(09) Semantic Web Technologies - OWL

Semantic Web Technologies

LectureDr. Harald Sack

Hasso-Plattner-Institut für IT Systems EngineeringUniversity of Potsdam

Winter Semester 2012/13

Lecture Blog: http://semweb2013.blogspot.com/This file is licensed under the Creative Commons Attribution-NonCommercial 3.0 (CC BY-NC 3.0)

Samstag, 15. Dezember 12

http://semweb2013.blogspot.com


http://creativecommons.org/licenses/by-nc/3.0/

http://creativecommons.org/licenses/by-nc/3.0/

Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

2 1. Introduction 2. Semantic Web - Basic Architecture

Languages of the Semantic Web - Part 1

3. Knowledge Representation and LogicsLanguages of the Semantic Web - Part 2

4. Applications in the ,Web of Data‘

Semantic Web Technologies Content


Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Rembrandt van Rijn, Die Anatomie des Dr. Tulp, 1632

3

Formal

Seman

tics

for RD

F(S)

last lecture


Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

4 3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Propositional Logic and First Order Logic

• Description Logics

• RDF(S) Semantics• OWL and OWL-Semantics• OWL 2 and Rules




OWL

Web On

tology

Langu

age5



63.5 OWL and OWL Semantics

3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax3.5.3 OWL 1 - Tools3.5.4 OWL Semantics

3. Knowledge Representation & Logic3.5 OWL and OWL Semantics


Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamTurmbau zu Babel, Pieter Brueghel, 1563

7

Why OWL and not WOL ...?



8• OWL - W3C Recommendation since 2004• OWL 2 - W3C Recommendation since 2009

• OWL Ontology consists of• Classes / properties / individuals (instances of Classes)

• Open World Assumption• „Absence of information must not be valued as negative

information.“• E.g.: sitsNextTo(PersonA, PersonB)

PersonA my also sit next to another person…• No Unique Name Assumption

• „Difference must be expressed explicitly“• E.g.: PersonA might denote the same individual as PersonB

OWL – Web Ontology Language



9


• OWL is a semantic fragment of FOL• OWL existists in different flavours• OWL Lite ⊆ OWL DL ⊆ OWL Full

FOL

SWRL/RIF OWL Full

OWL DL

OWL Lite RDFS

ConceptHierarchies

OWL ELOWL RLOWL QL

OWL1

OWL1Samstag, 15. Dezember 12


10


• OWL is a semantic fragment of FOL• OWL existists in different flavours• OWL Lite ⊆ OWL DL ⊆ OWL Full

• for OWL2:• OWL EL, OWL RL, OWL QL

⊆ OWL DL ⊆ OWL Full

FOL

SWRL/RIF OWL Full

OWL DL

OWL Lite RDFSOWL ELOWL RLOWL QL

OWL2

OWL2ConceptHierarchies



11


• OWL Lite SHIF(D)

• Subset of OWL DL , rather restricted (no nominal classes, no cardinality, no disjunctiveness)

• Complexity ExpTime (worst case)

• OWL DL (Description Logic) SHOIN (D) or SHROIQ (D) [OWL2]

• formally sound semantics

• decidable, complete, sound

• Complexity NExpTime (worst case)

• OWL Full• Union of OWL Syntax and RDF(S)

• Meta modeling (Nesting)• undecidable (is not a descrtion logic)

Lite

DLFull



12


Lite

DLFull

• Disjunctiveness of classes•E.g.: Classes Person and Beverage are disjunctive

• Inverse properties•E.g.: likes ↔ isLikedBy

• Difference of individuals•E.g.: PersonA != PersonB

• Class descriptions•E.g.: Class CoffeeLover consists of members of class Person, who for the Property likes have the value “Coffee“








14

OWL 1 – Syntax Variants

<owl:Class rdf:ID=“Wine“> <rdfs:subClassOf rdf:resource=“#Beverage“/></owl:Class>

class(a:Wine partial a:Beverage)

Wine ⊆ Beverage

RDF(S) Syntax

abstract Syntax

DL Syntax

:Beverage a owl:Class .:Wine a owl:Class ; rdfs:subClassOf :Beverage .

