassOf,?v)
  and
• (?v,rdfssubclassOf,?w)
• THEN E also contains the triple
  (?u,rdfssubClassOf,?w)
• IF E contains the triples (?x,rdftype,?u) and
• (?u,rdfssubClassOf,?v)
• THEN E also contains the triple (?x,rdftype,?v)

91
Examples of Inference Rules (2)

• Any resource ?y which appears as the value of a
  property ?p can be inferred to be a member of the
  range of ?p
• This shows that range definitions in RDF Schema
  are not used to restrict the range of a property,
  but rather to infer the membership of the range
• IF E contains the triples (?x,?p,?y) and
• (?p,rdfsrange,?u)
• THEN E also contains the triple (?y,rdftype,?u)

92
Lecture Outline

• Basic Ideas of RDF
• XML-based Syntax of RDF
• Basic Concepts of RDF Schema
• ?he Language of RDF Schema
• Axiomatic Semantics for RDF and RDFS
• Direct Semantics based on Inference Rules
• Querying of RDF/RDFS Documents using RQL

93
Why an RDF Query Language?Different XML
Representations

• XML at a lower level of abstraction than RDF
• There are various ways of syntactically
  representing an RDF statement in XML
• Thus we would require several XQuery queries,
  e.g.
• //unilecturer/unititle if unititle element
• //unilecturer/_at_unititle if unititle attribute
• Both XML representations equivalent!

94
Why an RDF Query Language?Understanding the
Semantics

• ltunilecturer rdfID"949352"gt
• ltuninamegtGrigoris Antonioult/uninamegt
• lt/unilecturergt
• ltuniprofessor rdfID"949318"gt
• ltuninamegtDavid Billingtonlt/uninamegt
• lt/uniprofessorgt
• ltrdfsClass rdfabout"professor"gt
• ltrdfssubClassOf rdfresource"lecturer"/gt
• lt/rdfsClassgt
• A query for the names of all lecturers should
  return both Grigoris Antoniou and David Billington

95
RQL Basic Queries

• The query Class retrieves all classes
• The query Property retrieves all properties
• To retrieve the instances of a class (e.g.
  course) we write
• course
• If we do not wish to retrieve inherited
  instances, then we have to write
• course

96
RQL Basic Queries (2)

• The resources and values of triples with a
  specific property (e.g. involves) are retrieved
  using the query
• involves
• The result includes all subproperties of involves
• If we do not want these additional results, then
  we have to write
• involves

97
Using select-from-where

• As in SQL
• select specifies the number and order of
  retrieved data
• from is used to navigate through the data model
• where imposes constraints on possible solutions
• Retrieve all phone numbers of staff members
• select X,Y
• from XphoneY
• Here X and Y are variables, and XphoneY
  represents a resource-property-value triple

98
Implicit Join

• Retrieve all lecturers and their phone numbers
• select X,Y
• from lecturerX.phoneY
• Implicit join We restrict the second query only
  to those triples, the resource of which is in the
  variable X
• Here we restrict the domain of phone to
  lecturers
• A dot . denotes the implicit join

99
Explicit Join

• Retrieve the name of all courses taught by the
  lecturer with ID 949352
• select N
• from courseX.isTaughtByY, CnameN
• where Y"949352" and XC

100
Querying the Schema

• Schema variables have a name with prefix (for
  classes) or _at_ (for properties)
• Retrieve all resources and values of triples with
  property phone, or any of its subproperties, and
  their classes
• select X,X,Y,Y
• from XXphoneYY

101
Querying the Schema (2)

• The domain and range of a property can be
  retrieved as follows
• select domain(_at_P),range(_at_P)
• from _at_P
• where _at_Pphone

102
A Sample RDFS Ontology (1)
103
A Sample RDFS Ontology (2)
104
A Sample RDFS Ontology (3)
105
Sample RQL Queries (1)

• Give all subclasses of the class Antique
• subClassOf(Antique)

106
Sample RQL Queries (2)

• What is the domain and range of property paints?
• seq( domain(paints), range(paints))

107
Sample RQL Queries (3)

• Is Money a subclass of Book?
• Coin lt Book

108
Sample RQL Queries (4)

• Find antiques which cost more than 10000 Euros,
  along with their respective prices.
• SELECT A, T
• FROM ApriceT
• WHERE T gt 10000

109
Sample RQL Queries (5)

• Find the paintings dating before 1942.
• SELECT P
• FROM PaintingP.dateA
• WHERE A lt 1942

