OWL Web Ontology Language

1
OWLWeb Ontology Language

• The Knowledge Presentation Language

2
Web Ontology Language (OWL)

• Web Ontology Language (OWL) extends RDF and RDFS
  languages by adding several other constructs such
  as class (in addition to the rdfsclass),
  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

3
Owl dialects

• OWL has three species OWL-Lite, OWL DL, and OWL
  Full
• The differences are on 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

4
Features of OWL

• Is 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 assignng logical metadata
  (e.g., transitivity)
• Has features to set two classes, properties, and
  individuals as equivalent

5

• 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)

6
OWL ontology header info

• Includes namespace declaration
• Information about the ontology within the
  owlOntology Qname, e.g., version, comments, and
  import
• The version includes owlversionInfo,
  owlpriorVersion, owlbackwardCompatibleWith,
  owlincompatibleWith, owl.deprecatedClass, and
  owldeprecatedProperty
• We can also use the rdfscomment, rdfslabel,
  rdfsseeAlso, and rdfsisDefinedBy

7
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"http//www.
Tectonics.org"gt ltrdftypegtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlOntology"
/gtlt/rdftypegt lt/rdfDescriptiongt
ltrdfDescription rdfabout"http//www.StructuralG
eology.org"gt ltrdftypegtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlOntology"
/gtlt/rdftypegt ltrdfscommentgtPart of
Structural Geologylt/rdfscommentgt
ltrdfslabelgtStructural Geologylt/rdfslabelgt
ltowlimportsgtltrdfDescription rdfabout"http//w
ww.Tectonics.org"/gt lt/owlimportsgt
ltowlpriorVersiongtltrdfDescription
rdfabout"http//www.StructuralGeology.org/v0"/gtlt
/owlpriorVersiongt lt/rdfDescriptiongt lt/rdfRD
Fgt
8
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 class to a set of
  instances of a datatype
• A datatype property is declared using the
  owlDatatypeProperty
• ltlength rdftype owlDatatypePropertygt
• Or
• ltowldatatypeProperty rdfaboutlength/gt

9
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 another
  class
• The subject and objects of a triple are both
  individuals
• Object properties are declared two different
  ways
• ltanalyze rdftype owlObjectPropertygt or
• ltowlobjectProperty rdfaboutanalyze/gt

10
Example in N3

• strucfoldDescription rdftype
  owlDatatypeProperty.
• struc foldDescription rdfs domain struc
  Fold.
• struc foldDescription rdfs range xsd
  string.
• struc foldAxis rdf type owl
  ObjectProperty.
• struc foldAxis rdfs domain struc Fold.
• struc foldAxis rdfs range struc Line.

11
Domain and range of properties

• Can be assigned in a short form
• ltowlobjectProperty rdfaboutinfiltrate/gt
• ltowldomain rdfresourceSurfaceWater/gt
• ltowlrange rdfresourceAquifer/gt
• lt/owlobjectPropertygt
• Or the long way, as is shown in the following
  slide!
• ltrdfDescription rdfabout"infiltrategtltrdftype
  gtltrdfDescription
• rdfabout"http//www.w3.org/2002/07/owlOb
  jectProperty"/gtlt/rdftypegt
• ltrdfsdomaingtltrdfDescription
  rdfabout"SurfaceWater"/gtlt/rdfsdomaingt
• ltrdfsrangegtltrdfDescription
  rdfabout"Aquifer"/gtlt/rdfsrangegt
• lt/rdfDescriptiongt

12
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"length"gt
ltrdftypegtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlDatatypeP
roperty"/gtlt/rdftypegt ltrdfsdomaingtltrdfDesc
ription rdfabout"Fault"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"http//www
.w3.org/2001/XMLSchemastring"/gtlt/rdfsrangegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"infiltrate"gt ltrdftypegtltrdfDesc
ription rdfabout"http//www.w3.org/2002/07/owlO
bjectProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription rdfabout"SurfaceW
ater"/gtlt/rdfsdomaingt ltrdfsrangegtltrdfDescr
iption rdfabout"Aquifer"/gtlt/rdfsrangegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"Fault"gt ltrdftypegtltrdfDescriptio
n rdfabout"http//www.w3.org/2002/07/owlClass"/
gtlt/rdftypegt lt/rdfDescriptiongt
ltrdfDescription rdfabout"SurfaceWater"gtltrdfty
pegt ltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"Aquifer"gt ltrdftypegtltrdfDescriptio
n rdfabout"http//www.w3.org/2002/07/owlClass"/
gtlt/rdftypegt lt/rdfDescriptiongt lt/rdfRDFgt
13
owlinveseOf

• Properties themselves have properties
• OwlinverseOf 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 analyzes and analyzedBy,
  investigates and investigatedBy, hasSample
  and sampleOf, wrote and writtenBy, and
  locatedIn and locationOf, reverses the
  direction of the second property
• These follow the definition of the mathematical
  inverse function that state if f(x) y, then
  f-1(y) x.

14
Inference of the owlinverseOf

• P owlinverseOf Q.
• If
• x P y.
• Then
• y 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

hasPart
Fold
Limb
x
y
partOf
15
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"Fold"gtltrd
ftypegt ltrdfDescription rdfabout"http//w
ww.w3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"Limb"gtltrdftypegt
ltrdfDescription rdfabout"http//www.w3.org/2002
/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"partOf"gtltrdftypegt
ltrdfDescription rdfabout"http//www.w3.org/2002
/07/owlObjectProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription rdfabout"Limb"/gtlt
/rdfsdomaingt ltrdfsrangegtltrdfDescription
rdfabout"Fold"/gtlt/rdfsrangegt
ltowlinverseOfgtltrdfDescription
rdfabout"hasPart"/gtlt/owlinverseOfgt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"hasPart"gtltrdftypegt
ltrdfDescription rdfabout"http//www.w3.org/2002
/07/owlObjectProperty"/gtlt/rdftypegt
lt/rdfDescriptiongt lt/rdfRDFgt
16
partOf owlinverseOf hasPart
17
owlsymmetricProperty

•  If the property that relates two classes is the
  same 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 owlSymmetricProperty.
• The inference for a symmetric property is as
  follows
• P owlinverseOf P.
• That is, the symmetric property is an inverse
  property.