Turtle



15

OWL 1 – RDF(S) Syntax

• OWL documents are RDF documents (at least according to the standard syntax)

• OWL documents (in RDF(S) syntax) consist of• Header with general information• Body with the actual ontology

<rdf:RDF xmlns ="http://www.semanticweb-fundamentals.de/exampleontology#" xmlns:rdf ="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:xsd ="http://www.w3.org/2001/XMLSchema#" xmlns:rdfs ="http://www.w3.org/2000/01/rdf-schema#" xmlns:owl ="http://www.w3.org/2002/07/owl#“ > ...</rdf:RDF>


http://www.semanticweb-grundlagen.de/beispielontologie#

http://www.semanticweb-grundlagen.de/beispielontologie#

http://www.w3.org/1999/02/22-rdf-syntax-ns#

http://www.w3.org/1999/02/22-rdf-syntax-ns#

http://www.w3.org/2001/XMLSchema#

http://www.w3.org/2001/XMLSchema#

http://www.w3.org/2000/01/rdf-schema#

http://www.w3.org/2000/01/rdf-schema#

http://www.w3.org/2002/07/owl#

http://www.w3.org/2002/07/owl#


16

3.5 OWL and OWL Semantics3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL13.5.3 OWL1 Tools3.5.4 OWL Semantics



17

OWL1 Document Header

<owl:Ontology rdf:about=""> <rdfs:comment rdf:datatype="http://www.w3.org/2001/XMLSchema#string“> SWRC Ontology in the version of january 2012 </rdfs:comment> <owl:versionInfo>v0.5</owl:versionInfo> <owl:imports rdf:resource="http://www.hpi.uni-potsdam.de/foo"/> <owl:priorVersion rdf:resource="http://www.semweb.de/swrc"/></owl:Ontology>


http://www.w3.org/2001/XMLSchema#string

http://www.w3.org/2001/XMLSchema#string

http://www.informatik.uni-jena.de/foo

http://www.informatik.uni-jena.de/foo

http://www.semweb.de/swrc

http://www.semweb.de/swrc


18

OWL Document Header

• inherited from rdfs:• rdfs:comment• rdfs:label• rdfs:seeAlso• rdfs:isDefinedBy

• other:• owl:imports

• OWL Versioning:• owl:versionInfo• owl:priorVersion• owl:backwardCompatibleWith• owl:incompatibleWith• owl:DeprecatedClass• owl:DeprecatedProperty



19




20

OWL – Classes, Properties and Individuals

• Ontology axioms consist of the following three building blocks:

• Classes•comparable with classes in RDFS

• Individuals•comparable with objects in RDFS

• Properties•comparable with properties in RDFS



21

• there exist two predefined classes• owl:Thing (class that contains all individuals)• owl:Nothing (empty class)

• Definition of a class

:Wine a owl:Class .

OWL – Classes

⊤

⊥



22 • Definition of individuals via class membership

:WegelerRheingauRiesling a :Wine .

OWL – Individuals



23

OWL – Properties

• there exist two variants: • object properties• datatype properties

• Object properties are defined like classes

• Domain and Range of object properties

:isMadeFrom a owl:ObjectProperty .

:isMadeOf a owl:ObjectProperty ; rdfs:domain :Wine ; rdfs:range :Grapes .



24• Datatype properties have datatypes as range

• Domain and range of datatype properties

• Many XML datatypes can be used.The standard provides integer and string.

:hasQuality a owl:DatatypeProperty .

OWL – Properties

:hasQuality a owl:DatatypeProperty ; rdfs:domain :Wine ; rdfs:range xsd:string .



25

OWL – Properties and Individuals

:Wine a owl:Class .:Grapes a owl:Class .:Riesling a :Grapes .:isMadeOf a owl:ObjectProperty ; rdfs:domain :Wine ; rdfs:range :Grapes .:hasQuality a owl:DatatypeProperty ; rdfs:domain :Wine ; rdfs:range xsd:string .:WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spätlese“ .



