1. Logics for Data and Knowledge Representation
Web Ontology Language (OWL)
Feroz Farazi 1

2. OWL
Web Ontology Language designed to be used when the document content is necessary to be processed by applications instead of making it understandable only by humans [OWL Overview]
It can be used to represent ontology
Vocabulary terms and the relationships between them
Concepts and relations between them
Provides more facilities than RDF and RDF Schema
In the representation of semantics
In performing reasoning tasks

3. OWL Sublanguages There are three sublanguages of OWL OWL Lite supports
OWL Lite: trades expressivity for efficiency
OWL DL: a balance between expressivity and computational completeness
OWL Full: trades computational completeness for expressivity
OWL Lite supports
Encoding simple classification hierarchy (e.g., taxonomy and thesaurus)
Assigning cardinality constraints 0 or 1
OWL DL supports
More expressive than OWL Lite while guarantees conclusions and decidability
Using all OWL constructs, some of them with certain restrictions
The restriction of not making a class an instance of another class

4. OWL Sublanguages
OWL DL is named so because of its connection with description logics, which form the formal basis of OWL
OWL Full
an extension of RDF with maximum expressiveness, e.g., a class can be represented also as an individual
For these sublanguages the following statements can be made:
Each OWL Lite representation belongs to OWL DL
Each OWL DL representation belongs to OWL Full
Each valid OWL Lite conclusion is also valid in OWL DL
Each valid OWL DL conclusion is also valid in OWL Full

5. OWL Lite
In OWL Lite
users are allowed to use a subset of the OWL, RDF and RDFS vocabulary
to define a class, one must use the OWL construct owl:Class
OWL constructs, namely: complementOf, disjointWith, hasValue, oneOf and unionOf are not allowed
Some OWL Constructs are allowed to use but their use is limited
all three cardinality constructs – cardinality, maxCardinality and minCardinality, can only have 0 or 1 in their value fields
Moreover, equivalentClass and intersectionOf cannot be used in a triple if the subject or object represents an anonymous class

6. OWL DL In OWL DL Each individual must be an extension of a class
Even if an individual cannot be classified under any user defined class, it must be classified under the general owl:Thing class
Individuals can not be used as properties, and vice versa
Moreover, properties can not be used as classes, and vice versa
It is allowed to use the intersectionOf construct with any number of classes and of any non negative integer in the cardinality restrictions value fields
The computational complexity is the same as the corresponding Description Logic

7. Properties
Inverse
Given that a property P is inverse of another property Q,
P owl:inverseOf Q, and two individuals x and y are connected using P as follows: x P y. We can infer that y Q x.
For example, the property hasChild can be an inverse property of hasParent
Symmetric
Given that a property P is symmetric,
P rdf:type owl:symmetricProperty, two individuals x and y are connected using P as follows: x P y. We can infer that y P x.
For example, the property isMarriedTo is symmetric
Transitive property is used with owl:TransitiveProperty

8. Properties Functional Property Equivalent Property
In RDFS, x rdfs:subPropertyOf y
y rdfs:subPropertyOf x
In OWL, x owl:equivalentProperty y
For example, buy and purchase can be equivalent properties
Functional Property
A functional property can have only one value attached to it for any individual
Given that a property P is functional,
P rdf:type owl:FunctionalProperty, the individuals x, y and z are connected using P as follows: x P y and x P z. We can infer that y owl:sameAs z.
For example, the property hasMother is functional

9. Properties Used Inverse Functional Property
An inverse functional property can have only one individual as a subject attached to it for any value
Given that a property P is inverse functional,
P rdf:type owl:InverseFunctionalProperty, the individuals x, y and z are connected using P as follows: x P y and z P y. We can infer that x owl:sameAs z.
For example, the property motherOf is inverse functional
Used
Especially in settings where data come from multiple sources
In entity matching on the Semantic Web

10. OWL 2 OWL 2: The new features of OWL 2 based on: Extends OWL 1
Inherits OWL 1 language features
The new features of OWL 2 based on:
Real applications
User experience
Tool developer experience

11. Features and Rationale
Syntactic sugar
New constructs for properties
Extended datatypes
Punning
Extended annotations
Some innovations
Minor features

12. Features and Rationale
Syntactic sugar
Makes some patterns easier to write
Does not change
Expressiveness
Semantics
Complexity
Can help implementations
For more efficient processing

13. Features and Rationale
Syntactic sugar:
DisjointUnion
DisjointClasses
NegativeObjectPropertyAssertion
NegativeDataPropertyAssertion
Union of a set of classes
All the classes are pairwise disjoint

14. Syntactic sugar Need for disjointUnion construct
A :CarDoor is exclusively either
a :FrontDoor,
a :RearDoor or
a:TrunkDoor
and not more than one of them
A disjointUnion example
<owl:Class rdf:about="CarDoor">
<owl:disjointUnionOf rdf:parseType="Collection"> <rdf:Description rdf:about="FrontDoor"/> <rdf:Description rdf:about="RearDoor"/> <rdf:Description rdf:about="TrunkDoor"/> </owl:disjointUnionOf>
</owl:Class>

15. Syntactic sugar DisjointClasses Need for DisjointClasses
A set of classes
All the classes are pairwise disjoint
Need for DisjointClasses
Nothing can be both
A LeftLung and
A RightLung

16. Syntactic sugar NegativeObjectPropertyAssertion
Two individuals
A property does not hold between them
Example, Patient “John” does not live in “Povo”
NegativeDataPropertyAssertion
An individual
A literal
Example, “John” is not “5” years old.