110
Sample RQL Queries (6)

• Find the titles of books written by Mahfouz.
• SELECT X
• FROM BookB.titleX,
• YwritesB, WriterY.creator_lnameW
• WHERE WMahfouz"

111
Sample RQL Queries (7)

• Find the first and last name of owners for which
  e-Bay sells their furniture.
• SELECT distinct X,Y
• FROM OwnerA.owner_nameX,
• OwnerA.owner_lnameY,
• Aowns.FurnitureF,
• SsellsF,
• SellerS.seller_nameN
• WHERE N"E-bay"

112
Sample RQL Queries (8)

• How many golden antiques does Smith own?
• count(
• SELECT FROM AntiqueA.use_materialM,Oowns
  A,OwnerO.owner_lnameN,
• Mhas_materialH
• WHERE H"Gold" and N"Michael" )

113
Sample RQL Queries (9)

• Find the title of the most expensive coin.
• SELECT T
• FROM CoinC.titleT,CoinC.priceB
• WHERE B max(
• SELECT P FROM CoinD.priceP)

114
Chapter 3Web Ontology Language OWL

115
Lecture Outline

• Basic Ideas of OWL
• The OWL Language
• Future Extensions

116
Requirements for Ontology Languages

• Ontology languages allow users to write explicit,
  formal conceptualizations of domain models
• The main requirements are
• a well-defined syntax
• efficient reasoning support
• a formal semantics
• sufficient expressive power
• convenience of expression

117
Tradeoff between Expressive Power and Efficient
Reasoning Support

• The richer the language is, the more inefficient
  the reasoning support becomes
• Sometimes it crosses the border of
  noncomputability
• We need a compromise
• A language supported by reasonably efficient
  reasoners
• A language that can express large classes of
  ontologies and knowledge.

118
Reasoning About Knowledge in Ontology Languages

• Class membership
• If x is an instance of a class C, and C is a
  subclass of D, then we can infer that x is an
  instance of D
• Equivalence of classes
• If class A is equivalent to class B, and class B
  is equivalent to class C, then A is equivalent to
  C, too

119
Reasoning About Knowledge in Ontology Languages
(2)

• Consistency
• X instance of classes A and B, but A and B are
  disjoint
• This is an indication of an error in the ontology
• Classification
• Certain property-value pairs are a sufficient
  condition for membership in a class A if an
  individual x satisfies such conditions, we can
  conclude that x must be an instance of A

120
Uses for Reasoning

• Reasoning support is important for
• checking the consistency of the ontology and the
  knowledge
• checking for unintended relationships between
  classes
• automatically classifying instances in classes
• Checks like the preceding ones are valuable for
• designing large ontologies, where multiple
  authors are involved
• integrating and sharing ontologies from various
  sources

121
Reasoning Support for OWL

• Semantics is a prerequisite for reasoning support
• Formal semantics and reasoning support are
  usually provided by
• mapping an ontology language to a known logical
  formalism
• using automated reasoners that already exist for
  those formalisms
• OWL is (partially) mapped on a description logic,
  and makes use of reasoners such as FaCT and RACER
  
• Description logics are a subset of predicate
  logic for which efficient reasoning support is
  possible

122
Limitations of the Expressive Power of RDF Schema

• Local scope of properties
• rdfsrange defines the range of a property (e.g.
  eats) for all classes
• In RDF Schema we cannot declare range
  restrictions that apply to some classes only
• E.g. we cannot say that cows eat only plants,
  while other animals may eat meat, too

123
Limitations of the Expressive Power of RDF Schema
(2)

• Disjointness of classes
• Sometimes we wish to say that classes are
  disjoint (e.g. male and female)
• Boolean combinations of classes
• Sometimes we wish to build new classes by
  combining other classes using union,
  intersection, and complement
• E.g. person is the disjoint union of the classes
  male and female

124
Limitations of the Expressive Power of RDF Schema
(3)

• Cardinality restrictions
• E.g. a person has exactly two parents, a course
  is taught by at least one lecturer
• Special characteristics of properties
• Transitive property (like greater than)
• Unique property (like is mother of)
• A property is the inverse of another property
  (like eats and is eaten by)

125
Combining OWL with RDF Schema

• Ideally, OWL would extend RDF Schema
• Consistent with the layered architecture of the
  Semantic Web
• But simply extending RDF Schema would work
  against obtaining expressive power and efficient
  reasoning
• Combining RDF Schema with logic leads to
  uncontrollable computational properties