26

OWL – Properties and Individuals

• Properties in general are not functional

:Tempranillo a :Grapes .:Garnacha a :Grapes .:Mazuelo a :Grapes .:Graciano a :Grapes .:MarquesDeRiscal a :Wine ; :isMadeOf :Tempranillo ; :isMadeOf :Garnacha ; :isMadeOf :Mazuelo ; :isMadeOf :Graciano .



27

OWL – Class Hierarchies

• via inference it can be entailed that „Wine“ is also a subclass of „Beverage“

:Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage .:AlcoholicBeverage a owl:Class ; rdfs:subClassOf :Beverage .:Beverage a owl:Class .



28

OWL – Class Hierarchies and Disjunctiveness

• via inference it can be entailed that „Wine“ and „Pizza“ are also disjoint classes.

:AlcoholicBeverage a owl:Class .:MainDish a owl:Class .:Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage .:Pizza a owl:Class ; rdfs:subClassOf :MainDish .

:AlcoholicBeverage owl:disjointWith :MainDish .



29

OWL – Class Hierarchies and Equivalence

:AlcoholicBeverage a owl:Class .:AlkoholischesGetraenk a owl:Class .:Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage .:AlcoholicBeverage owl:equivalentWith :AlkoholischesGetraenk .

• via inference it can be entailed that „Wine“ is also an „AlkoholischesGetraenk“



30

OWL – Individuals and Class Relationships

:WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spaetlese“ .:Wine a owl:Class ; rdfs:subClassOf AlcoholicBeverage .:AlcoholicBeverage a owl:Class.

• via inference it can be entailed that „WegelerRheingauRiesling“ is an „AlcoholicBeverage“



31

OWL – Relationships among Individuals

• via inference it can be entailed that „WRR012345“ is an „AlcoholicBeverage“

• Difference of Individuals via owl:differentFrom

:WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spaetlese“ ; owl:sameAs :WRR012345 .:Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage .:AlcoholicBeverage a owl:Class.

:WRR012346 a :Wine ; owl:differentFrom :WRR012345 .



32

OWL – Relationships among Individuals

• Abbreviation instead of writing many times owl:differentFrom.

_:x1 a owl:AllDifferent ; owl:distinctMembers (:WegelerRheingauRiesling :AltoAdigeChardonnay :ChateauxLafiteRothschild :MarquesDeRiscal) .



33

OWL – Enumerated Classes (Nominals)

• This says that there are only exactly two redwines available in the store.

:Wine a owl:Class ;:ChateauxLatourPauillac a :Wine .:ChateauxLafiteRothschild a :Wine .:RedwinesInStore a owl:Class ; owl:oneOf (:ChateauxLatourPauillac, :ChateauxLafiteRothschild) .



34

OWL – Class Membership (2)

• We define an additional third wine

• this entails that “AltoAdigeSauvignonBlanc“ is not available in the store.

:AltoAdigeSauvignonBlanc a :Wine .

_:x1 rdf:type owl:AllDifferent ; owl:distinctMembers (:ChateauxLatourPauillac :ChateauxLafiteRothschild :AltoAdigeSauvignonBlanc) .



35




36 • logical AND (conjunction): owl:intersectionOf ⊓

• logical OR (disjunction): owl:unionOf ⊔

• logical negation: owl:complementOf ¬

•Logical constructors are applied to create complex class descriptions from atomic classes.

OWL – Logical Class Constructors



37


• The class “WineInStore“ results from the intersection of all individuals of the classes “ThingsInStore“ and “Wine“

:Wine a owl:Class .

:ThingsInStore a owl:Class .:WineInStore a owl:Class ; owl:intersectionOf (:Wine :ThingsInStore) .

WineInStore ≣ ThingsInStore ⊓ Wine



38


• Dry, medium and sweet wines are also wines

:Wine a owl:Class ;

owl:equivalentClass [ owl:unionOf ( :DryWine :MediumWine :SweetWine)

] .

Wine ≣ DryWine ⊔ MediumWine ⊔ SweetWine



39

• semantically equivalent assertion:

:Wine a owl:Class ;

rdfs:subClassOf [ owl:complementOf :Pizza

] .

:Wine a owl:Class ;

owl:disjointWith :Pizza .


Wine ⊑ ¬Pizza



40

OWL – Property Restrictions

• are used to describe complex classes via properties

• restrictions on values:• owl:hasValue! ! !

