Ontologies in Semantic Web

1
Ontologiesin Semantic Web
www.ontoknowledge.org/oil

• Based on tutorials and presentations
• D. Lee, F. Harmelen, M. Arumugam, C. Goble, I.
  Horrocks, N. F. Noy, D.L. McGuinness, J.
  Broekstra, M. Klein, S. Decker, D. Fensel, DERI
  Group

2
Communication between people
3
The More or Less Global Agreement about Standard
Terminology and Conceptual Hierarchy for a Domain
Description is Necessary for the Interoperability
in the Intelligent Web
4
Contents

• Introduction to Ontologies
• Ontology Engineering
• OWL Web Ontology Language

5
Introduction to Ontologies
6
What are ontologies?

• Ontologies are content theories about the sorts
  of objects, properties of objects, and relations
  between objects that are possible in a
  specified domain of knowledge.

7
What are ontologies? (2)

• Ontology as vocabularyOntology is a
  representation vocabulary, often specialized to
  some domain or subject matter.
• Ontology as content theoryThe main contribution
  of ontology is to identify specific classes of
  objects and relations that exist in some domain.

8
What are ontologies? (3)
Studer(98) Formal, explicit specification of a
shared conceptualization
9
Why are ontologies important?

• Ontological analysis clarifies the structure of
  knowledge.
• Ontologies enable knowledge sharing.

10
Describing the world

• subtypes of concepts.
• task dependence of ontologies.

11
Requirement for an Ontology

• Ontologies to be shared need a standard
  representation and exchange language

12
Requirements for an Ontology-language (1)

• Well designed
• Useful and proven modelling primitives
• Intuitive to human users
• Expressive enough
• Efficient and complete reasoning support

13
Requirements for an Ontology-language (2)

• Well defined
• clear syntax - read ontologies
• Formal semantics understand (process)
  ontologies - to facilitate machine interpretation
  of that semantics

14
Requirements for an Ontology-language (3)

• Compatible
• Easy mapping to/from other ontology languages
• Maximum compatibility with XML and RDF(S)

15
Ontology Engineering
16
What Is Ontology Engineering?

• Ontology Engineering Defining terms in the
  domain and relations among them
• Defining concepts in the domain (classes)
• Arranging the concepts in a hierarchy
  (subclass-superclass hierarchy)
• Defining which attributes and properties (slots)
  classes can have and constraints on their values
• Defining individuals and filling in slot values

17
Tool for Ontology Engineering

• Screenshots in further examples are from
  Protégé-2000, which
• is a graphical ontology-development tool
• supports a rich knowledge model
• is open-source and freely available
  (http//protege.stanford.edu/index.shtml)

18
Determine Domain and Scope

• What is the domain that the ontology will cover?
• For what we are going to use the ontology?
• For what types of questions the information in
  the ontology should provide answers (competency
  questions)?
• Answers to these questions may change during the
  lifecycle

19
Example Ontology
A shared ONTOLOGY of wine and food
20
Competency Questions

• Which wine characteristics should I consider when
  choosing a wine?
• Is Bordeaux a red or white wine?
• Does Cabernet Sauvignon go well with seafood?
• What is the best choice of wine for grilled meat?
• Which characteristics of a wine affect its
  appropriateness for a dish?
• Does a flavor or body of a specific wine change
  with vintage year?

21
Enumerating Terms - The Wine Ontology

• wine, grape, winery, location,...
• wine color, wine body, wine flavor, sugar
  content,...
• white wine, red wine, Bordeaux wine,...
• food, seafood, fish, meat, vegetables, cheese,...

22
Define Classes and the Class Hierarchy

• A class is a concept in the domain
• a class of wines
• a class of wineries
• a class of red wines
• A class is a collection of elements (instances of
  classes) with similar properties

23
Class Inheritance

• Classes usually constitute a taxonomic hierarchy
  (a subclass-superclass hierarchy)
• A class hierarchy is usually an IS-A hierarchy
• an instance of a subclass is an instance of a
  superclass
• If you think of a class as a set of elements, a
  subclass is a subset

24
Class Inheritance - Example

• Apple is a subclass of Fruit
• Every apple is a fruit
• Red wines is a subclass of Wine
• Every red wine is a wine
• Chianti wine is a subclass of Red wine
• Every Chianti wine is a red wine

25
Levels in the Hierarchy
26
Modes of Development

• top-down define the most general concepts first
  and then specialize them
• bottom-up define the most specific concepts and
  then organize them in more general classes
• combination define the more salient concepts
  first and then generalize and specialize them

27
Documentation

• Classes (and slots) usually have documentation
• Describing the class in natural language
• Listing domain assumptions relevant to the class
  definition
• Listing synonyms
• Documenting classes and slots is as important as
  documenting computer code!