126
Three Species of OWL

• W3CsWeb Ontology Working Group defined OWL as
  three different sublanguages
• OWL Full
• OWL DL
• OWL Lite
• Each sublanguage geared toward fulfilling
  different aspects of requirements

127
OWL Full

• It uses all the OWL languages primitives
• It allows the combination of these primitives in
  arbitrary ways with RDF and RDF Schema
• OWL Full is fully upward-compatible with RDF,
  both syntactically and semantically
• OWL Full is so powerful that it is undecidable
• No complete (or efficient) reasoning support

128
OWL DL

• OWL DL (Description Logic) is a sublanguage of
  OWL Full that restricts application of the
  constructors from OWL and RDF
• Application of OWLs constructors to each other
  is disallowed
• Therefore it corresponds to a well studied
  description logic
• OWL DL permits efficient reasoning support
• But we lose full compatibility with RDF
• Not every RDF document is a legal OWL DL
  document.
• Every legal OWL DL document is a legal RDF
  document.

129
OWL Lite

• An even further restriction limits OWL DL to a
  subset of the language constructors
• E.g., OWL Lite excludes enumerated classes,
  disjointness statements, and arbitrary
  cardinality.
• The advantage of this is a language that is
  easier to
• grasp, for users
• implement, for tool builders
• The disadvantage is restricted expressivity

130
OWL Compatibility with RDF Schema

• All varieties of OWL use
• RDF for their syntax
• Instances are declared
• as in RDF, using RDF
• descriptions
• Typing information
• OWL constructors are
• specialisations of their
• RDF counterparts

131
OWL Compatibility with RDF Schema (2)

• Semantic Web design aims at downward
  compatibility with corresponding reuse of
  software across the various layers
• The advantage of full downward compatibility for
  OWL is only achieved for OWL Full, at the cost of
  computational intractability

132
Lecture Outline

• Basic Ideas of OWL
• The OWL Language
• Future Extensions

133
owlOntology

• ltowlOntology rdfabout""gt
• ltrdfscommentgtAn example OWL ontology
  lt/rdfscommentgt
• ltowlpriorVersion
• rdfresource"http//www.mydomain.org/uni-ns-old
  "/gt
• ltowlimports
• rdfresource"http//www.mydomain.org/persons"/gt
  
• ltrdfslabelgtUniversity Ontologylt/rdfslabelgt
• lt/owlOntologygt
• owlimports is a transitive property

134
Classes

• Classes are defined using owlClass
• owlClass is a subclass of rdfsClass
• Disjointness is defined using owldisjointWith
• ltowlClass rdfabout"associateProfessor"gt
• ltowldisjointWith rdfresource"professor"/gt
• ltowldisjointWith rdfresource"assistantProfes
  sor"/gt
• lt/owlClassgt

135
Classes (2)

• owlequivalentClass defines equivalence of
  classes
• ltowlClass rdfID"faculty"gt
• ltowlequivalentClass rdfresource
  "academicStaffMember"/gt
• lt/owlClassgt
• owlThing is the most general class, which
  contains everything
• owlNothing is the empty class

136
Properties

• In OWL there are two kinds of properties
• Object properties, which relate objects to other
  objects
• E.g. is-TaughtBy, supervises
• Data type properties, which relate objects to
  datatype values
• E.g. phone, title, age, etc.

137
Datatype Properties

• OWL makes use of XML Schema data types, using the
  layered architecture of the SW
• ltowlDatatypeProperty rdfID"age"gt
• ltrdfsrange rdfresource "http//www.w3.org/200
  1/XLMSchema
• nonNegativeInteger"/gt
• lt/owlDatatypePropertygt

138
Object Properties

• User-defined data types
• ltowlObjectProperty rdfID"isTaughtBy"gt
• ltowldomain rdfresource"course"/gt
• ltowlrange rdfresource "academicStaffMember"/
  gt
• ltrdfssubPropertyOf rdfresource"involves"/gt
• lt/owlObjectPropertygt

139
Inverse Properties

• ltowlObjectProperty rdfID"teaches"gt
• ltrdfsrange rdfresource"course"/gt
• ltrdfsdomain rdfresource "academicStaffMember
  "/gt
• ltowlinverseOf rdfresource"isTaughtBy"/gt
• lt/owlObjectPropertygt

140
Equivalent Properties

• owlequivalentProperty
• ltowlObjectProperty rdfID"lecturesIn"gt
• ltowlequivalentProperty rdfresource"teaches"/
  gt
• lt/owlObjectPropertygt