• owl:allValuesFrom• owl:someValuesFrom

• restrictions on cardinality:• owl:cardinality• owl:minCardinality• owl:maxCardinality



41

OWL – Property Restrictions with Constants

• Class „HaraldsCourses“ is described via fixed value assignment (=constant) of the individual „Harald“ to the property „isManagedBy“

HaraldsCourses ⊑ isManagedBy.(Harald)

:HaraldsCourses a owl:Class ; rdfs:subClassOf

[ a owl:Restriction ; owl:onProperty :isManagedBy ; owl:hasValue :Harald ] .

:Person a owl:Class .:Course a owl:Class .

:Harald a :Person .:isManagedBy a owl:ObjectProperty ; rdfs:domain :Course ; rdfs:range :Person .



42• owl:allValuesFrom

fixes all instances of a specific class C as allowed range for a property P → (Universal Quantification) ∀P.CWine ⊑ ∀hasProducer.Winemaker


:Wine a owl:Class ; rdfs:subClassOf

[ a owl:Restriction ; owl:onProperty :hasProducer ; owl:allValuesFrom :Winemaker ] .

:Producer a owl:Class .:Product a owl:Class .:Winemaker owl:subClassOf :Producer .

:hasProducer a owl:ObjectProperty ; rdfs:domain :Product ; rdfs:range :Producer .



43

• owl:someValuesFromdescribes that there must exist an individual for property P and fixes its range to class C → (existential quantification) ∃P.C

Animals ⊑ ∃feedsOn.Vegetables


:Animals a owl:Class ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :feedsOn ; owl:somelValuesFrom :Vegetables ] .

:Animal a owl:Class .:Food a owl:Class .:Vegetables owl:subClassOf :Food .

:feedsOn a owl:ObjectProperty ; rdfs:domain :Animal ; rdfs:range :Food .



44

OWL – Cardinality Restrictions

• owl:cardinality restricts to an exact number (for OWL Lite only 1/0)

• owl:minCardinality, owl:maxCardinality restricts to upper / lower bounds

Stringquartett ⊑ (=4)hasMembers

:Stringquartett a owl:Class ; rdfs:subClassOf

[ a owl:Restriction ; owl:onProperty :hasMembers ; owl:cardinality 4 ] .

:hasMembers a owl:DatatypeProperty ; rdfs:domain :Thing ; rdfs:range xsd:integer .



45




46

OWL – Property Relationships

• Property hierarchies can be created via specializations: rdfs:subPropertyOf

• Inverse properties are defined via owl:inverseOf• Identical properties are defined via owl:equivalentProperty

:isMadeOf a owl:ObjectProperty ; rdfs:subPropertyOf :consistsOf .

:isProcessedTo a owl:ObjectProperty ; owl:inverseOf :isMadeOf .



47 •owl:TransitiveProperty•E.g.: A isPartOf B, B isPartOf C ⇒ A isPartOf C

•owl:SymmetricProperty•E.g.: A isNeighborOf B ⇒ B isNeighborOf A

•owl:FunctionalProperty•E.g.: A hasMother B, A hasMother C ⇒ B=C

•owl:InverseFunctionalProperty•Bsp.: B isMotherOf A, C isMotherOf A ⇒ B=C

OWL – Property Relationships



48

OWL – Transitive Properties

•via inference it can be entailed that „Rheinhessen“ is located in „Germany“ .

:isLocatedIn a owl:ObjectProperty ; a owl:TransitiveProperty ; rdfs:domain owl:Thing ; rdfs:range :Region .

:Rheinhessen a :Region ; :isLocatedIn :Hessen .

:Hessen a :Region ; :isLocatedIn :Germany .

:Region a owl:Class .:Germany a :Region .



49



• OWL Lite SHIF(D)

• Subset of OWL DL , rather restricted (no nominal classes, no cardinality, no disjunctiveness)

• Complexity ExpTime (worst case)

• OWL DL (Description Logic) SHOIN (D) or SHROIQ (D) [OWL2]

• formally sound semantics

• decidable, complete, sound

• Complexity NExpTime (worst case)

• OWL Full• Union of OWL Syntax and RDF(S)

• Meta modeling (Nesting)• undecidable (is not a description logic)


50


Lite

DLFull

obsolete...