28
Define Properties of Classes Slots

• Slots in a class definition describe attributes
  of instances of the class and relations to other
  instances
• Each wine will have color, sugar content,
  producer, etc

29
Properties (Slots)

• Types of properties
• intrinsic properties flavor and color of wine
• extrinsic properties name and price of wine
• parts ingredients in a dish
• relations to other objects producer of wine
  (winery)
• Simple and complex properties
• simple properties (attributes) contain primitive
  values (strings, numbers)
• complex properties contain (or point to) other
  objects (e.g., a winery instance)

30
Slots for the Class Wine
(in Protégé-2000)
31
Slot and Class Inheritance

• A subclass inherits all the slots from the
  superclass
• If a wine has a name and flavor, a red wine also
  has a name and flavor
• If a class has multiple superclasses, it inherits
  slots from all of them
• Port is both a dessert wine and a red wine. It
  inherits sugar content high from the former
  and colorred from the latter

32
Property Constraints

• Property constraints (facets) describe or limit
  the set of possible values for a slot
• The name of a wine is a string
• The wine producer is an instance of Winery
• A winery has exactly one location

33
Common Facets

• Slot cardinality the number of values a slot
  has
• Slot value type the type of values a slot has
• Minimum and maximum value a range of values for
  a numeric slot
• Default value the value a slot has unless
  explicitly specified otherwise

34
Common Facets Slot Cardinality

• Minimum cardinality
• Minimum cardinality 1 means that the slot must
  have a value (required)
• Minimum cardinality 0 means that the slot value
  is optional
• Maximum cardinality
• Maximum cardinality 1 means that the slot can
  have at most one value (single-valued slot)
• Maximum cardinality greater than 1 means that the
  slot can have more than one value
  (multiple-valued slot)

35
Common Facets Value Type

• String a string of characters (Château Lafite)
• Number an integer or a float (15, 4.5)
• Boolean a true/false flag
• Enumerated type a list of allowed values (high,
  medium, low)
• Complex type an instance of another class
• Specify the class to which the instances belong
• The Wine class is the value type for the slot
  produces at the Winery class

36
Domain and Range of Slot

• Domain of a slot the class (or classes) that
  have the slot
• More precisely class (or classes) instances of
  which can have the slot
• Range of a slot the class (or classes) to which
  slot values belong

37
Facets and Class Inheritance

• A subclass inherits all the slots from the
  superclass
• A subclass can override the facets to narrow
  the list of allowed values
• Make the cardinality range smaller
• Replace a class in the range with a subclass

Wine
Winery
producer
is-a
is-a
French wine
French winery
producer
38
Create Instances

• Create an instance of a class
• The class becomes a direct type of the instance
• Any superclass of the direct type is a type of
  the instance
• Assign slot values for the instance frame
• Slot values should conform to the facet
  constraints
• Knowledge-acquisition tools often check that

39
Creating an Instance Example
40
Defining Classes and a Class Hierarchy

• The things to remember
• There is no single correct class hierarchy
• But there are some guidelines
• The question to ask
• Is each instance of the subclass is an instance
  of its superclass?

41
Transitivity of the Class Hierarchy

• The is-a relationship is transitive
• B is a subclass of A
• C is a subclass of B
• C is a subclass of A
• A direct superclass of a class is its closest
  superclass

42
Multiple Inheritance

• A class can have more than one superclass
• A subclass inherits slots and facet restrictions
  from all the parents
• Different systems resolve conflicts differently

43
Disjoint Classes

• Classes are disjoint if they cannot have common
  instances
• Disjoint classes cannot have any common
  subclasses either

Port
Wine
Dessert wine

• Red wine, White wine,Rosé wine are disjoint
• Dessert wine and Redwine are not disjoint

Red wine
Rosé wine
White wine
44
Avoiding Class Cycles

• Danger of multiple inheritance cycles in the
  class hierarchy
• Classes A, B, and C have equivalent sets of
  instances
• By many definitions, A, B, and C are thus
  equivalent

45
Siblings in a Class Hierarchy

• All the siblings in the class hierarchy must be
  at the same level of generality
• Compare to section and subsections in a book

46
The Perfect Family Size (1)

• If a class has only one child, there may be a
  modeling problem
• If the only Red Burgundy we have is Côtes dOr,
  why introduce the subhierarchy?
• Compare to bullets in a bulleted list

47
The Perfect Family Size (2)

• If a class has more than a dozen children,
  additional subcategories may be necessary
• However, if no natural classification exists, the
  long list may be more natural

48
Single and Plural Class Names

• A wine is not a kind-of wines
• A wine is an instance of the class Wines

49
Classes and Their Names

• Classes represent concepts in the domain, not
  their names
• The class name can change, but it will still
  refer to the same concept
• Synonym names for the same concept are not
  different classes
• Many systems allow listing synonyms as part of
  the class definition

50
A Completed Hierarchy of Wines
51
Back to the Slots Domain and Range
DOMAIN
RANGE
slot
class
allowed values

• When defining a domain or range for a slot, find
  the most general class or classes
• Consider the flavor slot
• Domain Red wine, White wine, Rosé wine
• Domain Wine
• Consider the produces slot for a Winery
• Range Red wine, White wine, Rosé wine
• Range Wine

52
Defining Domain and Range

• A class and a superclass replace with the
  superclass
• All subclasses of a class replace with the
  superclass
• Most subclasses of a class consider replacing
  with the superclass

53
Inverse Slots

• Maker and
• Producer
• are inverse slots

54
Default Values

• Default value a value the slot gets when an
  instance is created
• A default value can be changed
• The default value is a common value for the slot,
  but is not a required value
• For example, the default value for wine body can
  be FULL

55
Limiting the Scope (1)

• An ontology should not contain all the possible
  information about the domain
• No need to specialize or generalize more than the
  application requires
• No need to include all possible properties of a
  class
• Only the most salient properties
• Only the properties that the applications require

56
Limiting the Scope (2)

• Ontology of wine, food, and their pairings
  probably will not include
• Bottle size
• Label color
• My favorite food and wine
• An ontology of biological experiments will
  contain
• Biological organism
• Experimenter
• Is the class Experimenter a subclass of
  Biological organism?

