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 symmetric  Transitive 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 –

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 them Example, Patient “John” does not live in “Povo” NegativeDataPropertyAssertion – An individual – A literal – A property does not hold between them Example, “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 " " ) 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,  D. Allemang and J. Hendler. Semantic web for the working ontologist: modeling in RDF, RDFS and OWL. Morgan Kaufmann Elsevier, Amsterdam, NL, 2008.