51

OWL FULL

• Unrestricted Usage of all OWL and RDFS language elements (...must be valid RDFS).

• Problems: no strict type separation (classes, properties, individuals), therefore:• owl:Thing is the same as rdfs:Resource

• owl:Class is the same as rdfs:Class

• owl:DatatypeProperty becomes subclass of owl:ObjectProperty

• owl:ObjectProperty is the same as rdfs:Property



52

OWL DL

• Only explicitly allowed RDFS language elements are to be used (as e.g. in our examples).• not allowed: rdfs:Class, rdfs:Property

• type separation: • Classes and Properties must be explicitly declared.

• Datatype properties must not be transitive, symmetric, invers, or invers-functional.

• Number restrictions must not be applied with transitive properties, their subproperties, or their inverse properties.



53

OWL LITE (obsolete...)

•All restrictions as for OWL DL.•Not allowed:

•oneOf, •unionOf,•complementOf, •hasValue, •disjointWith

•Number restrictions only with 0 and 1.•Some restrictions according anonymous (complex) classes, i.e. in some cases the usage of class names or property names is mandatory.

obsolete...



54




55

Terminological OWL Queries

•Class Equivalence•Subclass relationships•Disjunctiveness of classes•Global consistency (satisfiability)•Class consistency: a class is inconsistent, if it is equivalent to owl:Nothing

• indicates often a modeling failure

:Wine a owl:Class;

owl:subClassOf :Beverage; owl:disjointWith :Beverage .



56

Assertional OWL Queries

• Class membership: • Does a given individual belong to a specific class?

• Class extension: • Search for all individuals that are contained in a

specific class.

• Property checking:• Are two given individuals connected via a given

property?• Property extension:

• Search or all pairs of individuals that are connected via a specific property.








58

OWL Tools

•Ontology Editors•Protegé, http://protege.stanford.edu•SWOOP, http://www.mindswap.org/2004/SWOOP/•KAON(2) OWL Tools, http://owltools.ontoware.org/

•Inference engines (Reasoner)•Pellet, http://clarkparsia.com/pellet•KAON2, http://kaon2.semanticweb.org•FACT++, http://owl.man.ac.uk/factplusplus/•Racer, http://www.racer-systems.com/•HermiT, http://hermit-reasoner.com/


http://protege.stanford.edu

http://protege.stanford.edu

http://www.mindswap.org/2004/SWOOP/

http://www.mindswap.org/2004/SWOOP/

http://owltools.ontoware.org

http://owltools.ontoware.org

http://www.mindswap.org/2003/pellet/index.shtml

http://www.mindswap.org/2003/pellet/index.shtml

http://kaon2.semanticweb.org

http://kaon2.semanticweb.org

http://owl.man.ac.uk/factplusplus/

http://owl.man.ac.uk/factplusplus/

http://www.racer-systems.com

http://www.racer-systems.com

http://hermit-reasoner.com

http://hermit-reasoner.com







60

Description Logics revisited

Operator/Constructor Syntax LanguageLanguage

Conjunction A ⊓ B

FLUniversal (Range) Restriction ∀R.C FL

Existential Quantification ∃R

Top ⊤

Bottom ⊥S*

Negation ¬AS*

Disjunction A ⊔ B AL*

Existential (Range) Restriction ∃R.C

AL*

Number Restriction (≤nR) (≥nR)

Enumerated Classes (Nominals) {a1,...,a2}

Property Hierarchy R ⊑ S HH

Inverse Property R-1 II

Qualified Number Restriction (≤nR.C) (≥nR.C) QQ



61

Description Logics revisited

•ALC: Attribute Language with Complement

•S: ALC + transitive Properties

•H: Property Hierarchies

•O: Nominals (enumerated classes)

•I: inverse Properties

•N: Number Restrictions ≤n R etc.

•Q: Qualified Number Restrictions ≤n R.C etc.