57
OWL Web Ontology Language
58
Three-layered architecture of the Semantic Web
59
RDF Schema

• RDF
• (very small) commitment to modelling primitives
• but no commitment to domain vocabulary
• RDF Schema
• Define vocabulary for RDF
• Organise this vocabulary in a typed hierarchy
• Class, SubClassOf, type
• Property, subPropertyOf,
• domain, range

60
State-of-the-art in W3C

• RDF to represent meta-data
• RDF-S to define vocabulary for RDF
• RDF is data-model syntax
• only a very weak semantic interpretation
• no inference model
• RDF-S goes a step further, but still
• no precisely described meaning
• no inference model

61
Quote from Ora Lassila (RDF)

• Future We Need More!
• Structural modeling obviously not enough
• we need a logic layer on top of RDF
• some type of description logic is a possibility
  (after all, we are talking about frame systems)
• Exposing a wide variety of data sources as RDF is
  useful, particularly if we have logic/rules which
  allow us to draw inference from this data
• My proposal RDF DL Frame System for WWW

62
Quote from Henry Thompson
The Semantic Web needs a logic on top
OIL modeling primitives from frames semantics
and inference from Description Logic syntax from
RDF(S) XML(S)
63
OIL Ontology Inference Layer
Description Logics formal semantics
automated reasoning support
Frames modeling primitives
Web languages XML RDF based syntax, RDFS
mapping
64
Defining a More Expressive Ontology Language (1)

• The RDF schema mechanism can be used to define
  elements of OIL

65
Defining a More Expressive Ontology Language (2)

• Defining herbivore as subclass-of animal, NOT
  carnivore

66
OIL Extends Frame Languages (1)

• Classes can be primitive (necessary conditions)
• elephant ? animal that has-colour grey
• or defined (necessary and sufficient conditions)
• vegetarian ? person who eats meat nor fish
• Classes allowed in slot constraints
• slot-constraint eats has-value meat (eats some
  meat)
• slot-constraint eats value-type meat (eats only
  meat)

67
OIL Extends Frame Languages (2)

• Can use arbitrary class expressions instead of
  only class names
• slot-constraint eats value-type NOT (OR meat
  fish)
• Cardinality constraints can include value-types
• slot-constraint eats max-cardinality 1 plant
• Supports sub-slot relation
• daughter-of sub-slot of child-of
• Slot properties
• transitive (e.g., part-of )
• symmetrical (e.g., connected-to)

68
OIL as RDFS Extension
69
OIL (explained by example)
class-def animal animals are a class class-def
plant plants are a class subclass-of NOT
animal that is disjoint from animals class-def
tree subclass-of plant trees are a type
of plants class-def branch slot-constraint
is-part-of branches are parts of some tree
has-value tree max-cardinality
1 class-def defined carnivore carnivores are
animals subclass-of animal
slot-constraint eats that eat any other
animals value-type animal class-def
defined herbivore herbivores are
animals subclass-of animal, NOT carnivore
that are not carnivores, and slot-constraint
eats they eat plants or parts of
plants value-type plant OR
(slot-constraint is-part-of has-value plant)
70
OIL as RDF(S) extension
ltrdfsClass rdfIDherbivoregt ltrdftype
rdfresourcehttp//www.ontoknowledge.org/
DefinedClass/gt ltrdfssubClassOf
rdfresourceanimal/gt ltrdfssubClassOfgt
ltoilNOTgt ltoilhasOperand
rdfresourcecarnivore/gt lt/oilNOTgt
lt/rdfssubClassOfgt lt/rdfsClassgt
71
Class Definition in OIL

• class-def associates a class name with a class
  description
• The class description consists of
• the type of the definition (either primitive,
  which means that the stated conditions for class
  membership are necessary but not sufficient, or
  defined, which means that these conditions are
  both necessary and sufficient)
• a subclass-of statement
• zero or more slot-constraints

72
Subclass Definition in OIL

• The value of a subclass-of statement is a (list
  of) class-expression(s), which can be either
• a class name,
• a slot-constraint,
• a Boolean combination of class expressions using
  the operators AND, OR and NOT, with the standard
  DL semantics.

73
Slot-Constraints in OIL (1)

• A slot-constraint (a slot may also be called a
  role or an attribute) is a list of one or more
  constraints (restrictions) applied to a slot.
  Typical constraints are
• has-value (class-expr)
• value-type (class-expr)
• max-cardinality n (class-expr)

74
Slot-Constraints in OIL (2)

• has-value (class-expr)
• Every instance of the class defined by the slot
  constraint must be related, via the slot
  relation, to an instance of each class expression
  in the list

75
Slot-Constraints in OIL (3)

• value-type (class-expr)
• If an instance of the class defined by the
  slot-constraint is related via the slot relation
  to some individual x, then x must be an instance
  of each class-expression in the list

76
Slot-Constraints in OIL (4)

• max-cardinality n (class-expr)
• An instance of the class defined by the
  slot-constraint can be related to at most n
  distinct instances of the class-expression via
  the slot relation (also min-cardinality and, as a
  shortcut for both min and max, cardinality)

77
Slot Definition in OIL

• A slot definition (slot-def) associates a slot
  name with a slot definition. A slot definition
  specifies global constraints that apply to the
  slot relation. A slot-def can consist of
• a subslot-of statement,
• domain and range restrictions,
• additional qualities of the slot
• inverse,
• transitive,
• symmetric.

