An Introduction to Ontologies in OWL

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An Introduction to Ontologies in OWL
Bibliography The OWL Guide The OWL
Overview Description Logic slides from Enrico
Franconi Artificial Intelligence A Modern
Approach by Russel and Nordig
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What is an Ontology?

• A representation of terms and their
  interrelationships (OWL Overview)
• A formal conceptualization of the world
• Smart data

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Ontology Languages

• Typically introduce concepts, properties,
  relationships between concepts and constraints
• May be expressed with diagrams
• ER Diagrams and UML Class Diagrams are ontology
  languages
• OWL (The Web Ontology Language) is expressed in
  XML
• OWL is a distributed ontology language

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The OWL Language

• February 10, 2004 OWL and RDF become W3C
  Recommendations
• See Jena from Hewlett-Packard Research for an
  existing Java API
• See Protégé-2000 at Stanford University for an
  existing OWL editor
• Big names in this space include Jim Hendler, and
  Debra McGuiness
• A large example can be found at
  http//www.mindswap.org/2003/CancerOntology/nciOnc
  ology.owl

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From the W3C
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The three sublanguages of OWL

• OWL Lite (decidable)
• OWL DL (Description Logic) (Decidable)
• OWL Full (Allows classes as instances)
• As we move from OWL Lite to OWL full we increase
  expressiveness and logical complexity.

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Decidability

• A proof procedure r is incomplete if there are
  true statements that the procedure cannot infer.
• Godel (1930s) showed that, for first order
  logic, any statement entailed by a set of
  statements can be proved from the set. In other
  words, a proof procedure exists.
• In 1965, Robinson found the resolution method.

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Decidability

• But, entailment is semi-decidable. If a statement
  does not follow from the premises it may go on
  and on.

If S follows the proof of S will emerge
after some time.
Resolution is complete
Premises
If S does not follow the procedure may loop
forever.
Statment S
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OWL Lite is a Decidable Language

• A Class is a set of individuals
• The class Thing is the superclass of all OWL
  classes
• The class Nothing is a subclass of all OWL
  classes and has no individuals members
• Classes may be defined as subClasses of other
  classes

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Three classes that subclass Thing

• ltowlClass rdfIDWinery/gt
• ltowlClass rdfIDRegion/gt
• ltowlClass rdfIDConsumableThing/gt
• These terms may be referred to from within this
• Document by Winery, Region and
• ConsumableThing.
• Other ontologies may refer to these terms with
• SomeURIWinery, SomeURIRegion and so on.

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Class Hierarchies built with subClassOf

• ltowlClass rdfIDPotableLiquidgt
• ltrdfssubClassOf rdfresource
  ConsumableThing /gt
• lt/owlClassgt
• ltowlClass rdfIDEdibleThinggt
• ltrdfssubClassOf rdfresource
  ConsumableThing /gt
• lt/owlClassgt

Deduction If x is a PotableLiquid then x is a
ConsumableThing
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Wine and Pasta

• ltowlClass rdfIDWinegt
• ltrdfssubClassOf rdfresource
  PotableLiquid /gt
• lt/owlClassgt
• ltowlClass rdfID Pasta
• ltrdfssubClassOf rdfresource EdibleThing /gt
• lt/owlClassgt

Deduction If x is Pasta then x is a
ConsumableThing
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SweetFruit and NonSweetFruit

• ltowlClass rdfIDSweetFruitgt lt! food.xml--gt
• ltrdfssubClassOf
• rdfresourceEdibleThing/gt
• lt/owlClassgt
• ltowlClass rdfIDNonSweetFruitgt lt!
  food.xml--gt
• ltrdfssubClassOf
• rdfresourceEdibleThing/gt
• lt/owlClassgt

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Defining Individuals

• ltRegion rdfIDCentralCoastRegion/gt
• Is identical to
• ltowlThing rdfIDCentralCoastRegion/gt
• ltowlThing rdfaboutCentralCoatRegiongt
• ltrdftype rdfresourceRegion/gt
• lt/owlThinggt

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Another individual

• ltowlClass rdfIDGrapegt lt! food.xml--gt
• ltrdfssubClassOf rdfresourceSweetFruit/gt
• lt/owlClassgt
• 
  lt! wine.xml --gt
• ltowlClass rdfIDWineGrapegt
• ltrdfssubClassOf rdfresourcefoodGrape/gt
• lt/owlClassgt
• ltWineGrape rdfIDCabernetSauvignonGrape /gt