18
owltransitiveProperty

•  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 owltransitiveProperty,
  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.

P
P
FaultBend
FaultSegment
Fault
x
y
z
19
partOf
partOf
partOf
FaultBend
FaultSegment
Fault
x
y
z

• The partOf property (containment) may be
  transitive (not always). Finger is part of hand,
  and hand is part of body
• However, someones 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
• strucFaultSegment strucpart of struc
  FaultSegment.
• strucpartOf rdf type owlTransitivePropert
  y.
• strucFaultSegment rdfssubClassOf strucFault.

20
Transitive partOfpartOf owlinverseOf hasPart
21
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"Fault"gt
ltrdftypegtltrdfDescription rdfabout"http//w
ww.w3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"FaultSegmentgt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"partOf"gtltrdftypegt
ltrdfDescription rdfabout"http//www.w3.org/2002
/07/owlObjectProperty"/gtlt/rdftypegt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlTransitiveProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription
rdfabout"FaultSegment"/gtlt/rdfsdomaingt
ltrdfsdomaingtltrdfDescription rdfabout"FaultBen
d"/gtlt/rdfsdomaingt ltrdfsrangegtltrdfDescript
ion rdfabout"Fault"/gtlt/rdfsrangegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"FaultBend"gtltrdftypegt
ltrdfDescription rdfabout"http//www.w3.org/2002
/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"hasPart"gt ltrdftypegtltrdfDescrip
tion rdfabout"http//www.w3.org/2002/07/owlObje
ctProperty"/gtlt/rdftypegt ltrdfsdomaingtltrdfD
escription rdfabout"Fault"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"FaultSe
gment"/gtlt/rdfsrangegt ltowlinverseOfgtltrdfDe
scription rdfabout"partOf"/gtlt/owlinverseOfgt
lt/rdfDescriptiongt lt/rdfRDFgt
22
locatedIn is transitive

• C locatedIn B B locatedIn A C locatedIn A
•  
• geolocatedIn rdftype owlTransitiveProperty.
•  
• If
• tectSanAndreasFault geolocatedIn geoCalifornia.
  
• geoCalifornia geolocatedIn geoUnited
  States.
• Then
• geoSanAndreasFault geolocatedIn geoUnited
  States.

23
owlfunctionalProperty

• A functional property p (e.g., hasBiologic
  Mother) can only have one unique value y for a
  particular individual x
• That is, there is a single value of y for a given
  x as is for a mathematical function
• Function yx2 has a square which is unique for
  each input x
• Given x (subject individual) we can find y
  (object individual) i.e., x ? y
• A functional property is therefore one for which
  there is only one value!
• There could be many x (e.g., children samples),
  but all relate only to one y (Mother Sampler)
• Functional properties have a global cardinality
  constraint

24
Inference

• The owlFunctionalProperty can only take one
  value for any individual, allowing sameness to be
  inferred
• The inference rule for this construct is as
  follows
•  
• If
• P rdftype owlFunctionalProperty.
• X P A
• X P B
• Then
• A owlsameAs B.

25

• A property p is functional if x p y1 and x p y2
  imply that y1 y2 i.e., the two object
  individuals are the same(owl sameAs)
• The subjects are not asserted to be the same
  only the objects are the same
• For example mineral type is a functional
  property
• minhasType rdftype owlFunctionalPropert
  y.
• minmineral1 minhasType minpyr.
• minmineral 1 minhasType minpyroxene.
• minpyr owlsameAs minpyroxene.
• Isotope daughterOf isotope
• sampleLocation and samplerOf are functional
  properties, because x sampleLocation y or x
  samplerOf y has one unique value y for each x
  (i.e., location for a sample or person who took
  the sample)

26
owlFunctionalProperty
27
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"Sample"gt
ltrdftypegtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlClass"/gtlt
/rdftypegt lt/rdfDescriptiongt
ltrdfDescription rdfabout"Location"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"sampleLocation"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlObjectProperty"/gtlt/rdftypegt
ltrdftypegtltrdfDescription rdfabout"http//ww
w.w3.org/2002/07/owlFunctionalProperty"/gtlt/rdfty
pegt ltrdfsdomaingtltrdfDescription
rdfabout"Sample"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"Location"
/gtlt/rdfsrangegt lt/rdfDescriptiongt
ltrdfDescription rdfabout"Geologist"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"samplerOfgt ltrdftypegtltrdfDescr
iption rdfabout"http//www.w3.org/2002/07/owlOb
jectProperty"/gtlt/rdftypegt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlFunctionalProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription
rdfabout"Geologist"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"Sample"/gt
lt/rdfsrangegt lt/rdfDescriptiongt lt/rdfRDFgt
28
Inverse Functional Property

• This property, which is the inverse of the
  owlFuncationalProperty, is very useful for
  merging data from different sources
• The owlFunctionalProperty and owlInverseFuncatio
  nalProperty allow merging data for a same
  individual from different sources
• The owlInverseFunctionalProperty is equivalent
  to the key in relational databases, such as SSN
  and driving license number
•  
• The inference rule of this construct is as
  follows
•  
• P rdftype owlInverseFunctionalProperty.
• A P X.
• B P X.
• Then
• A owlsameAs B.