78
Namespaces for OIL

• lt?xml version'1.0'?gt
• ltrdfRDF
• xmlnsrdf"http//www.w3.org/1999/02/22-rdf
  -syntax-ns"
• xmlnsrdfs"http//www.w3.org/TR/1999/PR-rd
  f-schema-19990303"
• xmlnsoil"http//www.ontoknowledge.org/oil
  /rdfschema"
• xmlnsdc"http//purl.org/dc/elements/1.1/"
  
• xmlnsdcq"http//purl.org/dc/qualifiers/1.
  1/"
• lt!-- The ontology defined in OIL with RDFS
  syntax--gt
• lt/rdfRDFgt

79
RuleBase Class in OIL

• ltrdfsClass rdfID"RuleBase"gt
• ltrdfscommentgt
• A user-defined rulebase possibly
  described
• by an external RDF-Schema
• lt/rdfscommentgt
• ltrdfssubClassOf rdfresource
• "http//www.w3.org/TR/1999/PR-rdf-
  schema-19990303Resource"/gt
• lt/rdfsClassgt

80
RuleBase Class Example

• ltrdfDescription xmlnssyllogism"http//old.greec
  e/syllogism/"gt
• ltrdftype rdfresource
• "http//www.ontoknowledge.o
  rg/oil/rdfschemaRuleBase"/gt
• ltsyllogismpremisegt
• if it rains, you get
  wet
• lt/syllogismpremisegt
• ltsyllogismfactgt
• it rains
• lt/syllogismfactgt
• ltsyllogismconclusiongt
• you get wet
• lt/syllogismconclusiongt
• lt/rdfDescriptiongt

81
Class Definitions in OIL (1)

• OIL primitive RDFS syntax type
• 
  
• class-def rdfsClass class
• subclass-of rdfssubClassOf property
• class-expression oilClassExpression class
• 
  (placeholder only)
• AND oilAND class
• 
  (subclass of ClassExpression)
• OR oilOR class
• 
  (subclass of ClassExpression)
• NOT oilNOT class
• 
  (subclass of ClassExpression)

82
Class Definitions in OIL (2)

• OIL primitive RDFS syntax type
• 
  
• slot-constraint oilSlotConstraint class
• 
  (placeholder only)
• oilhasSlotConstraint property
• 
  (rdftype of rdfsConstraintProperty)
• 
  oilNumberRestriction class
• 
  (placeholder only)
• 
  (subclass of oilSlotConstraint)
• has-value oilHasValue class
• 
  (subclass of oilSlotConstraint)
• value-type oilValueType class
• 
  (subclass of oilSlotConstraint)

83
Class Definitions in OIL (3)

• OIL primitive RDFS syntax type
• 
  
• max-cardinality oilMaxCardinality class
• 
  (subclass of oilNumberRestriction)
• min-cardinality oilMinCardinality class
• 
  (subclass of oilNumberRestriction)
• cardinality oilCardinality class
• 
  (subclass of oilNumberRestriction)

84
Example of OIL Definition

• has-part is inverse to is-part-of
• is in RDFS
• ltrdfProperty rdfID"has-part"gt
• ltrdftype rdfresource
• "http//www.ontoknowledge.org/oil/rdfschema/Trans
  itiveRelation"/gt
• ltoilinverseRelationOf rdfresource"is-pa
  rt-of"/gt
• lt/rdfPropertygt

85
OIL as RDF(S) extension
RDF(S)
OIL

• class-def
• subclass-of
• slot-def
• subslot-of
• domain
• range

• class-expressions
• AND, OR, NOT
• slot-constraints
• has-value, value-type
• cardinality
• slot-properties
• trans, symm

86
Web Ontology Language OWL
87
Outline

• Clarification
• What are Ontologies?
• Revisited
• How we already have learned to express ontologies
• Web Ontology Language -OWL
• extending expressivity
• Semantics of Reasoning with OWL
• using the extended expressivity

88
Clarification What are Ontologies?

• Ontology in Philosophy
• The metaphysical study of the nature of being
  and existence
• Ontology in Artificial Intelligence
• a shared and common understanding of some domain
  that can be communicated between people and
  application systems (Gruber)

89
Clarification What are Ontologies?

• Ontology (languages) for the Semantic Web
• We aim at a (XML-based) language to formally
  describe concepts, instances, relations and
  axioms, i.e. datastructure in order to enable
  machine-processable reasoning on and exchange of
  data.
• ? Knowledge representation, exchange, combination
  (inference of new knowledge!)

90
Whats inside an ontology?

• Concepts Classes class-hierarchy
• instances
• Properties often also called Roles or Slots
• labeled instance-value-pairs
• Axioms/Relations
• relations between classes (disjoint, covers)
• inheritance (multiple? defaults?)
• restrictions on slots (type, cardinality)
• Characteristics of slots (symm., trans., )
• reasoning tasks
• Classification Which classes does an instance
  belong to?
• Subsumption Does a class subsume another one?
• Consistency checking Is there a contradiction in
  my axioms/instances?