141
Property Restrictions

• In OWL we can declare that the class C satisfies
  certain conditions
• All instances of C satisfy the conditions
• This is equivalent to saying that C is subclass
  of a class C', where C' collects all objects that
  satisfy the conditions
• C' can remain anonymous

142
Property Restrictions (2)

• A (restriction) class is achieved through an
  owlRestriction element
• This element contains an owlonProperty element
  and one or more restriction declarations
• One type defines cardinality restrictions (at
  least one, at most 3,)

143
Property Restrictions (3)

• The other type defines restrictions on the kinds
  of values the property may take
• owlallValuesFrom specifies universal
  quantification
• owlhasValue specifies a specific value
• owlsomeValuesFrom specifies existential
  quantification

144
owlallValuesFrom

• ltowlClass rdfabout"firstYearCourse"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"isTaughtBy"/gt
• ltowlallValuesFrom
  rdfresource"Professor"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

145
owlhasValue

• ltowlClass rdfabout"mathCourse"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource
  "isTaughtBy"/gt
• ltowlhasValue rdfresource "949352"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

146
owlsomeValuesFrom

• ltowlClass rdfabout"academicStaffMember"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"teaches"/gt
• ltowlsomeValuesFrom rdfresource
  "undergraduateCourse"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

147
Cardinality Restrictions

• We can specify minimum and maximum number using
  owlminCardinality and owlmaxCardinality
• It is possible to specify a precise number by
  using the same minimum and maximum number
• For convenience, OWL offers also owlcardinality

148
Cardinality Restrictions (2)

• ltowlClass rdfabout"course"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"isTaughtBy"/gt
• ltowlminCardinality rdfdatatype
  "xsdnonNegativeInteger"gt
• 1
• lt/owlminCardinalitygt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

149
Special Properties

• owlTransitiveProperty (transitive property)
• E.g. has better grade than, is ancestor of
• owlSymmetricProperty (symmetry)
• E.g. has same grade as, is sibling of
• owlFunctionalProperty defines a property that
  has at most one value for each object
• E.g. age, height, directSupervisor
• owlInverseFunctionalProperty defines a property
  for which two different objects cannot have the
  same value

150
Special Properties (2)

• ltowlObjectProperty rdfID"hasSameGradeAs"gt
• ltrdftype rdfresource"owlTransitiveProperty"
  /gt
• ltrdftype rdfresource"owlSymmetricProperty"/
  gt
• ltrdfsdomain rdfresource"student"/gt
• ltrdfsrange rdfresource"student"/gt
• lt/owlObjectPropertygt

151
Boolean Combinations

• We can combine classes using Boolean operations
  (union, intersection, complement)
• ltowlClass rdfabout"course"gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlcomplementOf rdfresource
  "staffMember"/gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

152
Boolean Combinations (2)

• ltowlClass rdfID"peopleAtUni"gt
• ltowlunionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"staffMember"/gt
• ltowlClass rdfabout"student"/gt
• lt/owlunionOfgt
• lt/owlClassgt
• The new class is not a subclass of the union, but
  rather equal to the union
• We have stated an equivalence of classes

153
Boolean Combinations (3)

• ltowlClass rdfID"facultyInCS"gt
• ltowlintersectionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"faculty"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"belongsTo"/gt
• ltowlhasValue rdfresource "CSDepartmen
  t"/gt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt

154
Nesting of Boolean Operators

• ltowlClass rdfID"adminStaff"gt
• ltowlintersectionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"staffMember"/gt
• ltowlcomplementOfgt
• ltowlunionOf rdfparseType"Collection"gt
• ltowlClass rdfabout"faculty"/gt
• ltowlClass rdfabout "techSupportStaf
  f"/gt
• lt/owlunionOfgt
• lt/owlcomplementOfgt
• lt/owlintersectionOfgt
• lt/owlClassgt

155
Declaring Instances

• Instances of classes are declared as in RDF
• ltrdfDescription rdfID"949352"gt
• ltrdftype rdfresource "academicStaffMember"/gt
  
• lt/rdfDescriptiongt
• ltacademicStaffMember rdfID"949352"gt
• ltuniage rdfdatatype"xsdinteger"gt
  39ltuniagegt
• lt/academicStaffMembergt

156
Distinct Objects

• To ensure that different individuals are indeed
  recognized as such, we must explicitly assert
  their inequality
• ltlecturer rdfabout"949318"gt
• ltowldifferentFrom rdfresource"949352"/gt
• lt/lecturergt