29
owlInverseFuncationalProperty

• If 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 owlInverseFunctiona
  lProperty 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!
• e.g., Isotope parentOf isotope
• e.g., hasSingleAuthorArticle a person may have
  many published papers (objects), but all are
  authored by one author (subject).
• Person hasSingleAuthorArticle SingleAuthorArticle
• Given a singleAuthorArticle object individual (y)
  we can find a unique subject individual (x)

y
x
y
y
30

hasSingleAuthorPaper
Author
Article

• A single value of the property (object y) cannot
  be shared by two x subject entities, e.g.,
  describes as in Geologist describes ThinSection
• Declaring a property to be inverse functional,
  puts a global cardinality constraints on the
  property
• Datatype properties cannot be declared
  inverse-functional in OWL DL

describes
Geologist
ThinSection
31
Example
locatedAt
Station
Location

• Assume location of any measurement is uniquely
  identified by the longitude and latitude (defined
  by Location class), i.e., no two samples can be
  taken at the same exact spot
• Station134 locatedAt LocationA.
• Station346 locatedAt LocationA.
•  
• We infer that
• Station134 owl sameAs Station346

32
One-to-one Property
x
y

• For a one-to-one relationship, we use a
  combination of the owlFunctionalProperty and
  owlinverseFunctionalProperty.
• Note Sample sampleId XSDInteger is not a good
  example, because it is a datatype property, and
  not every number gives you the sample
•  
• hasimage rdfsdomain ThinSection.
• hasImage rdfsrange Image.
• hasImage rdftype owlFunctionalProperty.
• hasImage rdftype owlInverseFuncationalPropert
  y.
•  
• So, any two thin sections with the same image
  must be the same thin section!

sampleId
X
Sample
XSDInteger
hasImage
ThinSection
Image
33

• 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 individuals can
  share that same composition (if they belong to
  the same class) (compare with hasFather)
• 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

34
owlequivalentProperties
folds
owlequivalentProperty

• Already we have learned about asserting thattwo
  properties behave in the same way
• To make two properties equivalent, we do exactly
  as we did to make to classes equivalent (by using
  rdfssubclassOf), i.e., use the
  rdfssubPropertyOf twice or using
  owlequivalentProperty
• e.g., make the folds and buckles properties
  equivalent
•  
• struc folds rdfs subPropertyOf buckles.
• struc buckles rdfs subPropertyOf strucfolds.
• This can also be done with the owlequivalentPrope
  rty
•  
• strucfolds owlequivalentProperty struc
  buckles.

buckles
35
One-to-one hasImage Property
36

• ltrdfDescription rdfabout"hasImage"gt
• ltrdftypegt
• ltrdfDescription rdfabout"http//www.w3.org/20
  02/07/owlObjectProperty"/gtlt/rdftypegt
• ltrdftypegtltrdfDescription rdfabout"http//www
  .w3.org/2002/07/owlFunctionalProperty"/gtlt/rdftyp
  egt
• ltrdftypegtltrdfDescription rdfabout"http//www
  .w3.org/2002/07/owlInverseFunctionalProperty"/gtlt/
  rdftypegt
• ltrdfsdomaingt ltrdfDescription
  rdfabout"ThinSection"/gtlt/rdfsdomaingt
• ltrdfsrangegtltrdfDescription rdfabout"Image"/
  gtlt/rdfsrangegt
• lt/rdfDescriptiongt
• ltrdfDescription rdfabout"ThinSection"gt
• ltrdftypegtltrdfDescription rdfabout"http//www
  .w3.org/2002/07/owlClass"/gtlt/rdftypegt
• lt/rdfDescriptiongt
• ltrdfDescription rdfabout"Image"gt
• ltrdftypegtltrdfDescription rdfabout"http//www
  .w3.org/2002/07/owlClass"/gtlt/rdftypegt
• lt/rdfDescriptiongt
• lt/rdfRDFgt

37
Example
folds
shortening
Bedding
equivalentProperty
buckles

• Which means any triple using the folds
  property, can use its equivalent property
  buckles
• strucShortening strucfolds strucBedding.
• strucshortening strucbuckles strucBedding.
•  
•  
• Note
• owlequivalentProperty rdftype owl
  symmetricPropert 

38
Combining Properties

•  Writing procedures or modeling processes, for
  example in a laboratory experiment, workflow
  management, and modeling geological processes, we
  commonly combine several types of properties
  (e.g., inverseOf, transitiveProperty,
  subPropertyOf)
• In such cases, some activities may depend on the
  completion of others
• For example, making thin section may require the
  following steps, each may depend on the
  completion of others. Here is the workflow
• Slice the rock specimen, square the slice into
  chip, polish the chip to fine grit, mount the
  chip to slide, cut and polish the section, and
  finally, mount with cover slide

39
Workflow

• Since these steps are in order, then each step
  may enable the next step, or each step depends or
  requires the previous step

40
code

• dependsOn owl inverseOf enables
• sliceSpecimen enables makeChip.
• makeChip enables polishChip.
• polishChip enables mountChip.
• mountChip enables polishSection.
• polishSection enables putCoverslide.
•  
• dependsOn rdfs subPropertyOf requires.
• requires rdf type owl TransitiveProperty.
• enables rdfs subPropertyOf requiredFor.
• requiredFor rdf type owl
  TransitiveProperty
• From the above statements we infer the following
  requirements for mountChip
•  
• mountChip requires polishChip
• requires makechip
• requires sliceSpecimen.