•(D): Datentype

•F: functional Properties

•R: Property Constructor

•OWL 1 DL is SHOIN(D) / OWL 2 DL is SHROIQ(D)



62

OWL1 and ALC

•The following OWL1 DL language elements can be represented in ALC:

•classes, properties, individuals•class membership, property instances•owl:Thing and owl:Nothing•Class subsumption, equivalence, disjunctiveness

•owl:intersectionOf, owl:unionOf•owl:complementOf•owl:allValuesFrom, owl:someValuesFrom•rdfs:range and rdfs:domain



63

OWL1 DL as SHOIN(D)

•owl:sameAs•indicates that two individuals denote the same element

•DL: a=b•FOL: extension via equality predicate

•owl:differentFrom•indicates that two individuals denote the different elements

•DL: a≠b•FOL: ¬(a=b)



64

OWL1 DL as SHOIN(D)

•Enumerated Classes (Nominals)•owl:oneOf

•defines a class by extension of all its members•DL: C ≡ {a,b,c}•FOL: (∀x) (C(x) ↔ (x=a ∨ x=b ∨ x=c))

•owl:hasValue•„forces“ property to a specific individual•can be represented via owl:someValuesFrom and owl:oneOf



65

OWL1 DL as SHOIN(D)

•Number Restrictions

•An examination has at most 2 examiners.•DL: Examination ⊑ ≤2hasExaminer

•FOL: (E… Examination, h…hasExaminer)• (∀x)(E(x) ! ¬((∃x1)(∃x2)(∃x3)

(x1 ≠ x2 Λ x2 ≠ x3 Λ x1 ≠ x3 Λ h(x,x1) Λ h(x,x2) Λ h(x,x3))))

:Examination a owl:Class; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :hasExaminer; owl:maxCardinality 2 ] .



66

OWL1 DL as SHOIN(D)

•Property Hierarchies•rdfs:subPropertyOf

•DL: R ⊑ S

•FOL: (∀x)∀(y)(R(x,y) ! S(x,y))•Property equivalency likewise

•owl:inverseOf•DL: R ≡ S-•FOL: (∀x)(∀y)(R(x,y) ↔ S(y,x))

•owl:TransitiveProperty•DL: R ⊑+ R

•FOL: (∀x)(∀y)(∀z)(R(x,y)ΛR(y,z)!R(x,z))•Symmetric Properties: R ≡ R-•Functional Properties: ⊤ ⊑ ≤1R

•Inverse Functionality: ⊤ ⊑ ≤1R-



67

OWL1 DL as SHOIN(D)

•For OWL DL the following is permitted:

•ALC•Equality and Inequality of individuals•Enumerated classes•Number restrictions•Property hierarchies and property equivalences• Inverse and transitive properties•Datatypes

•Datatypes are allowed to use as 2nd argument of datatype properties in the ABox.

•A set of specific typed data might form an enumerated class.•Datatypes cannot simply be expressed in FOL. But FOL

semantics can be extended accordingly.



68

OWL1 DL Syntax - Overview

Concepts

Atomic A, B

Not ¬C

And C ⊓ D

Or C ⊔ D

Exists ∃R.C

For all ∀R.C

At least ≥n R.C (≥n R)

At most ≤n R.C (≤n R)

Nominal {i1,...in}

ALC

Q(N)

O

Properties

Atomic Properties

Inverse R-I

Concept Axioms (TBox)Concept Axioms (TBox)

Subclass C ⊑ D

Equivalent C ≡ D

Property Axioms (TBox)Property Axioms (TBox)

Subproperty R ⊑ S

Transitivity R+

Assertional Axioms (ABox)Assertional Axioms (ABox)

Instance C(a)

Property R(a,b)

Same a=b

Different a≠b

HS



69

OWL1 DL Syntax - Class Constructors

Constructor DL Syntax Example FOL Syntax

intersectionOf C1 ⊓… ⊓ Cn Person ⊓ Male C1(x)∧…∧Cn(x)

unionOf C1 ⊔… ⊔ Cn Student ⊔ Professor C1(x)⋁…⋁Cn(x)

complementOf ⌐C ⌐ Male ⌐C(x)

oneOf {x1} ⊔… ⊔ {xn} {john} ⊔ {mary} x=x1 ⋁…⋁ x=xn

allValuesFrom ∀P.C ∀attends.Seminar ∀y,P(x,y)→C(y)

someValuesFrom ∃P.C ∃attends.Seminar ∃y,P(x,y)→C(y)

maxCardinality ≤nP ≤2 attends ∃≤n y,P(x,y)

minCardinality ≥nP ≥1 attends ∃≥n y,P(x,y)



