1. Ontology representation
Guus Schreiber, VU
Ontology Engineering course

2. RDF/OWL
 Ontology language used in this course
 OWL = W3C Ontology Web Language
 RDF is basis of representation
– Triples = binary relation format
– Turtle is the triple syntax format most frequently
used
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3. Background reading
OWL Primer, W3C Recommendation, October
2009, http://www.w3.org/TR/owl2-primer/.
 Section 4 contains the basic constructs
 Secs. 5-8 describe the advanced features (not all
of these will be used in the course).
 The Turtle syntax is easiest to read. You can hide
the other in the beginning of the document.
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4. Some notes about syntax
 Protégé hides most of the syntax details
 OWL has quite a few syntax formats
 If you want to look at OWL syntax we
recommend that you use the Turtle syntax
 Background reading on Turtle):
h
http://wikitravel.org/en/Wikitravel:Turtle_RDF
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5. Class
 Central grouping construct
 Its instances are called “members”
 Classes can have multiple sub-classes
 Classes can have multiple super-classes
 Root class is conventionally called Thing: the
super-class of all classes
– Nothing is a sub-class of all classes
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6. Property
 Properties define relationships
 RDF/OWL properties have a direction
Artist creates Artwork
– Compare with UML!
 Two types of properties
– Object property: relationship between two classes
– Datatype property: relationship between a class and a
value space (integers, strings, dates)
 Terminology:
– Subject = left hand of relation
– Object = right hand of relation
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7. Property hierarchy
 Properties may have sub-properties
hasChild
hasDaugther
hasSon
 Logically sub-properties represent
relationships between subsets of the super-
property
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8. hasChild Judith
Peter Bob
Mary Sue
hasDaugther
Peter Judith
Mary Sue
hasSon
Peter Bob
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9. Domain and range
 Artist creates Artwork
 Artist is the domain
– Class of allowed “values” at the left side (origin( of
the relationship
 Artwork is the range
– Class of allowed “values” at the right side
(destination) of the relationship
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10. Property characteristics (1)
 Functional property
– For each subject this relation has at most one
object
– hasBiologicalMother
 Inverse-functional property
– For each object this relation has are most one
subject
– hasStudentNumber
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11. Property characteristics (2)
 Symmetric property
– IF i1 p i2 THEN i2 p i1
– Example: friend
 Asymmetric property
– IF i1 p i2 THEN NOT i2 p i1
– Example: parent
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12. Property characteristics (3)
 Transitive property
– IF i1 p i2 AND i2 p i3 THEN i1 p i3
 Example: partOf
– If Amsterdam is a part of North-Holland and
North-Holland is a part of The Netherlands, then
Amsterdam is a part of the The Netherlands.
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13. Property characteristics (4)
 Inverse property
– P1 inverseOf p2 implies that
IF i1 p1 i2 THEN i2 p2 i1
– Example: hasPart is the inverse of partOf, so if
Amsterdam is a part of North-Holland, then
North-Holland must have Amsterdam as one of its
parts.
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14. Property characteristics (5)
 Reflexive property
– FORALL p HOLDS i p i
– Example: for the property knows holds that
everybody knows him/herself
 Irreflexive property
– FORALL p MUST NOT HOLD I p I
– Example: for the parent relation holds that no one
can be his own parent
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15. Individual
 Instances of classes
– Rembrandt is and individual and member of the
Artist class
 Note: Protégé-OWL supports meta-classes
(classes which members are classes) poorly!
 Enumerated class: a class for which all
individual members can be listed
– Da Ponte opera’s of Mozart: Nozze di Figaro, Cosi
fan tutte, Don Giovanni
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16. Equality and inequality of individuals
 Equality example: two people (with different
URLs) are actually the same:
ex:Jim sameAs ex:James
 Inequality example: two people are different
Ex1:Jim differentFrom ex2:Jim
 Important on the Web!
– Difference between closed and open world
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17. Cardinality restrictions of properties
 Defines how many relationships of a certain
type there can be for a particular subject
 Examples:
– Person marriedTo max 1
– Course hasTutor min 1
– Person hasParent exactly 2
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18. Value restrictions of properties
 Defines to what objects a subject can be related
through a particular relation
 Examples
– Wine producedBy only Vineyard
Wine is only produced by vineyards
– RedWine color value “Red”
Red wines have a red color
– Bicycle hasPart some Wheel
Bicycles consist, amongst others, of at least one wheel
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19. Equivalent classes & properties:
simple
 States that two classes are the same, for example
two classes in different ontologies
wn-en:Dog = wn-it:Cane
 You can do the same for properties
ex1:hasPart = ex2:hasComponent
 Question: do you think equivalence occurs
frequently?
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20. Interlude:
the notion of class extension
 OWL is derived from “description logic”
 Description logic takes an “extensional” view of
classes:
– Two classes are the same if - and only if- they have
the same class extension
– The class extension is the set of members of the class
 Question: does this correspond to your intuition?
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21. Equivalent classes: complex (1)
 A class as the union of other classes
Parent = Mother or Father
 In terms of class extensions:
– The class extension of the class Parent is the union
of the class extensions of the classes Mother and
Father
– OWL calls such formulas “class expressions” (term
used in Protégé)
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22. Equivalent classes: complex (2)
 A class as the intersection of other classes
Mother =Woman and Parent
 In words: members of the Mother class must
be members of both the Woman and the
Parent class
 You can build even more complex
expressions:
Mother = Woman and some hasChild
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23. Class expressions
 Statements such as Woman and Parent and
Woman and some hasChild are called class
expressions
 Description logic treats class expressions as
anonymous classes
– i.e. concepts with no symbol, cf. the concept triad
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24. Equivalent classes: complex (3)
 Defining a class as the negation
(“complement”) of other classes
ChildlessPerson = Person and not Parent
 In words: a childless person is a member of
the person class who does not belong to the
extension of the parent class
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25. Necessary class definitions
 Description logic is used for classification
reasoning
 A necessary definition state a constraint which
must be true for class membership, but is not
enough to classify it as a member of the class
 Example: red wine must have a red color
– But: not all red things are red wines
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26. Necessary class definitions in
description logic
 The red-wine constraint is expressed as follows:
– Red wine is subclass of the class of all red things
 More formally: necessary conditions are stated
as a constraint that the class in question (red
wine) is a subclass of the anonymous class
represented by the class expression (class of all
red things)
 This explains how Protégé uses the
“Superclasses”
– Test this now; you’ll get the hang of it
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27. Sufficient class definitions
 Sufficient definitions allow us to classify an
individual as a member of a class
 Example: if we know someone belongs to the
Woman and Parent class, we also know she
belongs to the Mother class
 The equivalent-class expression represent
sufficient definitions
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28. Annotations
 Annotations are used to add metadata to
classes and properties
 Annotations play no role in classification
 Example annotations:
– Human-readable label (in multiple languages)
– Time created
– See also Dublin Core elements
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29. Class exercise: comparison with UML
class diagrams
 Make list of
– Similarities
– Differences
 Don’t forget that OWL is a Web language!
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30. Guidelines for naming concepts
 Keep original names, where possible
 Prefer more specific names over general ones
 Don’t be afraid of long names if you have to
invent a name
 Use a consistent format
– Here: ClassName propertyName
– But alternatives are fine
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31. Class room exercise
 “Artefacts are created by humans. Art works
are a kind of artefact. If a person has created
an art work we call him/her an artist.”
 Exercise: create with the help of Protégé an
OWL ontology for this domain description.
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