41
OWL Class

• OWL allows constructing complex classes using
  restrictions of the properties of existing
  classes
• It also includes
• owldisjointWith, owlThing, owlNothing,,
  owlequivalentClass, owlone of,
  owlintersectionOf, owlunion, and
  owlcomplementOf

42
Declaring classes in OWL

• An owl class is defined in two different ways
• ltowlDescription rdfaboutClassNamegt
• ltrdftype rdfresourceowlClassgt
• lt/owlDescriptiongt
• Or in short hand, using the owlClass constructor
• ltowlClass rdfaboutclassName/gt
• Or
• ltowlClass rdfIDname/gt

43
Owl uses the rdfssubClassOf

• This is used to create class a hierarchy
• rdfssubClassOf is transitive
• ltowlClass rdfaboutStrikeSlipFaultgt
• ltrdfssubClassOf rdfresourceFault/gt
• ltowlClassgt
• Every owl class is a subclass of the owlThing

44
owldisjointWith

• Two classes can be declared to be disjoint if
  they cannot have a common instance
• i.e., their intersection is empty
• For example
• Solid and Liquid Solid and Gas
• Inorganic and Organic
• Crystalline and Amorph
• Mineral and Gas, Mineral and Organic

45
Mineral is naturally occurring, inorganic, solid,
crystalline substance with definite chemical
composition. It is disjoint with amorph,
artificial, gas, and organic substances.
46
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-synta
x-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-
schema"gt ltrdfDescription rdfabout"Mineral"gt
ltrdftypegtltrdfDescription rdfabout"http//ww
w.w3.org/2002/07/owlClass"/gtlt/rdftypegt
ltowldisjointWithgtltrdfDescription
rdfabout"Amorph"/gtlt/owldisjointWithgt
ltowldisjointWithgtltrdfDescription
rdfabout"Artificial"/gtlt/owldisjointWithgt
ltowldisjointWithgtltrdfDescription
rdfabout"Gas"/gtlt/owldisjointWithgt
ltowldisjointWithgtltrdfDescription
rdfabout"Organic"/gtlt/owldisjointWithgt
ltowldisjointWithgtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlClass"/gtlt
/owldisjointWithgt lt/rdfDescriptiongt ltrdfDescri
ption rdfabout"Amorph"gt ltrdftypegtltrdfDescr
iption rdfabout"http//www.w3.org/2002/07/owlCl
ass"/gtlt/rdftypegt lt/rdfDescriptiongt ltrdfscomment
gtthe Artificial, Gas, and Organic classes
herelt/rdfscommentgt ltrdfDescription
rdfabout"hasComposition"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlDatatypeProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription
rdfabout"Mineral"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"http//www
.w3.org/2001/XMLSchemastring"/gtlt/rdfsrangegt lt/rd
fDescriptiongt lt/rdfRDFgt
47
owlThing (?)owlNothing (?)

• OWL has two predefined classes owlThing and
  owlNothing
• All individuals are members of the owlThing
• OwlThing is the top, most general class, and
  represents the universe, which means all
  individuals are its instances
• OwlNothing has no instance
• Because the intersection of two disjoint sets is
  empty, it is represented by the owlNothing

48
Intersection (?) of two disjoint classes that
subclass owlThing is owlNothing
49
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"Liquid"gt
ltrdftypegtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlClass"/gtlt
/rdftypegt ltrdfssubClassOfgtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlThing"/gt
lt/rdfssubClassOfgt ltowldisjointWithgtltrdfDe
scription rdfabout"Solid"/gtlt/owldisjointWithgt
lt/rdfDescriptiongt ltrdfDescription
rdfabout"MyNothing"gt ltrdftypegtltrdfDescr
iption rdfabout"http//www.w3.org/2002/07/owlCl
ass"/gtlt/rdftypegt ltowlintersectionOf
rdfparseType"Collection"gt
ltrdfDescription rdfabout"Solid"/gt
ltrdfDescription rdfabout"Liquid"/gt
lt/owlintersectionOfgt lt/rdfDescriptiongt
ltrdfDescription rdfabout"Solid"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
ltrdfssubClassOfgtltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlThing"/gtlt
/rdfssubClassOfgt lt/rdfDescriptiongt lt/rdfRDF
gt
50
Set Equivalence (?) by owlequivalentClass

•  When we want to assert that two URIs refer to
  the same thing, we use owlequivalentClass
• ltowlClass rdfaboutSaturatedZonegt
• ltowlequivalentClass rdfresourceZoneOfSaturatio
  n/gt
• lt/owlClassgt
• XRD owlequivalentClass XRayDiffraction.
• strucJoint owlequivalentClass strucTensileFract
  ure.
• We can also make two classes to be equal if we
  make each a subclass of the other, for example,
  if we want to say that a joint is the same thing
  as a tensile fracture, we assert
• strucJoint rdfssubClassOf
  strucTensileFracture.
• strucTensileFracture rdfssubClassOf
  strucJoint.
•  

51
Inference for owlequivalentClass

• A owlequivalentClass B.
• x rdftype A
• then
• x rdftype B
• Moreover, from the subClassOf property we
  additionally infer that the two classes have
  exactly the same members
•  
• A rdfssubClassOf B.
• x rdftype B.
• then
• x rdftype A.
•  
•  
• Notice that
• owlequivalentClass rdfstype
  owlSymmetricProperty.

A
B
?
x
xy
52
owlone of ?x1,, xn?

• Allows defining a class by enumerating its
  member, using owl one of
• Enumeration is a list of options that a user can
  select from
• The list is usually exhaustive, like the list of
  planets, types of rock or minerals, names of
  oceans