91
Use Cases for ontologies (from OWL requirements
doc.)

• Web portal
• ontology-based, portal for a community of users
  which have shared interest
• Multi-media collections
• annotating, searching, ontological search instead
  of keyword search
• Corporate Website
• knowledge management
• Documentation
• engineering design
• Agents Services, Ubiquitous computing
• Interoperability!

92
Outline

• Clarification
• What are Ontologies?
• Revisited
• How we already have learned to express ontologies
• Web Ontology Language -OWL
• extending expressivity
• Semantics of Reasoning with OWL
• using the extended expressivity

93
RDF/RDFS
Vehicle
producedBy
Company
subClassOf
subClassOf
SeaVehicle
LandVehicle
subClassOf
subClassOf
NumberOfEngines
Hovercraft
Number

• Recall from last lecture RDF RDFS
• RDF triples for making assertions about
  resources
• RDFS extends RDF with schema vocabulary, e.g.
• Class, Property
• type, subClassOf, subPropertyOf
• range, domain
• ? representing simple assertions, taxonomy
  typing

94
RDFSLimitations of RDFS

• RDFS too weak to describe resources in sufficient
  detail
• No localised range and domain constraints
• Cant say that the range of hasChild is person
  when applied to persons and elephant when applied
  to elephants
• No existence/cardinality constraints
• Cant say that all instances of person have a
  mother that is also a person, or that persons
  have exactly 2 parents
• No transitive, inverse or symmetrical properties
• Cant say that isPartOf is a transitive property,
  that hasPart is the inverse of isPartOf or that
  touches is symmetrical
• No in/equality
• Cant say that a class/instance is the same as
  some other class/instance, cant say that somthe
  classes/instances are definitely
  disjoint/different.
• No boolean algebra
• Cant say that that one class is the union,
  intersection, complement of other classes, etc.

95
(In)famous Layer Cake
? Semanticsreasoning
OWL
?
? Relational Data
? Data Exchange
96
Outline

• Clarification
• What are Ontologies?
• Revisited
• How we already have learned to express ontologies
• Web Ontology Language -OWL
• extending expressivity
• Semantics of Reasoning with OWL
• using the extended expressivity

97
OWL-RDFS Relationship

• Both use the same data model
• OWL extends vocabulary and adds axioms

hasAuthor
page.html
Dieter Fensel
Resource (subject)
Property (predicate)
Value (object)
98
Origins of OWL
DAML
OIL
RDF
DAMLOIL
OWL
99
History

• Two languages developed to satisfy above
  requirements
• OIL (Object Inference Layer) developed by group
  of (largely) European researchers (several from
  EU OntoKnowledge project)
• DAML-ONT developed by group of (largely) US
  researchers (in DARPA DAML programme)
• Efforts merged to produce DAMLOIL
• Development was carried out by Joint EU/US
  Committee on Agent Markup Languages
• Extends (DL subset of) RDF
• DAMLOIL submitted to W3C as basis for
  standardisation
• Web-Ontology (WebOnt) Working Group formed
• WebOnt group developed OWL language based on
  DAMLOIL
• OWL language now a W3C Recommendation
  (01.02.2004)

100
OWL Language - Overview
Full

• Three species of OWL
• OWL DL stays in Description Logic fragment
• OWL Lite is easier to implement subset of OWL
  DL
• OWL Full is union of OWL syntax and RDF
• OWL DL based on SHIQ Description Logic
• In fact it is equivalent to SHOIN(Dn) DL
• OWL DL Benefits from many years of DL research
• Well defined semantics
• Formal properties well understood (complexity,
  decidability)
• Known reasoning algorithms
• Implemented systems (highly optimised)
• OWL full has all that and all the possibilities
• of RDF/RDFS which destroy decidability

DL
Lite
Syntactic layering Semantic layering
101
Description Logic Family

• DLs are a family of logic based KR formalisms
• Particular languages mainly characterized by
• Set of constructors for building complex concepts
  and roles from simpler ones
• Set of axioms for asserting facts about concepts,
  roles and individuals
• Examples
• Female persons
• Person ? Female
• Non-female persons
• Person ? ?Female
• Persons that have a child
• Person ? ?hasChild.Person
• Persons all of whose children are female
• Person ? ?hasChild.Female
• Persons that are employed or self-eployed
• Person ? (Employee ? SelfEmployed)
• Persons the have at most one father
• Person ? 1.hasFather

102
Description Logic Family Necessary and
sufficient conditions

• Inclusion axioms provide necessary conditions
• concept ? definition
• Equivalence axioms provide necessary and
  sufficient conditions

concept definition
concept ? definition and definition ? concept
103
Description LogicVocabulary and Semantics
Dom Domain I Interpretation
T (T)I Dom (a class which ANY legal instance is a member of owlThing)
- (-)I
?C (?C)I Dom\CI
C ? D (C ? D)I CI ? DI
C ? D (C ? D)I CI ? DI
?R.C (?R.C)I x (x,y) ? RI ? y ? CI
?R.C (?R.C)I x (x,y) ? RI ? y ? CI
?nR.C (?nR.C)I x y (x,y) ? RI ? y ? CI ? n
?nR.C (?nR.C)I x y (x,y) ? RI ? y ? CI ? n
nR.C (nR.C)I x y (x,y) ? RI ? y ? CI n
?nR (?nR)I x y (x,y) ? RI ? n
?nR (?nR)I x y (x,y) ? RI ? n
nR (nR)I x y (x,y) ? RI n
104
Describing Classes in OWL
105
Classes OWL vs. RDFS

