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Logics for Data and Knowledge Representation
Web Ontology Language (OWL)
Feroz Farazi
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
OWL Sublanguages
There are three sublanguages of OWL 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
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
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
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
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 symmetricTransitive property is used with owl:TransitiveProperty
Properties 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
Properties 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
• OWL 2:– Extends OWL 1– Inherits OWL 1 language features
• The new features of OWL 2 based on:– Real applications– User experience– Tool developer experience
OWL 2
Features and Rationale
• Syntactic sugar• New constructs for properties• Extended datatypes• Punning• Extended annotations• Some innovations• Minor features
Features and Rationale
• Syntactic sugar– Makes some patterns easier to write– Does not change• Expressiveness• Semantics• Complexity
– Can help implementations• For more efficient processing
Features and Rationale
• Syntactic sugar:– DisjointUnion– DisjointClasses– NegativeObjectPropertyAssertion– NegativeDataPropertyAssertion
• DisjointUnion• Union of a set of classes• All the classes are pairwise disjoint
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>
Syntactic sugar
• DisjointClasses– A set of classes– All the classes are pairwise disjoint
• Need for DisjointClasses– Nothing can be both• A LeftLung and• A RightLung
Syntactic sugar
• NegativeObjectPropertyAssertion– Two individuals– A property does not hold between themExample, Patient “John” does not live in “Povo”
• NegativeDataPropertyAssertion– An individual– A literal– A property does not hold between themExample, “John” is not “5” years old.
New constructs for properties
• Self restriction• Qualified cardinality restriction• Object properties• Disjoint properties• Property chain• keys
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
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
Qualified cardinality restrictions
• ObjectMinCardinality• ObjectMaxCardinality• ObjectExactCardinality• DataMinCardinality• DataMaxCardinality• DataExactCardinality
Object properties
• ReflexiveObjectProperty– 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
Disjoint propertis
• DisjointObjectProperties– Deals with object properties– Pairwise disjointness can be asserted– E.g., connectedTo and contiguousWith
• DisjointDataProperties– Deals with data properties– Pairwise disjointness can be asserted– E.g., startTime and endTime of a surgery
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
• SubObjectPropertyOf ( ObjectPropertyChain( locatedIn partOf) locatedIn)
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 "123-45-6789" )
• HasKey( :Transplantation :donorId :recipientId :ofOrgan )
Features and Rationale
• Syntactic sugar• New constructs for properties• Extended datatypes• Punning• Extended annotations• Some innovations• Minor features
Extended datatypes
• Extra datatypes– 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))
Extended datatypes
• Data range combinations– Intersection of• DataIntersectionOf( xsd:nonNegativeInteger
xsd:nonPositiveInteger )
– Union of• DataUnionOf( xsd:string xsd:integer )
– Complement of data range• DataComplementOf( xsd:positiveInteger )
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 Deprecated_Properties class
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
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
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 :part of– This makes writing ontologies easier by avoiding
the need to name an inverse
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
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
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
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
Profiles
• Profile selection depends on– Expressivenss required by the application– Priority given to reasoning on classes or data– Size of the datasets
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.