Deduction CabernetSauvignon is a SweetFruit
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So far we have

• Thing

Winery
Region
ConsumableThing

• CentralCoastalRegion

PotableLiquid
EdibleThing
SweetFruit
NonSweetFruit
Pasta
Wine
Grape
WineGrape

• CabernetSauvignonGrape

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So far we have

• Classes
• Individuals
• We now need properties to state facts about
  classes and facts about individuals

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Properties

• Properties are binary relations
• A binary relation R from a set X to a set Y is a
  subset of the Cartesian product X x Y. If (x,y) e
  R, we write xRy and say x is related to y.

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Binary Relations

• Suppose the set X has members a,b and
• the set Y has members c,d,e.
• XxY (a,c),(a,d),(a,e),(b,c),(b,d),(b,e)
• Let R (a,c),(b,e)
• Since (a,c) e R and (b,e) e R we write aRc
• and bRe.
• Notice that a binary relation is a set of ordered
  pairs.

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Domain and Range
The set x e X (x,y) e R for some y e Y is
called the domain of R. The domain of R
(a,c),(b,e) is a,b. The set y e Y (x,y) e
R for some x e X is called the range of R. The
range of R (a,c),(b,e) is c,e.
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Properties

• R is Transitive if and only if
• xRy and yRz imply xRz
• locateIn is transitive in the wine ontology
• R is Symmetric if and only if
• xRy iff yRx
• adjacentTo is symmetric in the wine ontology

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Properties

• R is Functional if and only if
• xRy and xRz implies y z
• hasVintageYear is functional in the wine
• ontology
• R1 and R2 are Inverse Properties if and only if
• xR1y iff yR2x
• hasMaker and producesWine are inverse
• relations in the wine ontology

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OWLs Property Hierarchy

• Thing is a superset of Property
• Property is a superset of ObjectProperty
• Property is a superset of DataProperty
• An ObjectProperty associates a class instance
  with another class instance.
• A DataProperty associates a class instance with a
  datatype value

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OWLs Property Hierarchy Example
Thing
Mammal
Indentation shows subset relationships. Set
elements are marked with dots.
Person

• Mike
• Sue

Property
ObjectProperty DataProperty
hasRelative

hasSibling

• (Mike,Sue)

hasAge

• (Mike,23)

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OWL Property Syntax

• ltowlObjectProperty rdfIDlocatedIngt
• ltrdfsdomain
• rdfresourceOWLURIThing/gt
• ltrdfsrange
• rdfresourceRegion/gt
• lt/owlObjectPropertygt
• OWLURI will actually appear as the official OWL
  URI.

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Adding pairs to locatedIn

• ltRegion rdfIDSantaCruzMountainsRegiongt
• ltlocatedIn rdfresourceCaliforniaRegion/gt
• lt/Regiongt
• ltCabernetSauvignon
• rdfID SantaCruzMountainVinyardCabernetSauvi
  gnongt
• ltlocatedIn rdfresourceSantaCruzMountainsRe
  gion/gt
• lt/CabernetSauvignongt

Can we make a deduction?
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locatedIn

• locatedIn is defined as a set of ordered pairs.
• Each pair must contain an owlThing (maybe a
  Region)
• followed by value from the set Region.
• For example
• locatedIn
• (SantaCruzMountainsRegion, CaliforniaRegion),
• (SantaCruzMountainVinyardCabernetSauvignon,
• SantaCruzMountainsRegion)
• A deduction like the following is not yet
  possible
• The Thing SantaCruzMountainVinyardCabernetSau
  vignon
• is locatedIn CaliforniaRegion

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locatedIn is Transitive

• ltowlObjectProperty rdfIDlocatedIngt
• ltrdftype rdfresourceTransitiveProperty
  /gt lt! include an OWLURI --gt
• ltrdfsdomain
• rdfresourceOWLURIThing/gt
• ltrdfsrange
• rdfresourceRegion/gt
• lt/owlObjectPropertygt
• A deduction like the following is now possible
• The Thing SantaCruzMountainVinyardCabernetSau
  vignon
• is locatedIn CaliforniaRegion

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Given the madeFromGrape property

• ltowlObjectProperty rdfIDmadeFromGrapegt
• ltrdfsdomain rdfresourceWine/gt
• ltrdfsrange rdfresourceWineGrape/gt
• lt/owlObjectPropertygt

madeFromGrape
(Wine,WineGrape)
(Wine,WineGrape)
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And

• ltowlThing refIDLindemansBin65Chardonnaygt
• ltmadeFromGrape rdfresourceChardonnayGrape/
  gt
• ltowlThinggt
• We can deduce that LindemansBin65Chardonnay is a
  Wine.