• OWL allows greater expressiveness, but
• OWL (DL/Lite) puts certain constraints on the use
  of RDF
• For instance a class may not act as an instance
  of another (meta)class (the same holds for
  properties)
• ? OWL has got its own Class identifier

RDFS
OWL
ltowlClass rdfID"River"gt
ltrdfssubClassOf rdfresource"Stream"/gt lt/owlCl
assgt
ltrdfsClass rdfID"River"gt
ltrdfssubClassOf rdfresource"Stream"/gt lt/rdfsC
lassgt
106
Class Description RDF constructs

• What can you express in RDF/RDFS?
• Not too much
• rdfssubClassOf class hierarchy, necessary
  conditions (also equivalence is expressible
  because A ? B and B ? A ? A B)
• rdftype class membership
• OWL provides more expressive constructs to
  express
• the DL features!

Employee ? Person
Employee(axel)
107
Complex ClassesUnion of Classes

• Instances of the Union of two Classes are either
  the instance of one or both classes

Person Man ? Woman
ltowlClass rdfIDPerson"gt ltowlunionOf
rdfparseType"Collection"gt ltowlClass
rdfabout"Woman" /gt ltowlClass
rdfabout"Man" /gt lt/owlunionOfgt
lt/owlClassgt
108
Complex ClassesIntersection of Classes

• Instances of the Intersection of two Classes are
  simultaneously instances of both class

Man Person ? Male
ltowlClass rdfIDMan"gt ltowlintersectionOf
rdfparseType"Collection"gt ltowlClass
rdfabout"Person" /gt ltowlClass
rdfabout"Male" /gt lt/owlintersectionOfgt
lt/owlClassgt
109
one of Enumerated Classes

• Specify a class via a direct enumeration of its
  members

WhineColor White, Rose, Red
ltowlClass rdfID"WineColor"gt ltrdfssubClassOf
rdfresource"WineDescriptor"/gt ltowloneOf
rdfparseType"Collection"gt ltowlThing
rdfabout"White"/gt ltowlThing
rdfabout"Rose"/gt ltowlThing
rdfabout"Red"/gt lt/owloneOfgt lt/owlClassgt
110
Necessary vs. necessary and sufficient conditions
in OWL

• Necessary condition (?) via
• rdfssubclass
• Necessary and sufficient () either by
• ? ?, i.e. 2 subclass definitions or
• owlequivalentClass

111
Complex Classes Property Restrictions

• Defining a Class by restricting its possible
  instances via their property values
• OWL distinguishes between the following two
• Value constraint
• (Mother Woman ? ?hasChild.Person)
• Cardinality constraint
• (MotherWithManyChildren Mother ? 3hasChild)
• Property restrictions are local
• remember RDFS allows only global properties

112
Complex Classes - Property Restrictions
someValuesFrom

• A Mother is a Woman that has a child (some
  Person)

Mother ? Woman ? ?hasChild.Person

• ltowlClass rdfIDMother"gt
• ltrdfssubClassOf rdfresource"Woman" /gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasChild"
  /gt
• ltowlsomeValuesFrom rdfresource"Person"
  /gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/owlClassgt

113
Complex Classes - Property Restrictions
allValuesFrom

• To express the set of parents that only have
  female children (daughters) you would write

ParentsWithOnlyDaughters ? Person ?
?hasChild.Woman

• ltowlClass rdfIDParentsWithOnlyDaughters"gt
• ltrdfssubClassOf rdfresource"Person" /gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasChild"
  /gt
• ltowlallValuesFrom rdfresource"Woman"
  /gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• ...
• lt/owlClassgt

114
Complex Classes - Property Restrictions hasValue

• hasValue allows to define classes based on the
  existence of particular property values, their
  must be at least one matching property value
• The set of all childs of the woman MARY would be
  expressed like following

MarysChildren ? Person ? hasParent.MARY

• ltowlClass rdfIDMarysChildren"gt
• ltrdfssubClassOf rdfresource"Person" /gt
• ltrdfssubClassOfgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasParent"
  /gt
• ltowlhasValue rdfresource"MARRY" /gt
• lt/owlRestrictiongt
• lt/rdfssubClassOfgt
• lt/rdfssubClassOfgt
• ...
• lt/owlClassgt

115
Complex Classes - Property Restrictions
cardinality

• Definition of cardinality the number of
  occurrences, either maximum (maxCardinality) or
  minimum (minCardinality) or exact (cardinality)
  based upon the context (class) in which it is
  used
• To define a half-orphan (Halbwaise) you would
  write the following

HalfOrphan ? Person ? 1hasParent.Person
ltowlClass rdfIDHalfOrphan"gt
ltrdfssubClassOf rdfresource"Person" /gt
ltrdfssubClassOfgt ltowlRestrictiongt
ltowlonProperty rdfresource"hasParent"/gt
ltowlcardinality rdfdatatype"xsdNonNegativ
eInteger"gt1lt/owlcardinalitygt
lt/owlRestrictiongt lt/rdfssubClassOfgt
lt/rdfssubClassOfgt lt/owlClassgt
116
Classes as Restrictions on Properties

