The Knowledge Presentation Language

Web Ontology Language (OWL)Web Ontology Language (OWL) extends RDF

and RDFS languages by adding several other constructs such as owl:class (in addition to the rdfs:class), relationships between class and individuals, and property characteristics These new constructs facilitate

interoperability among distributed resources OWL is encoded in RDF/XML

OWL is said to be ‘monotonic’, meaning that addition of new information to a knowledge base does not falsify previous conclusions

Owl dialects OWL has three species (dialects):

OWL-Lite, OWL DL, and OWL Full

The differences are on the limitations on restrictions on classes

OWL Lite: supports class and property hierarchies and simple restrictions, allowing us to develop thesauri and simple ontologies

OWL DL is the decidable version of OWL Full, with some limitation; it is a restricted version of RDF

OWL Full has no limitation, but may not be decidable

Features of OWLIs compatible with (serializable in) XML. Uses XSD

datatypes

Follows description logic in having class, property, and individuals

Has constructs that are identified by the URIref

Allow us to define complex classes with Boolean combinations (intersection, union, complement)

Makes it possible to define properties and subproperties and assigning logical metadata (e.g., transitivity)

Has features to set two classes, properties, and individuals as equivalent

…Allows setting the cardinality constraints

Setting classes as instances

Resources defined by it can have labels such that they can be displayed in different natural languages

Allows developing Web-distributed ontologies

Lets us import and reuse other owl code (ontologies) by extension

Allows saving the same ontologies with different versions

Allows defining metadata for ontologies (e.g., author, version)

OWL ontology header infoIncludes namespace declarationInformation about the ontology is put within the

owl:Ontology Qname, e.g., version, comments, and import

The version includes: owl:versionInfo, owl:priorVersion, owl:backwardCompatibleWith, owl:incompatibleWith, owl.deprecatedClass, and owl:deprecatedProperty

We can also use the rdfs:comment, rdfs:label, rdfs:seeAlso, and rdfs:isDefinedBy

<rdf:Description rdf:about="http://www.Tectonics.org"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Ontology"/> </rdf:type> </rdf:Description>

<rdf:Description rdf:about="http://www.StructuralGeology.org"> <rdf:type>

<rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Ontology"/> </rdf:type>

<rdfs:comment>Part of Structural Geology</rdfs:comment>

<rdfs:label>Structural Geology</rdfs:label>

<owl:imports><rdf:Description rdf:about="http://www.Tectonics.org"/>

</owl:imports>

<owl:priorVersion><rdf:Description rdf:about="http://www.StructuralGeology.org/v0"/>

</owl:priorVersion> </rdf:Description>

Two Types of Property in OWL Datatype Property has a typed literal (e.g., XSD or

RDF literal) as its range

As a binary relation, the datatype property relates a set of instances of a [domain] class to a set of instances of a datatype (range; object)

A datatype property is declared using the owl:DatatypeProperty

<length rdf:type owl:DatatypeProperty> Or:<owl:datatypeProperty rdf:about=“length”/>

Object Property Object property has a URIref as its range

As a binary property, it relates a set of individuals of one class to the set of individuals of another class

That is, the subject and objects of a triple using an object property are both individuals

Object properties are declared in two different ways:

<analyze rdf:type owl:ObjectProperty> or:<owl:ObjectProperty rdf:about=“analyze”/>

Example in N3struc:foldDescription rdf:type owl:DatatypeProperty.

struc:foldDescription rdfs:domain struc:Fold.

struc:foldDescription rdfs:range xsd:string.

struc: Fold struc: foldDescription xsd:tring

struc:foldAxis rdf:type owl:ObjectProperty.

struc:foldAxis rdfs:domainstruc:Fold.

struc:foldAxis rdfs:range struc:Line.

struc:Fold struc:foldAxis struc:Line

Domain and range of properties Can be assigned in a short form:<owl:objectProperty rdf:about=“infiltrate”/>

<owl:domain rdf:resource=“SurfaceWater”/>

<owl:range rdf:resource=“Aquifer”/>

</owl:objectProperty>

Or the long way, as is shown in the following slide!