53
Mercury, Venus, Earth, Mars, Jupiter, Saturn,
Uranus, Neptune
54
ltrdfDescription rdfabout"SolarPlanet"gt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlClass"/gtlt/rdftypegt
ltowloneOf rdfparseType"Collection"gt
ltrdfDescription rdfabout"Mercury"/gt
ltrdfDescription rdfabout"Venus"/gt
ltrdfDescription rdfabout"Earth"/gt
ltrdfDescription rdfabout"Mars"/gt
ltrdfDescription rdfabout"Jupiter"/gt
ltrdfDescription rdfabout"Saturn"/gt
ltrdfDescription rdfabout"Uranus"/gt
ltrdfDescription rdfabout"Neptune"/gt
lt/owloneOfgt ltrdfscommentgtDeclare each planet
as an instance of the SolarPlanetlt/rdfscommentgt lt
/rdfDescriptiongt ltrdfDescription
rdfabout"Mercury"gt ltrdftypegtltrdfDescription
rdfabout"SolarPlanet"/gtlt/rdftypegtlt/rdfDescri
ptiongt ltrdfscommentgtlt/rdfscommentgt ltrdfDescri
ption rdfabout"Sun"gt ltrdftypegtltrdfDescript
ion rdfabout"http//www.w3.org/2002/07/owlClass
"/gtlt/rdftypegt lt/rdfDescriptiongt ltrdfDescription
rdfabout"hasPlanet"gt ltrdftypegtltrdfDescrip
tion rdfabout"http//www.w3.org/2002/07/owlObje
ctProperty"/gt lt/rdftypegt
ltrdftypegtltrdfDescription rdfabout"http//www.w
3.org/2002/07/owlFunctionalProperty"/gtlt/rdftypegt
ltrdfsdomaingtltrdfDescription
rdfabout"Sun"/gtlt/rdfsdomaingt
ltrdfsrangegtltrdfDescription rdfabout"SolarPlan
et"/gtlt/rdfsrangegt lt/rdfDescriptiongt
55
Individuals

• These are instances of physical or virtual types,
  i.e., same type individuals are members of the
  same class
• Any individual belongs to the owlThing class
• An individual can belong to one or more classes
• Individuals may be assigned to a class as
  follows
• ltrdfDescription rdfaboutinstanceNamegt
• ltrdftype rdfresourceClassNamegt
• ltrdfDescriptiongt

56
Short form of class assignment

• Alternatively, we can instantiate a class as
• ltClassName rdfaboutinstanceName/gt
• ltFault rdfaboutSanAndreasFault/gt
• Or, use the rdfID
• ltowl Thing rdfID ZagrosFault/gt
• ltowl Person rdfID Babaie/gt
• Or we can do it using rdftype as shown on next
  slide!
• These statements say that the ZagrosFault is a
  Thing, and Babaie is of type Person

57
Instantiating and individual
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltrdfDescription rdfabout"Mineral"gt
ltrdftypegt ltrdfDescription
rdfabout"http//www.w3.org/2002/07/owlClass"/gt
lt/rdftypegt lt/rdfDescriptiongt
ltrdfDescription rdfabout"Mineral1"gt
ltrdftypegtltrdfDescription rdfabout"Mineral"/gtlt
/rdftypegt lt/rdfDescriptiongt lt/rdfRDFgt
58
Same Individuals (owlsameAs)

• In many cases we want to assert that two things
  are actually the same
• For example, two samples with different numbers
  may actually be the same, or two faults with
  different names may actually be the same fault
• ltFault rdfaboutSanAndreasFault/gt
• ltFault rdfaboutSanAndreasShearZone/gt
• ltrdfDescription rdfabout SanAndreasFaultgt
• ltowlsameAs rdfresourceSanAndreasShearZone/gt
• lt/rdfDescriptiongt
• For example, Zagros Fault, Zagros shear zone,
  Zagros Crash zone, Zagros Thrust
• geochemsample1 owlsameAs strucsample22.
• tectZagrosFault owlsameAs strucZagrosShearZone.

59
Inference

• Notice that owlsameAs is a symmetric Property
•  
• owlsameAs rdf type owlSymmetricProperty.
• Therefore, we can infer that
• strucsample22 owlsameAs geochemsample1.
• strucZagrosShearZone owlsameAs
  tectZagrosFault.
•  

60
owldifferentFrom

• Is used to declare that individuals are mutually
  different
• It uses owldistinctMembers and
  rdfparseTypeCollection to represent an
  exhaustive list
• ltowldifferentFromgt
• ltowldistinctMembers rdfparseTypeCollection
  gt
• ltFault rdfaboutBrevardFault/gt
• ltFault rdfaboutTowaligaFault/gt
• lt/owldistinctMembersgt
• lt/owldifferentFromgt

61
Merging Different Databases w/ owlsameAs

• The owlsameAs is very useful when merging data
  from different databases
• For example, lets assume that the following
  Sample and Sampling tables (next slide) are
  from two autonomous relational databases
• As we can see, some concepts are named
  differently in the two databases. We want to
  merge data from the two tables
• Recall that in a relational database, every row
  is a record of an individual
• The Sample table has 6 rows and 6 columns, which
  means that we can extract 36 triples from this
  table
• The Sampling table has 8 columns and 6 rows,
  yielding 48 triples

62
Sample Table
SAMPLE (Petrology Database) SAMPLE (Petrology Database) SAMPLE (Petrology Database) SAMPLE (Petrology Database) SAMPLE (Petrology Database) SAMPLE (Petrology Database)
Sample ID Sample Number Paleont Age Rock Absolute Age Researcher
1 N100 Basalt 75 Ma Babaie
2 N110 Miocene Limestone Babaie
3 N120 Miocene Limestone Babaie
4 N130 Basalt 73 Ma Babaie
5 N140 Oligocene Shale Babaie
6 N150 Gabbro 70 Ma Babaie
63
Make the Triples

• To make the triples, we use the namespace for
  each group (e.g., petr for the petrology, and
  tect for the tectonics domains)
• Every cell of each table is a triple, with
  subject (individual corresponding to the row)
  designated with the namespace and table name
  attached to the id of the row
• The predicate for each triple is designated with
  the namespace and table name attached to field
  name for the corresponding cell
• The object is the content of the corresponding
  cell

64
Some of the triples are shown below

• Triples for the first row shown below (only
  triples of two rows are shown)
• petr Sample1 petr Sample_Sample_Number
  N100.
• petr Sample1 petr Sample_Paleont_Age .
• Petr Sample1 petr Sample_Rock Basalt.
• petr Sample1 petr Sample_Absolute_Age 75 Ma.
• petr Sample1 petr Sample_Researcher Babaie.
•  
• petr Sample2 petr Sample_Sample_Number
  N110.
• petr Sample2 petr Sample_Paleont_Age
  Miocene.
• Petr Sample2 petr Sample_Rock Limestone.
• petr Sample2 petr Sample_Absolute_Age .
• petr Sample2 petr Sample_Researcher Babaie.