• In summarydefine a class using LOCAL
  restrictions on a specific Property

rdfsClass
owlClass
owlRestriction

• Properties
• allValuesFrom rdfsClass (lite/DL owlClass)
• hasValue specific Individual
• someValuesFrom rdfsClass (lite/DL owlClass)
• cardinality xsdnonNegativeInteger (in lite
  0,1)
• minCardinality xsdnonNegativeInteger (in lite
  0,1)
• maxCardinality xsdnonNegativeInteger (in lite
  0,1)

117
Describing Properties in OWL
118
Properties OWL vs. RDF

• RDF Schema provides a couple of pre defined
  properties
• rdfsrange used to indicate the range of values
  for a property.
• rdfsdomain used to associate a property with a
  class.
• rdfssubPropertyOf used to specialize a property.
• OWL provides additional poperty classes, which
  allow reasoning and inferencing, i.e.
• owlfunctionalProperty
• owltransitiveProperty
• owlsymetricProperty

119
Properties OWL vs. RDF

• OWL (DL and Lite) distinguishes between data type
  ptoperties and object properties (RDFS does not)

An ObjectProperty relates one Resource to another
Resource
ObjectProperty
Resource
Resource
A DatatypeProperty relates a Resource to a
Literal or an XML Schema data type
DatatypeProperty
Resource
Value
120
Why separate Classes and Datatypes?

• Philosophical reasons
• Datatypes structured by built-in predicates
• Not appropriate to form new datatypes using
  ontology language
• Practical reasons
• Ontology language remains simple and compact
• Semantic integrity of ontology language not
  compromised
• Implementability not compromised can use hybrid
  reasoner

121
Datatype Properties Example

• for instance, usage of XSD dattypes
• object properties in OWL allow for some more
  sophisticated definitions than only domain and
  range, see following slides

ltowlDatatypeProperty rdfID"yearValue"gt
ltrdfsdomain rdfresource"VintageYear" /gt
ltrdfsrange rdfresource"xsdpositiveInteger"/gt
lt/owlDatatypePropertygt
122
Properties in OWLTransitive Property

• Example If person A is a ancestor of person B
  and B of C then A is also an ancestor of C.

ancestor ? ancestor
ltowlObjectProperty rdfIDancesotor"gt
ltrdftype rdfresource"owlTransitiveProperty"
/gt ltrdfsdomain rdfresource"Person" /gt
ltrdfsrange rdfresource"Person"
/gt lt/owlObjectPropertygt
123
Properties in OWLSymmetric Property

• Example If Mary is akin to John then John is
  also akin to Mary

akin- ? akin and akin ? akin-
ltowlObjectProperty rdfIDakin"gt ltrdftype
rdfresource"owlSymmetricProperty" /gt
ltrdfsdomain rdfresource"Person" /gt
ltrdfsrange rdfresource"Person"
/gt lt/owlObjectPropertygt
124
Properties in OWLInverse Property

• Example If Mary is a child of John then John is
  the Father of Mary

hasChild ? hasParent-
ltowlObjectProperty rdfIDhasChild"gt
ltowlinverseOf rdfresource"hasParent"
/gt lt/owlObjectPropertygt
125
Properties in OWLFunctional Properties

• A functional property states that the value of
  range for a certain object in the domain is
  always the same
• Example A child has always the same Father
  (biological)

Person ? ?1hasFather
ltowlObjectProperty rdfIDhasFather"gt
ltrdftyoe rdfresource"owlFunctionalProperty"/gt
lt/owlObjectPropertygt
126
OWL Property Classes

• The symmetric and transitive property may only
  used for connecting two resources

127
Summary
128
OWL as DL Axioms
First Order Logic
Description Logic
129
OWL as DL Axioms
Social Security Number
130
Outline

• Revisited
• How we already have learned to express ontologies
• Web Ontology Language -OWL
• extending expressivity
• Reasoning with OWL
• using the extended expressivity

131
Subsumption

• The presented examples contain a number of
  classes and properties intended to illustrate
  particular aspects of reasoning in OWL.
• We can make inferences about relationships
  between classes, in particular subsumption
  between classes
• Recall that A subsumes B when it is the case that
  any instance of B must necessarily be an instance
  of A.

A
B
132
Subsumption An Example

• Woman Person ? Female
• Man Person ? ?Woman
• Mother Woman ? ?hasChild.Person
• Father Man ? ?hasChild.Person
• Parent Father ? Mother
• Grandmother Mother ? ?hasChild.Parent
• We can further infer (though not explicitly
  stated)
• ? Grandmother ? Person
• Grandmother ? Man ? Woman
• etc.

133
Subsumption Example in Protégé
134
Subsumption Inferred Hierarchy in Protégé
135
Inconsistency

• You may define Classes were no individual can
  fulfill its definition. Via reasoning engines
  such a definition can be found also in big
  ontologies.