<rdf:Description rdf:about=":infiltrate“>

<rdf:type>

<rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/>

</rdf:type>

<rdfs:domain><rdf:Description rdf:about=":SurfaceWater"/></rdfs:domain>

<rdfs:range><rdf:Description rdf:about=":Aquifer"/></rdfs:range>

</rdf:Description>

<?xml version="1.0" encoding="UTF-8"?><rdf:RDF xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"> <rdf:Description rdf:about=":length"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#DatatypeProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":Fault"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about="http://www.w3.org/2001/XMLSchema#string"/></rdfs:range> </rdf:Description> <rdf:Description rdf:about=":infiltrate"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":SurfaceWater"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about=":Aquifer"/></rdfs:range> </rdf:Description>

<rdf:Description rdf:about=":Fault"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

<rdf:Description rdf:about=":SurfaceWater"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

<rdf:Description rdf:about=":Aquifer"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

</rdf:RDF>

owl:inveseOf Properties themselves have properties

owl:inverseOf property relates two properties to each other

Many properties in one direction have an inverse property in the opposite direction

For example, the first property in each of the following pairs reverses the direction of the second property

‘analyzes’ and ‘analyzedBy’ ‘investigates’ and ‘investigatedBy’ ‘hasSample’ and ‘sampleOf ‘wrote’ and ‘writtenBy’ ‘locatedIn’ and ‘locationOf’

These follow the definition of the mathematical inverse function that state: if f(x) = y, then f-1(y) = x.

Inference of the owl:inverseOfP owl:inverseOf Q.Ifx P y.Theny Q x.

Example: The partOf property is an inverse property

struc : Fold hasPart struc : limb.partOf owl : inveseOf struc : hasPart.

This means that if fold has limb as part, then limb is part of fold

Fold Limb

x y

hasPart

partOfQ

P

<?xml version="1.0" encoding="UTF-8"?><rdf:RDF xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"> <rdf:Description rdf:about=":Fold"><rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

<rdf:Description rdf:about=":Limb"><rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

<rdf:Description rdf:about=":partOf"><rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":Limb"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about=":Fold"/></rdfs:range> <owl:inverseOf><rdf:Description rdf:about=":hasPart"/></owl:inverseOf> </rdf:Description>

<rdf:Description rdf:about=":hasPart"> <rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/> </rdf:type> </rdf:Description></rdf:RDF>

Fold Limbx y

hasPart

partOf

partOf owl:inverseOf hasPart

owl:symmetricProperty If the property that relates two classes is the

same (has the same name) in both directions, we declare the property as symmetric

For example: ‘equals’ or ‘siblingOf’ is a symmetric property

if x is siblingOf y, then y is siblingOf x

Symmetric properties must be declared as such P rdf : type owl:SymmetricProperty.

The inference for a symmetric property is as follows:P owl:inverseOf P.

That is, the symmetric property is an inverse property.

owl:transitiveProperty  In mathematics, a relation is said to be

transitive if P(a,b) and P(b,c) implies P(a,c). This is represented by the owl:TransitiveProperty, which applies to a property.

 P rdf : type owl:TransitiveProperty. The inference for this property is as follows:IF 

x P y.

y P z.

THEN x P z.

C part of B B part of A C part of A.

ABC

FaultBend FaultSegmentx y

PFault

z

P

partOf The partOf property (containment) may be transitive

(not always). Finger is part of hand, and hand is part of body

However, someone’s hand is not part of the group to which the person is part of

Geologically, being fractal, faults have segments that have smaller fault segments, which have even smaller segments which are themselves fault

struc:FaultSegment struc:partOf struc: FaultSegment.struc:partOf rdf :type owl:TransitiveProperty.struc:FaultSegment rdfs:subClassOf struc:Fault.