65
SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database) SAMPLING (Tectonics Database)
ID Sample Number Region SamplingDate Project Investigator Map Name Isotopic Age
1 N130 Neyriz 11/2/2007 Neyriz Ophiolite Babaie Neyriz 124000 73 Ma
2 N150 Neyriz 11/6/2007 Neyriz Ophiolite Babaie Neyriz 124000 70 Ma
3 N100 Neyriz 11/6/2007 Neyriz Ophiolite Babaie Neyriz 124000 75 Ma
4 N120 Neyriz 11/3/2007 Neyriz Ophiolite Babaie Neyriz 124000
5 N140 Neyriz 11/3/2007 Neyriz Ophiolite Babaie Neyriz 124000
6 N110 Neyriz 11/5/2007 Neyriz Ophiolite Babaie Neyriz 124000
66

• RDF triples for the Sampling table (only triples
  of two rows are shown)
•  
• tect Sample1 tect Sampling_Sample_Number
  N130.
• tect Sample1 tect Sampling_Region Neyriz.
• tect Sample1 tect Sampling_Sampling_Date
  11/2/2007.
• tect Sample1 tect Sampling_Project Neyriz
  Ophiolite.
• tect Sample1 tect Sampling_Investigator
  Babaie.
• tect Sample1 tect Sampling_Map_Name Neyriz
  124000.
• tect Sample1 tect Sampling_Isotopic_Age 73
  Ma.
•  
• tect Sample2 tect Sampling_Sample_Number
  N150.
• tect Sample2 tect Sampling_Region Neyriz.
• tect Sample2 tect Sampling_Sampling_Date
  11/6/2007.
• tect Sample2 tect Sampling_Project Neyriz
  Ophiolite.
• tect Sample2 tect Sampling_Investigator
  Babaie.
• tect Sample2 tect Sampling_Map_Name Neyriz
  124000.
• tect Sample2 tect Sampling_Isotopic_Age 70
  Ma.
•  

67
Mapping the Databases

• We need to map the two tables to each other using
  some of the rdfs and owl construct if we want to
  run a federated query on the two tables
• Because the records (rows) in each table are
  actually individual data, we use the owlsameAs
  to assert that some individuals are the same
•   
• Notice that sample number 130 is in the 4th row
  for the Sample table, but is in the 1st row of
  the Sampling table (same situation for other
  samples)

68
The merging assertions

• petr Sample1 owl sameAs tect Sample3.
• petr Sample2 owl sameAs tect Sample6.
• petr Sample3 owl sameAs tect Sample4.
• petr Sample4 owl sameAs tect Sample1.
• petr Sample5 owl sameAs tect Sample5.
• petr Sample6 owl sameAs tect Sample2.

69
Boolean class constructors

• OWL provides Boolean constructors such as
  owlintersectionOf, owlunionOf, and
  owlcomplementOf to allow modeling complex
  knowledge
• These constructors represent logical
• and (?, conjunction)
• or (?, disjunction)
• not (?, negation)
• The purpose of these constructors is to combine
  simple classes into more complex classes with
  increased expressivity

70
owlintersectionOf (A?B)

• The class defined by the intersection of two
  classes contains instances of both classes
• ltowlClass rdfaboutSemibrittlegt
• ltowlintersectionOf rdfparseTypeCollectiongt
• ltowlClass rdfaboutBrittle/gt
• ltowlClass rdfaboutDuctile/gt
• lt/owlintersectionOfgt
• lt/owlClassgt

71
OwlunionOf (A U B)

• The class defined by the union of two classes has
  instances of either or both classes
• ltowlClass rdfaboutMigmatitegt
• ltowlunionOf rdfparseTypeCollectiongt
• ltowlClass rdfaboutMetamorphicRock/gt
• ltowlClass rdfaboutIgneousRock/gt
• lt/owlunionOfgt
• lt/owlClassgt
• We can use the owlintersectionOf and owlunionOf
  constructor s with the owlsubClassOf as in next
  slide for the case of owlcomplementOf

72
owlcomplementOf (A)

• The complement of a class contains no instance of
  the class
• For example, the complement of Fault contains
  instances of Cat, Fruit, and River
• ltowlClass rdfaboutLandgt
• ltowlsubClassOf gt
• ltowlClassgt
• ltowlcomplementOf rdfresourceBodyOfWa
  tergt
• lt/owlClassgt
• lt/owlcomplementOfgt
• lt/owlClassgt
• Even though this looks correct, but it is not ,
  because the instances of the Land class can
  include

73
Combination of Boolean constructors

• A better definition of the Land class may, for
  example, be defined by first defining a class
  (e.g., SolidGround) that annotates all land
  features, such as continents, islands, and then
  declare Land at the intersection of this class
  and the complement of the BodyOfWater class
• See next slide

74
lt?xml version"1.0" encoding"UTF-8"?gt ltrdfRDF
xmlnsowl"http//www.w3.org/2002/07/owl"
xmlnsrdf"http//www.w3.org/1999/02/22-rdf-syntax
-ns" xmlnsrdfs"http//www.w3.org/2000/01/rdf-sc
hema"gt ltowlClass rdfabout"Land"gt
ltowlintersectionOf rdfparseType"Collection"gt
ltowlClassgt ltowlcomplementOf
rdfresource"BodyOfWater"/gt
lt/owlClassgt ltowlClass
rdfabout"SolidGround"/gt
lt/owlintersectionOfgt lt/owlClassgt
ltowlClass rdfabout"BodyOfWater"/gt lt/rdfRDFgt
75
owl.disjointUnionOf