136
Inconsistency Example

• Cow Animal ? Vegetarian
• Sheep ? Animal
• Vegetarian ?eats ? Animal
• MadCow Cow ? ?eats.Sheep

137
Inconsistency Example in Protégé
138
Inconsistency Detected Inconsistency in Protégé
139
Some more aspects of Reasoning in OWL

• Open world assumption
• No unique name assumption

140
Open world assumption (OWA)

• In Database Systems, usually the closed world
  assumption is made The fact in the databases
  describe completely what I know, all that is not
  in the database is assumed to be false.
• This assumption is usually not valid in an open
  context such as the web!
• Example resource1 says There is a train at
  1400
• There is a train at 1500
• My query Is there a train at 1700?
• CWA answer No!
• OWA answer unknown! (i.e. there could be another
  resource2 which has info on another train at
  1700!)
• Reasoning in OWL is OWL! Assume we have an RDF
  file with the following triples
• T1 rdftype Train .
• T2 rdftype Train .
• T1 departureTime 1500 .
• T1 departureTime 1500 .

141
No unique name assumption

• What does it mean? E.g. A Child has two parents,
  but Marry hasParents John Doe, Lissa Doe, Lissa
  Minelly??
• Some facts
• familyMarry rdftype familyperson.
• familyMarry exhasParent familyJohnDoe.
• familyMarry exhasParent familyLissaDoe.
• familyMarry exhasParent familyLissaMinelly.
• Some cardinality axiom (in DL)
• familyperson ? ?2 hasParent.T
• There is no unique name assumption, this means
  that JohnDoe, LissaDoe and LissaMinelly are not
  necessarily different objects.
• Three possible options which can be inferred
  from the above example
• familyLissaDoe familyLissaMinelly
• familyJohnDoe familyLissaMinelly
• familyJohnDoe familyLissaMinelly

142
Individual Identity and Mapping

• To explicitly state that individuals are
  different
• owldifferentFrom(between 2 individuals)
• owlallDifferent(between a set of individuals)
• To explicitly state that two individuals are
  identical
• owlsameIndividualAs / owlsameAS
• To explicitly state that two classes are
  identical
• owlequivalentClass
• To explicitly state that two properties are
  identical
• owlequivalentProperty

143
OWL on one Slide

• Symmetric if P(x, y) then P(y, x)
• Transitive if P(x,y) and P(y,z) then P(x, z)
• Functional if P(x,y) and P(x,z) then yz
• InverseOf if P1(x,y) then P2(y,x)
• InverseFunctional if P(y,x) and P(z,x) then yz
• allValuesFrom P(x,y) and yallValuesFrom(C)
• someValuesFrom P(x,y) and ysomeValuesFrom(C)
• hasValue P(x,y) and yhasValue(v)
• cardinality cardinality(P) N
• minCardinality minCardinality(P) N
• maxCardinality maxCardinality(P) N
• equivalentProperty P1 P2
• intersectionOf C intersectionOf(C1, C2, )
• unionOf C unionOf(C1, C2, )
• complementOf C complementOf(C1)
• oneOf C one of(v1, v2, )
• equivalentClass C1 C2
• disjointWith C1 ! C2
• sameIndividualAs I1 I2

Legend Properties are indicated by P, P1, P2,
etc Specific classes are indicated by x, y,
z Generic classes are indicated by C, C1,
C2 Values are indicated by v, v1, v2 Instance
documents are indicated by I1, I2, I3, etc. A
number is indicated by N P(x,y) is read as
property P relates x to y
144
Back to the OWL Layers (Lite, DL, Full)
Full
DL
Lite
145
Meta Information in OWL
146
Imports

• Since OWL makes an open world assumption it is
  possible to extend/import classes from other
  ontologies
• Consequences of additional propositions are
  monotonic
• New information can not retract existing (but may
  be contradictory, i.e. cause inconsistency)
• owlimports imports another ontology in the sense
  that it becomes part of the ontology doing the
  import
• owlimports is transitive
• (if A imports B and B imports C, A import B and
  C)
• Note Import is different to just declare a
  namespace and reference to i.e. a concept, since
  this does not imply to import associated
  constraints

147
Versioning

• owlversionInfo provides a construct to include
  version information but has no impact on model
  theory
• owlpriorVersion, owlbackwardCompatibleWith and
  owlincompatibleWith can be used to track changes
  and reference other ontologies
• owlDeprecatedClass and owlDeprecatedProperty
  allow versioning on a high level of granularity

148
Things OWL doesnt do

• default values
• closed world option
• arithmetic
• string operations
• involved axioms on axiom values, such
• as functional dependencies
• partial imports
• view definitions (it is not a query language)
• procedural attachment

149
Summary

• Compared with RDF/RDFS, OWL provides a more
  formal language which allows expressing more
  axioms, but also adds some restrictions
• We can do inferences such as classify instances,
  detect inconsistencies, etc.
• Last version Feb. 2004, but still under progress
• http//www.w3.org/2004/OWL/

150
Resources

• W3C Documents
• Guide http//www.w3.org/TR/owl-guide/
• Reference http//www.w3.org/TR/owl-ref/
• Semantics and Abstract Syntaxhttp//www.w3.org/T
  R/owl-semantics/
• OWL Tutorials
• Ian Horrocks, Sean Bechhoferhttp//www.cs.man.ac
  .uk/horrocks/Slides/Innsbruck-tutorial/
• Roger L. Costello, David B. Jacobs
  http//www.xfront.com/owl/
• Example Ontologies, e.g. here
• http//www.daml.org/ontologies/