FaultBend FaultSegmentx y

partOfFault

z

partOf

Transitive partOfpartOf owl:inverseOf hasPart

<?xml version="1.0" encoding="UTF-8"?><rdf:RDF xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"> <rdf:Description rdf:about=":Fault"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description>

<rdf:Description rdf:about=":FaultSegment“> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description> <rdf:Description rdf:about=":partOf"><rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/></rdf:type> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#TransitiveProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":FaultSegment"/></rdfs:domain> <rdfs:domain><rdf:Description rdf:about=":FaultBend"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about=":Fault"/></rdfs:range> </rdf:Description> <rdf:Description rdf:about=":FaultBend"><rdf:type> <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type> </rdf:Description> <rdf:Description rdf:about=":hasPart"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":Fault"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about=":FaultSegment"/></rdfs:range> <owl:inverseOf><rdf:Description rdf:about=":partOf"/></owl:inverseOf> </rdf:Description></rdf:RDF>

locatedIn is transitive

C locatedIn B B locatedIn A C locatedIn A.  geo:locatedIn rdf:type owl:TransitiveProperty. If

tect:SanAndreasFault geo:locatedIn geo:California.geo:California geo:locatedIn geo:United States.

Thengeo:SanAndreasFault geo:locatedIn geo:United States.

ABC

Functional Property …A functional property is a property that can have

only one unique value y (object) for each instance x (subject)

e.g., hasBirthMother is functional This means that there cannot be two distinct values y1 and y2 if

(x, y1) and (x, y2) are instances of the functional property

If x p y1 and x p y2, then y1=y2

Ashley hasBirthMother Jane

Ashley hasBirthMother Maria then jane=MariaGiven x (subject individual) we can find y (object individual)!Both object and datatype properties can be declared

functional!There could be many x’s, but all relate to one y

Example: husband property may be functional in some cultures: Woman husband Man(not in polygamy or same sex marriages)

If x husband y1 and x husband y2, then y1=y2

If Jane husband Jack and Jane husband Jeff, then Jack = Jeff

y2x

y1p

p

x

xy

xx

x

Inference The owl:FunctionalProperty can only take one value for

any [object] individual, allowing sameness to be inferred

The inference rule for this construct is as follows Note: x is a subject individual and A and B are object

individuals

 IfP rdf:type owl:FunctionalProperty.

X P A

X P B

Then

A owl:sameAs B.

x Ap

Bp

x

A property p is functional if x p y1 and x p y2 imply that y1 = y2

We infer that the two object individuals are the same (y1 owl:sameAs y2)

Note that the subjects are not asserted to be the same; only the objects are the same

DaughterProduct daughterProductOf ParentIsotopeSample sampleLocation LocationdaughterProductOf and sampleLocation are functional properties, because there is one unique value y for x in the following triples:

x sampleLocation y or x daughterProductOf yThere is a unique location for each sampleThere is a unique ParentIsotope for each daughterProduct

ParentIsotope

DaughterProduc

t

daughterProductOf

LocationSamplesampleLocation

<?xml version="1.0" encoding="UTF-8"?><rdf:RDF xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"> <rdf:Description rdf:about=":Sample"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/> </rdf:type></rdf:Description> <rdf:Description rdf:about=":Location"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/> </rdf:type> </rdf:Description> <rdf:Description rdf:about=":sampleLocation"> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/></rdf:type> <rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#FunctionalProperty"/></rdf:type> <rdfs:domain><rdf:Description rdf:about=":Sample"/></rdfs:domain> <rdfs:range><rdf:Description rdf:about=":Location"/></rdfs:range> </rdf:Description>

</rdf:RDF>

Sample LocationsampleLocation

Inverse Functional PropertyThis is the inverse property of the functional property.e.g., isBirthMotherOf which is the inverse of

hasBirthMoterhThe object y of an inverse functional property p uniquely

determines the subject x (some individual)y can only be the value for p for a single instance xThere cannot be two distinct x1 and x2 such that (x1, y)

and (x2, y) are instances of p.

If there are, then x1 = x2

Liz isBirthMotherOf Steven

Myra isBirthMotherOf Steven then, Liz = Myra (same individual)

Note: People’s name is not inverse functional (different people can have the same name)

x1

y

p

px2 Steven

Liz

Myra

isBirthMotherOf

isBirthMotherOf

Inverse Functional Property This property is the inverse of the owl:FunctionalProperty It is very useful for merging data from different sources The owl:FunctionalProperty and owl:InverseFunctionalProperty

allow merging data for a same individual from different sources

The owl:InverseFunctionalProperty is equivalent to the key in relational databases, such as SSN and driving license number

These are unique The inference rule of this construct is as follows:P rdf:type owl:InverseFunctionalProperty.