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Given a Property

• ltowlClass rdfIDWineDescriptor/gt
• ltowlClass rdfIDWineColorgt
• ltrdfssubClassOf rdfresourceWineDescriptor
  /gt
• ltowlClassgt
• ltowlObjectProperty rdfIDhasWineDescriptorgt
• ltrdfsdomain rdfresourceWine/gt
• ltrdfsrange rdfresourceWineDescriptor/gt
• ltowlObjectPropertygt

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We can define a subproperty

• ltowlObjectProperty rdfIDhasColorgt
• ltrdfssubPropertyOf rdfresourcehasWineDescr
  iptor/gt
• ltrdfsdomain rdfresourceWine/gt
• ltrfdsrange rdfresource WineColor /gt
• lt/owlObjectPropertygt

hasWineDescriptor
(Wine,WineDescriptor) (Wine,WineDescriptor) (
Wine,WineDescriptor) (Wine,WineDescriptor) (Wi
ne,WineColor) (Wine,WineColor)
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And make it functional.

• ltowlObjectProperty rdfIDhasColorgt
• ltrdftype rdfresourceowlFunctionalProperty
  /gt
• ltrdfssubPropertyOf rdfresourcehasWineDescr
  iptor/gt
• ltrdfsdomain rdfresourceWine/gt
• ltrfdsrange rdfresource WineColor /gt
• lt/owlObjectPropertygt

hasWineDescriptor
(Wine,WineDescriptor) (Wine,WineDescriptor) (
Wine,WineDescriptor) (Wine,WineDescriptor) (Wi
ne,WineColor) (Wine,WineColor)
Now, for each Wine, there can be at most one
WineColor.
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Anonymous Classes
ltowlClass rdfIDWinegt ltrdfssubClassOf
rdfresource foodPotableLiquid /gt
ltrdfssubClassOfgt ltowlRestrictiongt
ltowlonProperty rdfresourcemadeFromGra
pe/gt ltowlminCardinality
rdfdatatype
xsdnonNegativeIntegergt1
lt/owlminCardinaltygt lt/owlrestrictiongt
ltrdfssubClassOfgt lt/owlClassgt
So, those Things that are in the PotableLiquid
set that are also in the set of things made from
at least one grape are Wines. If we know that x
is a Wine then we know it has at least one
madeFromGrape property defined.
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A Wine Individual

• ltCabernetSauvignon
• rdfID SantaCruzMountainVinyardCabernetSauvi
  gnongt
• ltlocatedIn rdfresourceSantaCruzMountainsRe
  gion/gt
• lt/CabernetSauvignongt
• This says nothing about what grape its made
  from. To find that out
• we must look to the class CabernetSauvignon.
  There we learn all
• wines of this variety are madeFromGrape
  CabernetSauvignon.
• So, individuals inherit properties and property
  values from their class.

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What does this mean?

• ltowlClass rdfID"Student"gt
• ltowlintersectionOf rdfparseType"Collection"gt
  
• ltowlClass rdfabout"Person"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"enrolledIn
  "/gt
• ltowlminCardinality rdfdatatype
• "xsdnonNegativeInteger"gt 1
• lt/owlminCardinalitygt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt

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And this?

• ltStudent rdfID"John"gt
• ltfriendOfgt
• ltStudent
  rdfresource"Peter" /gt
• lt/friendOfgt
• lt/Studentgt

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How about this one?

• ltStudent rdfabout" http//www.student.orgDaniel
  aRenuncio "gt
• ltowlsameIndividualAs rdfresource
• "http//www.student.orgDaniela_de_Senna_E
  yng_Renuncio"/gt
• lt/Studentgt