70

OWL1 DL Syntax - Axioms

Axioms DL Syntax Example

subClassOf C1 ⊑ C2 Human ⊑ Animal ⊓ Biped

equivalentClass C1 ≡ C2 Woman ≡ Human ⊓ Female

disjointWith C1 ⊑ ⌐C2 Male ⊑ ⌐ Female

sameAs {x1} ≡ {x2} {JamesBond} ≡ {007}

differentFrom {x1} ⊑ ⌐{x2} {John} ⊑ ⌐{Mary}

subPropertyOf P1 ⊑ P2 hasDaughter ⊑ hasChild

equivalentProperty P1 ≡ P2 cost ≡ price

inverseOf P1 ≡ P2-

dsdsd

hasChild ≡ hasParent_

TransitiveProperty P1 ⊑+ P2 hasAncester ⊑+ hasAncester

FunctionalProperty ⊤ ⊑ ≤1P ⊤ ⊑ ≤1hasMother

InverseFunctionalProperty ⊤ ⊑ ≤1P_ ⊤ ⊑ ≤1isMotherOf_



71

OWL1 DL Syntax

• Nesting of constructors:• Person ⊓

∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)

• General Class Inclusion (⊑) is sufficient:

• C ≡ D iff (C ⊑ D and D ⊑ C)

• Obvious FOL Equivalences

• C ≡ D corresponds to (∀x)(C(x)⟺D(x))

• C ⊑ D corresponds to (∀x)(C(x)⇒D(x))



72

OWL1 DL und OWL RDF Syntax

• Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)

<owl:Class> <owl:intersectionOf rdf:parseType="collection"> <owl:Class rdf:about="Person"/> <owl:Restriction> <owl:onProperty rdf:resource="hasChild"/> <owl:allValuesFrom> <owl:unionOf rdf:parseType="collection"> <owl:Class rdf:about="Doctor"/> <owl:Restriction> <owl:onProperty rdf:resource="hasChild"/> <owl:someValuesFrom rdf:resource="Doctor"/> </owl:Restriction> </owl:unionOf> </owl:allValuesFrom> </owl:Restriction> </owl:intersectionOf></owl:Class>



73

OWL1 DL und OWL RDF Syntax

[ a owl:Class; owl:IntersectionOf ( :person [ a owl:Restriction ; owl:onProperty :hasChild ; owl:allValuesFrom [ owl:unionOf ( :Doctor [ a owl:Restriction ; owl:onProperty :hasChild ; owl:someValuesFrom :Doctor ] ) ] ] )] .

• Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)








75 3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Propositional Logic and First Order Logic

• Description Logics

• RDF(S) Semantics• OWL and OWL-Semantics• OWL 2 and Rules




76

next Lecture

OWL

OWL 2

Extension

SHROIQ(D)

SHOIN(D)



77

• P. Hitzler, S. Roschke, Y. Sure: Semantic Web Grundlagen, Springer, 2007.

• P. Hitzler, M. Krötzsch, S. Rudolph:Foundations of Semantic Web Technologies,CRC Press, 2009.

Bibliography



http://www.amazon.de/gp/product/3540339930/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=3540339930

http://www.amazon.de/gp/product/3540339930/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=3540339930

http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X

http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X


78

□Bloghttp://semweb2013.blogspot.com/

□Webseitehttp://www.hpi.uni-potsdam.de/studium/lehrangebot/itse/veranstaltung/semantic_web_technologien-3.html

□bibsonomy - Bookmarkshttp://www.bibsonomy.org/user/lysander07/swt1213_09





http://www.hpi.uni-potsdam.de/studium/lehrangebot/itse/veranstaltung/semantic_web_technologien-3.html






http://www.bibsonomy.org/user/lysander07/swt1213_09




Education

(09) Semantic Web Technologies - OWL