A P X.

B P X.

Then

A owl:sameAs B.

A

x

p

pB

owl:InverseFunctionalPropertyIf x p y, and p is inverse functional, then there can be only a

single value of x for a given y, that is:The object individual y of an

owl:InverseFunctionalProperty p uniquely determines a single subject individual x

Given the object individual (y), we can find a unique subject individual (x) (i.e., x y-1)

In this case, if x1 p y and x2 p y, then x1 and x2 are the same! If x1 ssn 123445555 and x2 ssn 123445555, then x1=x2e.g., hasSingleAuthorArticle: a person (subject) may have

many published papers (objects), but all are authored by one author (subject).

Person hasSingleAuthorArticle SingleAuthorArticleGiven a singleAuthorArticle object individual (y) we can find a

unique subject individual (x)

yy

yx

…

A single value of the property (object y, e.g., doi of an Article) cannot be shared by two x subject entities (e.g., Authors).

Example:Let’s assume that an isotope is produced by the decay

of some unique isotope (may not be true in all cases!)

Isotope parentOf DaughterIsotope

An object individual y (some daughterIsotope) uniquely determines a single subject individual x (parent isotope)

Author ArticlehasSingleAuthorPaper

yx

Example

Let’s assume location of any measurement is uniquely identified by the longitude and latitude (defined by the Location class), i.e., assume no two samples of a rock can be taken at the same exact spot

:Station134 : locatedAt : LocationA.

:Station346 : locatedAt : LocationA.

 We infer that:Station134 owl:sameAs :Station346

Station LocationlocatedAt

One-to-one Property For a one-to-one relationship, we use a combination of

the owl:FunctionalProperty and owl:inverseFunctionalProperty.

Note: Sample sampleId XSD:Integer is not a good example, because it is a datatype property, and not every number gives you the sample

 :hasimage rdfs:domain :ThinSection.

:hasImage rdfs:range Image.

:hasImage rdf:type owl:FunctionalProperty.

:hasImage rdf:type owl:InverseFunctionalProperty.

  So, any two thin sections with the same image must be

the same thin section!

Sample XSD:IntegersampleId

x y

X

ThinSection ImagehasImage

One-to-one hasImage Property

<rdf:Description rdf:about=":hasImage">

<rdf:type>

<rdf:Description rdf:about="http://www.w3.org/2002/07/owl#ObjectProperty"/>

</rdf:type>

<rdf:type>

<rdf:Description rdf:about="http://www.w3.org/2002/07/owl#FunctionalProperty"/>

</rdf:type>

<rdf:type>

<rdf:Description rdf:about="http://www.w3.org/2002/07/owl#InverseFunctionalProperty"/>

</rdf:type>

<rdfs:domain><rdf:Description rdf:about=":ThinSection"/></rdfs:domain>

<rdfs:range><rdf:Description rdf:about=":Image"/></rdfs:range>

</rdf:Description>

<rdf:Description rdf:about=":ThinSection">

<rdf:type><rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type>

</rdf:Description>

<rdf:Description rdf:about=":Image">

<rdf:type>rdf:Description rdf:about="http://www.w3.org/2002/07/owl#Class"/></rdf:type>

</rdf:Description>

</rdf:RDF>ThinSection ImagehasImage

Note that not every functional property can also be an inverse functional property

For example, mineral composition can be functional only, because every mineral has a unique composition, but many individual minerals can share that same composition (if they belong to the same class) (compare with hasFather)

Every individual child has one biological father, but the father can have more than one child

Some properties can only be inverse functional, but not functional

For example, a single-author publication of an author (or description of an outcrop or a thin section by one person) may be inverse functional, because it only belongs to one person◦ The person can have several such publications or

descriptions

Mineral CompositionhasComposition

x1 x2