157
Distinct Objects (2)

• OWL provides a shorthand notation to assert the
  pairwise inequality of all individuals in a given
  list
• ltowlallDifferentgt
• ltowldistinctMembers rdfparseType"Collection"gt
• ltlecturer rdfabout"949318"/gt
• ltlecturer rdfabout"949352"/gt
• ltlecturer rdfabout"949111"/gt
• lt/owldistinctMembersgt
• lt/owlallDifferentgt

158
Data Types in OWL

• XML Schema provides a mechanism to construct
  user-defined data types
• E.g., the data type of adultAge includes all
  integers greater than 18
• Such derived data types cannot be used in OWL
• The OWL reference document lists all the XML
  Schema data types that can be used
• These include the most frequently used types such
  as string, integer, Boolean, time, and date.

159
Combination of Features

• In different OWL languages there are different
  sets of restrictions regarding the application of
  features
• In OWL Full, all the language constructors may be
  used in any combination as long as the result is
  legal RDF

160
Restriction of Features in OWL DL

• Vocabulary partitioning
• Any resource is allowed to be only a class, a
  data type, a data type property, an object
  property, an individual, a data value, or part of
  the built-in vocabulary, and not more than one of
  these
• Explicit typing
• The partitioning of all resources must be stated
  explicitly (e.g. a class must be declared if used
  in conjunction with rdfssubClassOf)

161
Restriction of Features in OWL DL (2)

• Property Separation
• The set of object properties and data type
  properties are disjoint
• Therefore the following can never be specified
  for data type properties
• owlinverseOf
• owlFunctionalProperty
• owlInverseFunctionalProperty
• owlSymmetricProperty

162
Restriction of Features in OWL DL (3)

• No transitive cardinality restrictions
• No cardinality restrictions may be placed on
  transitive properties
• Restricted anonymous classes Anonymous classes
  are only allowed to occur as
• the domain and range of either owlequivalentClass
  or owldisjointWith
• the range (but not the domain) of rdfssubClassOf

163
Restriction of Features in OWL Lite

• Restrictions of OWL DL and more
• owloneOf, owldisjointWith, owlunionOf,
  owlcomplementOf and owlhasValue are not allowed
  
• Cardinality statements (minimal, maximal, and
  exact cardinality) can only be made on the values
  0 or 1
• owlequivalentClass statements can no longer be
  made between anonymous classes but only between
  class identifiers

164
Inheritance in Class Hierarchies

• Range restriction Courses must be taught by
  academic staff members only
• Michael Maher is a professor
• He inherits the ability to teach from the class
  of academic staff members
• This is done in RDF Schema by fixing the
  semantics of is a subclass of
• It is not up to an application (RDF processing
  software) to interpret is a subclass of

165
Lecture Outline

• Basic Ideas of OWL
• The OWL Language
• Future Extensions

166
Future Extensions of OWL

• Modules and Imports
• Defaults
• Closed World Assumption
• Unique Names Assumption
• Procedural Attachments
• Rules for Property Chaining

167
Modules and Imports

• The importing facility of OWL is very trivial
• It only allows importing of an entire ontology,
  not parts of it
• Modules in programming languages based on
  information hiding state functionality, hide
  implementation details
• Open question how to define appropriate module
  mechanism for Web ontology languages

168
Defaults

• Many practical knowledge representation systems
  allow inherited values to be overridden by more
  specific classes in the hierarchy
• treat inherited values as defaults
• No consensus has been reached on the right
  formalization for the nonmonotonic behaviour of
  default values

169
Closed World Assumption

• OWL currently adopts the open-world assumption
• A statement cannot be assumed true on the basis
  of a failure to prove it
• On the huge and only partially knowable WWW, this
  is a correct assumption
• Closed-world assumption a statement is true when
  its negation cannot be proved
• tied to the notion of defaults, leads to
  nonmonotonic behaviour

170
Unique Names Assumption

• Typical database applications assume that
  individuals with different names are indeed
  different individuals
• OWL follows the usual logical paradigm where this
  is not the case
• Plausible on the WWW
• One may want to indicate portions of the ontology
  for which the assumption does or does not hold

171
Procedural Attachments

• A common concept in knowledge representation is
  to define the meaning of a term by attaching a
  piece of code to be executed for computing the
  meaning of the term
• Not through explicit definitions in the language
• Although widely used, this concept does not lend
  itself very well to integration in a system with
  a formal semantics, and it has not been included
  in OWL

172
Rules for Property Chaining

• OWL does not allow the composition of properties
  for reasons of