• OWL 2 DLs owl.disjointUnionOf defines a class
  as the union of other classes, all of which are
  pairwise disjoint
• It is a shorthand for separate axioms making the
  classes pairwise disjoint and one setting up the
  union class
• For example, we can define Mesozoic as the
  disjointUnionOf Triassic, Jurassic, and
  Cretaceous
• ltowl.Class rdfaboutMesozoicgt
• ltowl.disjointUnionOf rdfparseTypeCollection
  gt
• ltowlClass rdfaboutCretaceous/gt
• ltowlClass rdfaboutJurassic/gt
• ltowlClass rdfaboutTriassic/gt
• lt/owldisjointUnionOfgt
• lt/owl.Class

76
owlAlldisjointClasses

• OWL 2 also defines the owlAlldisjointClasses to
  collectively define a set of classes as mutually
  disjoint
• Use the owlmembers and rdfparseTypeCollection
  
• ltowlAllDisjointClassesgt
• ltowlmembers rdfparseTypeCollectiongt
• ltowlClass rdfaboutCretaceous/gt
• ltowlClass rdfaboutJurassic/gt
• ltowlClass rdfaboutTriassic/gt
• lt/owlmembersgt
• lt/owlAllDisjointClassesgt

77
Other alternative ways

• We can also use OWL 1 and mutually define the
  Triassic, Jurassic, and Cretaceous periods as
  disjoint, with the owldisjointWith
• ltowlClass rdfaboutCretaceous/gt
• ltowlClass rdfaboutJurassic/gt
• ltowldisjointWith rdfresourceCretaceous/gt
• lt/owlClassgt
• Or we can define the Cretaceous, Jurassic, and
  Triassic classes as disjoint, and then find the
  union of these disjoint sets (see owl code
  below), which is equivalent to the owl 2.0
  disjointUnionOf shortcut

78
Example Laramide Orogeny

• The Laramide orogeny in Montana and Wyoming
  occurred during the Late Cretaceous and Eocene
  (i.e., some processes occurred in either
  Cretaceous or Eocene, which are disjoint)
• The two periods have no intersection!
• Lets define timeLateCretaceousEocene (may be
  defined in the Time ontology) using the
  owl.disjointUnion, that occurred either in
  Cretaceous or in Eocene, but not in their
  intersection (i.e., A xor B)
• AxorB Exclusive disjunction or exclusive or
  One or the other, but not both (red is true in
  the image), and is false if neither or both are
  true

79
N3 Code for Laramide Orogeny

• owldisjointUnionOf (timeLateCretaceousEocene
  timeCretaceous timeEocene).
• Assuming that we have the LateCretaceousEocene
  class
• tectLaramide rdf type
  tectOrogeny.
• tect Laramide timeoccurredIn
  timeLateCretaceousEocene.
• timeintervalFor owl.inverseOf time
  occurredInInterval.
• We infer that
• time LateCretaceousEocene intervalFor tect
  Laramide
• Query Which orogeny occurred in Late
  Cretaceous-Eocene?)
• ?orogeny time occurredInInterval time
  LateCretaceousEocene.
• Will return Laramide

80
LateCretaceousEocene

• ltowl.Class rdfaboutLateCretaceousEocenegt
• ltowl.disjointUnionOf rdfparseTypeCollection
  gt
• ltowlClass rdfaboutEocene/gt
• ltowlClass rdfaboutCretaceous/gt
• lt/owldisjointUnionOfgt
• lt/owl.Class
• ltowlClass rdfaboutLaramideOrogeny/gt
• ltowlobjectProperty rdfaboutoccurredIn/gt
• ltrdfsdomain rdfresourceLaramideOrogeny
• ltrdfsrange rdfresource LateCretaceousEocenegt

81
Property Restriction

• OWL allows modifying the description of an
  existing class C to include a restriction R
  (based on some property P) on members of the
  class
• Restriction in OWL is a class (owlRestriction),
  meaning that it has individual members which are
  constrained by modified properties
• The individuals that satisfy R, do not have to be
  members of C (they could be in an unnamed class),
  because R defines a necessary but not sufficient
  condition for membership in C
• owl Restriction rdfs subClassOf owl
  Class.

82
Example

• A restriction limits the things that can be said
  (i.e., the values for its properties) about an
  individual of a class
• This means that a class may be modified by
  constraining the possible values for its
  properties
• For example, assume that we have the Fold class,
  which has a property called limb, and another
  property called intersectsAlong, which is a
  subproperty of the intersects property
• The intersectsAlong can mean intersect along
  anything
• However, we want to say that the limb of the fold
  intersects the axial plane of the fold along the
  fold axis. Thus, we want to restrict the
  intersectsAlong property of the Fold class to
  have a fold axis range

83

• Since we are constraining the values for
  properties, we use the keyword owlonProperty
  when we want to limit the way a property is used
  for the restricted class. For example, if we are
  constraining the use of the intersectsAlong
  property of the Fold class, we write
  owlonProperty intersectsAlong.
• Property restrictions are done using the
  following format
• 1 ltowlClass rdfabout Cgt
• 2
• 3 ltrdfssubClassOfgt
• 4 ltowlRestrictiongt
• 5 ltowlonProperty rdfresource
  Pgt
• 6 R (restrictions here)
• 7 lt/owl Restriction
• 8 lt/rdfssubClassOfgt
• 9
• lt/owlClassgt
• Line 3 indicates that C is a subclass of an
  unnamed restriction class (defined in lines 4-7),
  that satisfies R.

