Logics for Data and Knowledge Representation Web Ontology

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

OWL q 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] q It can be used to represent ontology Ø Vocabulary terms and the relationships between them Ø Concepts and relations between them q Provides more facilities than RDF and RDF Schema Ø In the representation of semantics Ø In performing reasoning tasks

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

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

OWL Lite q In OWL Lite Ø users are allowed to use a subset of the OWL, RDF and RDFS vocabulary Ø to define a class, one must use the OWL construct owl: Class Ø OWL constructs, namely: complement. Of, disjoint. With, has. Value, one. Of and union. Of are not allowed Ø Some OWL Constructs are allowed to use but their use is limited Ø all three cardinality constructs – cardinality, max. Cardinality and min. Cardinality, can only have 0 or 1 in their value fields Ø Moreover, equivalent. Class and intersection. Of cannot be used in a triple if the subject or object represents an anonymous class

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

Properties q Inverse Ø Given that a property P is inverse of another property Q, P owl: inverse. Of Q, and two individuals x and y are connected using P as follows: x P y. We can infer that y Q x. Ø For example, can inverse property an be the has. Child property of has. Parent q Symmetric Ø Given that a property P is symmetric, P rdf: type owl: symmetric. Property, two individuals x and y are connected using P as follows: x P y. We can infer that y P x. Ø For example, the property is. Married. To is symmetric q Transitive property is used with owl: Transitive. Property

Properties q Equivalent Property Ø In RDFS, x rdfs: sub. Property. Of y y rdfs: sub. Property. Of x Ø In OWL, x owl: equivalent. Property y Ø For example, buy and purchase can be equivalent properties q Functional Property Ø A functional property can have only one value attached to it for any individual Ø Given that a property P is functional, P rdf: type owl: Functional. Property, 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: same. As z. Ø For example, the property has. Mother is functional

Properties q Inverse Functional Property Ø An inverse functional property can have only one individual as a subject attached to it for any value Ø Given that a property P is inverse functional, P rdf: type owl: Inverse. Functional. Property, 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: same. As z. Ø For example, the property mother. Of is inverse functional Ø Used Ø Especially in settings where data come from multiple sources Ø In entity matching on the Semantic Web

OWL 2 • 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

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: – Disjoint. Union – Disjoint. Classes – Negative. Object. Property. Assertion – Negative. Data. Property. Assertion • Disjoint. Union • Union of a set of classes • All the classes are pairwise disjoint

Syntactic sugar • Need for disjoint. Union construct – A : Car. Door is exclusively either • • a : Front. Door, a : Rear. Door or a: Trunk. Door and not more than one of them • A disjoint. Union example – <owl: Class rdf: about="Car. Door"> <owl: disjoint. Union. Of rdf: parse. Type="Collection"> <rdf: Description rdf: about="Front. Door"/> <rdf: Description rdf: about="Rear. Door"/> <rdf: Description rdf: about="Trunk. Door"/> </owl: disjoint. Union. Of> </owl: Class>

Syntactic sugar • Disjoint. Classes – A set of classes – All the classes are pairwise disjoint • Need for Disjoint. Classes – Nothing can be both • A Left. Lung and • A Right. Lung

Syntactic sugar • Negative. Object. Property. Assertion – Two individuals – A property does not hold between them Example, Patient “John” does not live in “Povo” • Negative. Data. Property. Assertion – 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 • • • Object. Min. Cardinality Object. Max. Cardinality Object. Exact. Cardinality Data. Min. Cardinality Data. Max. Cardinality Data. Exact. Cardinality

Object properties • Reflexive. Object. Property – Globally reflexive – Everything is part of itself • Irreflexive. Object. Property – Nothing can be a proper part of itself • Asymmetric. Object. Property – If x is proper part of y, then the opposite does not hold

Disjoint propertis • Disjoint. Object. Properties – Deals with object properties – Pairwise disjointness can be asserted – E. g. , connected. To and contiguous. With • Disjoint. Data. Properties – Deals with data properties – Pairwise disjointness can be asserted – E. g. , start. Time and end. Time of a surgery

Property chain inclusion • Properties can be defined as a composition of other properties • If disease A is located. In body part B and B is part of body part C then A is located. In C • Sub. Object. Property. Of ( Object. Property. Chain( located. In part. Of) located. In)

Keys • Individuals can be identified uniquely • Identification can be done using – A data property – An object property or – A set of properties • Has. Key( : Registered. Patient : has. Waiting. List. N ) Class. Assertion( : Registered. Patient : This. Patient ) Data. Property. Assertion( : has. Waiting. List. N : This. Patient "123 -45 -6789" ) • Has. Key( : Transplantation : donor. Id : recipient. Id : of. Organ )

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 – Datatype. Restriction(xsd: integer min. Inclusive 18) • Datatype definitions – New datatypes – Datatype. Definition( : adult. Age Datatype. Restriction(xsd: integer min. Inclusive 18))

Extended datatypes • Data range combinations – Intersection of • Data. Intersection. Of( xsd: non. Negative. Integer xsd: non. Positive. Integer ) – Union of • Data. Union. Of( xsd: string xsd: integer ) – Complement of data range • Data. Complement. Of( xsd: positive. Integer )

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, Sub. Class. Of( Annotation( rdfs: comment "Middle lobes of lungs are necessarily right lobes since left lungs do not have middle lobe. ") : Middle. Lobe : Right. Lobe ) • 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, part. Of and has. Part – Object. Inverse. Of( : part. Of ): 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 q OWL Overview (2004). W 3 C Recommendation. q OWL 2 New Features and Rationale (2009). W 3 C Recommendation. q 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. q D. Allemang and J. Hendler. Semantic web for the working ontologist: modeling in RDF, RDFS and OWL. Morgan Kaufmann Elsevier, Amsterdam, NL, 2008.