17. New constructs for properties
Self restriction
Qualified cardinality restriction
Object properties
Disjoint properties
Property chain
keys

18. Self restriction
Classes of objects that are related to themselves by a given property
For example, the class of processes that regulate themselves
It is also called local reflexivity
An example: Auto-regulating processes regulate themselves

19. Qualified cardinality restrictions
Qualifies the instances to be counted
Restrain the class or data range of the instances to be counted
For example,
Persons that have exactly three children who are girls
Each individual has at most one SSN

20. Qualified cardinality restrictions
ObjectMinCardinality
ObjectMaxCardinality
ObjectExactCardinality
DataMinCardinality
DataMaxCardinality
DataExactCardinality

21. Object properties ReflexiveObjectProperty IrreflexiveObjectProperty
Globally reflexive
Everything is part of itself
IrreflexiveObjectProperty
Nothing can be a proper part of itself
AsymmetricObjectProperty
If x is proper part of y, then the opposite does not hold

22. Disjoint propertis DisjointObjectProperties DisjointDataProperties
Deals with object properties
Pairwise disjointness can be asserted
E.g., connectedTo and contiguousWith
DisjointDataProperties
Deals with data properties
E.g., startTime and endTime of a surgery

23. Property chain inclusion
Properties can be defined as a composition of other properties
If disease A is locatedIn body part B and B is part of body part C then A is locatedIn C
SubPropertyOf ( ObjectPropertyChain( :locatedIn :partOf) :locatedIn)

24. Keys Individuals can be identified uniquely
Identification can be done using
A data property
An object property or
A set of properties
HasKey( :RegisteredPatient :hasWaitingListN )
ClassAssertion( :RegisteredPatient :ThisPatient )
DataPropertyAssertion( :hasWaitingListN :ThisPatient " " )
HasKey( :Transplantation :donorId :recipientId :ofOrgan )

25. Features and Rationale
Syntactic sugar
New constructs for properties
Extended datatypes
Punning
Extended annotations
Some innovations
Minor features

26. Extended datatypes Extra datatypes Datatype restrictions
For example, owl:real and owl:rational
Datatype restrictions
Range of datatypes
For example, adult has an age >= 18
DatatypeRestriction(xsd:integer minInclusive 18)
Datatype definitions
New datatypes
DatatypeDefinition( :adultAge DatatypeRestriction(xsd:integer minInclusive 18))

27. Extended datatypes Data range combinations Intersection of Union of
DataIntersectionOf( xsd:nonNegativeInteger xsd:nonPositiveInteger )
Union of
DataUnionOf( xsd:string xsd:integer )
Complement of data range
DataComplementOf( xsd:positiveInteger )

28. Punning Punning: “What's black and white and red all over?”
Classes and individuals can have the same name thanks to punning
E.g., Eagle as a class and as an individual
Properties and individuals can have the same name
E.g., is_located_in as a property and as an individual of the class Deprecated_Properties

29. Punning Classes and object properties also can have the same name
But classes and datatype properties can not have the same name
Also datatype properties and object properties can not have the same name

30. Features and Rationale
Extended Annotations
Axioms can be annotated
For example, SubClassOf( Annotation( rdfs:comment "Middle lobes of lungs are necessarily right lobes since left lungs do not have middle lobe.") :MiddleLobe :RightLobe )
Innovations
Top and Bottom properties
IRI: Internationalized Resource Identifier

31. Features and Rationale
Inverse object properties:
some object property can be inverse of another property
For example, partOf and hasPart
ObjectInverseOf( :partOf ): this expression represents the inverse property of :partOf
This makes writing ontologies easier by avoiding the need to name an inverse

32. Profiles Profiles are sublanguages of OWL 2 Profiles considered
Useful computational properties, e.g., reasoning complexity
Implementation possibilities, e.g., using RDBs
There are three profiles
OWL 2 EL
OWL 2 QL
OWL 2 RL

33. OWL 2 EL
The EL acronym reflects the profile’s basis in the EL family of description logics
This logic is also called small description logic (DL) EL
This logic allows for conjunction and existential restrictions
It does not allow disjunction and universal restrictions
It can capture the expressive power used by many large-scale ontologies, e.g., SNOMED CT

34. OWL 2 QL
The QL acronym reflects its relation to the standard relational Query Language
It does not allow existential and universal restrictions to a class expression or a data range
These restrictions
enable a tight integration with RDBMSs,
reasoners can be implemented on top of standard relational databases
Can answer complex queries (in particular, unions of conjunctive queries) over the instance level (ABox) of the DL knowledge base

35. OWL 2 RL The RL acronym reflects its relation to the Rule Languages
OWL 2 RL is desgined to accommodate
OWL 2 applications that can trade the full expressivity of the language for efficiency
RDF(S) applications that need some added expressivity from OWL 2
Existential quantification to a class, union and disjoint union to class expressions are not allowed
These restrictions
allow OWL 2 RL to be implemented using rule-based technologies such as rule extended DBMSs

36. Profiles Profile selection depends on
Expressivenss required by the application
Priority given to reasoning on classes or data
Size of the datasets

37. References OWL Overview (2004). W3C Recommendation.
OWL 2 New Features and Rationale (2009). W3C Recommendation.
F. Giunchiglia, F. Farazi, L. Tanca, and R. D. Virgilio. The semantic web languages. In Semantic Web Information management, a model based perspective. Roberto de Virgilio, Fausto Giunchiglia, Letizia Tanca (Eds.), Springer, 2009.
D. Allemang and J. Hendler. Semantic web for the working ontologist: modeling in RDF, RDFS and OWL. Morgan Kaufmann Elsevier, Amsterdam, NL, 2008.