84
Types of Restriction

• Restrictions in OWL may be of three types
  quantified, cardinality, and value (filter
  information)
• A quantified restrictions may be
• Existential (?) declared with the owl
  someValuesFrom
• Universal (?), declared with owl allValuesFrom
  or owlhasValue

85
Quantified Restriction Existential
owlsomeValuesFrom

• This restriction says All individuals for which
  at least one (some) value of the property P comes
  from class C.
• This means that there is at least one member of
  the class with the P property

P
C
86
Example

• We would like to make a new restricted REE (Rare
  Earth Elements) class out of existing Analysis
  and RareEarth classes, by constraining the REE
  class to contain only individuals, at least one
  of which is a rare earth (this can better be done
  by defining what the REE are with a different
  restriction!)
• ltowlClass rdfabout REEgt
• ltrdfssubClassOf rdfresource Analysis/gt
  ltowlRestrictiongt ltowlonProperty
  rdfresource elements/gt
  ltowlsomeValuesFrom rdfresource
  RareEarth/gt lt/owlRestrictionlt/rdfssubClass
  Ofgt
• lt/owlClassgt

87
Restricted REE class
88
Example courses taught at GSU

• Assume that we have the two existing classes
  Course and GSU, and we want to define a new
  restricted class called GSUCourse from the Course
  class
• So, we declare GSUCourse a subclass of Course,
  and constrain it with an unnamed Restriction
  class
• Assume that an existing property called
  taughtIn is defined for the Course class. The
  GSUCourse restricted class can only have
  individuals some of which are taughtIn GSU
• ltowl Class rdf about GSUCoursegt ltrdfs
  subClassOf rdf resource Course/gt
  ltowl Restrictiongt ltowl onProperty
  rdf resource taughtIn/gt ltowl
  someValuesFrom rdf resource GSU/gt
  lt/owl Restriction lt/rdfs subClassOfgtlt/owl
  Classgt

89
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90
Quantified RestrictionUniversal owlallValuesFrom

• This produces a restriction class that says
• the individuals for which all values of the
  property P come from class C.
• This means that if there are any members, then
  they all must have this property P

91
Example Planar Structure

• ltowlClass rdfabout PlanarStructuregt
  ltrdfssubClassOf rdfresource Structure/gt
  ltowlRestrictiongt ltowlonProperty
  rdfresource attitude/gt
  ltowlallValuesFrom rdfresource
  PlanarAttitude/gt lt/owlRestriction
  lt/rdfssubClassOfgtlt/owlClassgt

92
Example XRF Analysis

• Assume that we have defined the Analysis and XRF
  classes before
• We would like to define a new restricted class
  constrained to have all of its individuals be of
  type XRF
• ltowl Class rdf about XRFAnaysisgt ltrdfs
  subClassOf rdf resource Analysis/gt
  ltowl Restrictiongt ltowl onProperty
  rdf resource typeOfAnalysis/gt ltowl
  allValuesFrom rdf resource XRF/gt
  lt/owl Restriction lt/rdfs subClassOfgt
• lt/owl Classgt

93
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94
Cardinality Restriction (Constraint)

• Cardinality restriction imposes a limit on the
  number of occurrences of property P that each
  member of a class C can have
• i.e., it provides constraints on the number of
  individuals that can be related to a member of a
  restriction class
• Cardinality restriction can be used to create
  special sets
•  
• Exact cardinality restriction, declared by owl
  cardinality, defines the exact number of
  occurrences of property P for members of class C
• For example, every mineral may have exactly one
  refractive index

95
Example Single Authored publication

• ltowl Class rdf about SingleAuthorPublicatio
  ngt ltrdfs subClassOf rdf resource
  Publication/gt ltowl Restrictiongt
  ltowl onProperty rdf resource
  hasAuthor/gt ltowl cardinality
  rdf datatype xsdnonNegativeInte
  gergt 1 ltowl cardinalitygt lt/owl
  Restriction lt/rdfs subClassOfgt
• lt/owl Classgt

96
Max or min cardinality restrictions

• Are declared with maxCardinality or
  minCardinality, and give the maximum or minimum
  number of occurrences of property P for members
  of class C
• Example A box fold can have at least two axes.
• ltowl Class rdf about BoxFoldgt ltrdfs
  subClassOf rdf resource Fold/gt
  ltowl Restrictiongt ltowl onProperty
  rdf resource axis/gt ltowl
  minCardinality rdf datatype
  xsdnonNegativeIntegergt 2 ltowl
  mincardinalitygt lt/owl Restriction
  lt/rdfs subClassOfgtlt/owl Classgt

97
Hydrogen has a maximum of three isotopes

• ltowl Class rdf about HydrogenIsotopegt
  ltrdfs subClassOf rdf resource
  Isotope/gt ltowl Restrictiongt
  ltowl onProperty rdf resource
  numberOfIsotopes/gt ltowl
  maxCardinality rdf datatype
  xsdnonNegativeIntegergt 3 ltowl
  maxcardinalitygt lt/owl Restriction
  lt/rdfs subClassOfgtlt/owl Classgt

98
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99
Value Restriction (Filter Information) owl
hasValue

• This is a special case of owl someValueFrom
  restriction in which the class C is a singleton
  set A
• It imposes a limit on the values the occurrences
  of property P may have
• This kind of restriction applies to cases in
  which we want to say all individuals that have
  the value A for the property P.

100
Planets that orbit around the sun

• Assume orbits has a Planet domain and an XSD
  string range
• ltowl Class rdf about PlanetOrbitingSungt
  ltrdfs subClassOf rdf resource
  Planet/gt ltowl Restrictiongt
  ltowl onProperty rdf resource orbits/gt
  ltowl hasValue rdf resource Sun/gt
  lt/owl Restriction lt/rdfs subClassOfgt
• lt/owl Classgt

101
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102
Zagros folds are those located in the Zagros Range

• ltowl Class rdf about ZagrosFoldgt ltrdfs
  subClassOf rdf resource Fold/gt
  ltowl Restrictiongt ltowl onProperty
  rdf resource locatedIn/gt ltowl
  hasValue rdf resource ZagrosRange/gt
  lt/owl Restriction lt/rdfs subClassOfgt
• lt/owl Classgt