This is a lecture note #8 for my class of Graduate School of Yonsei University, Korea. It describes what ontology is and its representation scheme.

1. Linked Data &
Semantic Web
Technology
The Semantic Web
Part 8. Ontology
Dr. Myungjin Lee

2. Ontology
• Origin of Ontology
– onto
• ὄντος : "being; that which is“
– logy
• -λογία : "science, study, theory“
• Ontology in Philosophy
– the philosophical study of the nature of being, becoming, existence, or
reality, as well as the basic categories of being and their relations
• what entities exist or can be said to exist
• how such entities can be grouped, related within a hierarchy
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3. Types of Ontology
• Upper ontology
– concepts supporting development of an ontology, meta-ontology
• Domain ontology
– concepts relevant to a particular topic or area of interest, for example,
information technology or computer languages, or particular branches of
science
• Interface ontology
– concepts relevant to the juncture of two disciplines
• Process ontology
– inputs, outputs, constraints, sequencing information, involved in business
or engineering processes
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4. Ontology in Information Science
• What is Ontology?
– to represent knowledge as a set of concepts within a domain, and the
relationships between pairs of concepts
• "formal, explicit specification of a shared conceptualisation"
by Thomas R. Gruber
– shared
• to represent consensual knowledge
– conceptualisation
• abstract model
– formal
• machine readable, processible, and understandable
– explicit
• fully and clearly expressed
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5. Conceptualization
• What is Conceptualization?
– the process of development and clarification of concepts
Object
refer to
stand for
Concept
symbolize
“Namdeamun”
Symbol
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6. Component of Ontology
• Class
– concepts that are also called type, sort, category, and kind
– Vehicle, the class of all vehicles
• Property
– characteristics that objects (and classes) can have
– <has by definition as part> 6-speed transmission
• Relationship
– how objects are related to other objects
– Ford Explorer is defined as a successor of : Ford Bronco
• Restriction
– formally stated descriptions of what must be true in order for some assertion to be
accepted as input
– door (with as minimum and maximum cardinality: 4)
• Axiom
– assertions in a logical form that together comprise the overall theory that the ontology
describes in its domain of application
• Instance
– the basic, "ground level" components of an ontology
– Ford Explorer object
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7. How to Represent Ontology
• Logic
– the study of modes of reasoning (which are valid, and which are fallacious)
• Topics in Logic
– Propositional Logic
– First Order Logic
– Description Logic
– …
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8. Propositional Logic
• a formal system in which formulas of a formal language may be
interpreted as representing propositions
• How to model facts?
Simple Assertions Modeling
The moon is made of green cheese g
It rains r
The street is getting wet. n
Simple Assertions Modeling
if it rains, then the street will get wet. rn
If it rains and the street does not get wet, (r ˄ ¬ n)  g
then the moon is made of green cheese.
• not powerful enough to represent all types of assertions
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9. First Order (Predicate) Logic
• Predicate Logic
– logic using a verb phrase template that describes a property of objects,
or a relationship among objects represented by the variables
• "x is blue"  blue(x)
– the existential ∃ ("there exists") and universal ∀ ("for all") quantifiers
• "for every object x in the universe, x > 1"  ∀(x) x > 1
• First Order Logic
– predicate logic that individuals can be quantified only
• FOL contains
– Objects : people, houses, numbers, theories, Ronald McDonald, …
– Relations : red, round, bogus, prime, brother of, bigger than, inside, ….
– Functions : father of, best friend, third inning of, one more than, end of…
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10. First Order Logic
• Syntax of FOL: Basic elements
– Constants KingJohn, 2, UCB,…
– Predicates Brother, >,……
– Functions Sqrt, LeftLegOf,…..
– Variables x, y, a, b,…
– Connectives ∧∨ ¬ ⇒ ⇔
– Equality =
– Quantifiers ∀, 
• How to model facts?
– “the father of a person is a male parent.”
∀x ∀y: isFather(x, y) ↔ (Male(x) ˄ isParent(x, y))
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11. First Order Logic
• FOL is perfectly suited for the description of ontologies, but
– FOL is high expressivity
– too bulky for modeling
– not appropriate to find consensus in modeling
– proof theoretically very complex (semi-decidable)
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12. Description Logic
• What is Description Logic?
– fragment of FOL
– a family of formal knowledge representation languages for representing
information about individuals, classes of individuals and their description
– more expressive than propositional logic but has more efficient decision
problems than first-order predicate logic
FOL DL
class concept
property or predicate role
object individual
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13. Concepts of Description Logic
• The core is a concept language
– use it for expressing factual assertions, intentional knowledge and queries
• Concepts – denote entities, classes
Student ≡ { x | STUDENT(x) }
• Roles – denote properties, relations
Friend ≡ { (x, y) | FRIEND(x, y) }
• Constructors for concept expressions
Student ⊓ Friend.Rich ≡ { x | STUDENT(x) ∧ y.FRIEND(x, y) ∧ RICH(y) }
• Individuals – instances of classes
a27, Colin, Green …
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14. DL Concept and Role Constructors
• Range of other constructors found in DLs, including:
– Number restrictions (cardinality constraints) on roles
⩾3 hasChild, ⩽1 hasMother
– Qualified number restrictions,
⩾2 hasChild.Female, ⩽1 hasParent.Male
– Nominals (singleton concepts)
{Italy}
– Concrete domains (datatypes)
hasAge.(⩾21)
– Inverse roles
hasChild- ≡ hasParent
– Transitive roles
hasChild*
– Role composition
hasParent.hasBrother ≡ uncle
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15. Syntax and Semantics of DL
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16. Syntax and Semantics of DL
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17. Naming Convention of Description Logic
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18. DL Knowledge Base
• DL Knowledge Base (KB) normally separated into 2 parts:
– TBox is a set of axioms describing structure of domain
HappyFather  Man ⊓ hasChild.Female ⊓ …
Elephant ⊏ Animal ⊓ Large ⊓ Grey
transitive(ancestor)
– ABox is a set of axioms describing a concrete situation (data)
John : HappyFather
<John,Mary> : hasChild
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19. TBox and ABox
• For terminological knowledge: TBox contains
– Concept definitions
• A  C (A a concept name, C a complex concept)
Father  Man ⊓ has-child.Human
Human  Mammal ⊓ has-child-.Human
• introduce macros/names for concepts, can be (a)cyclic
– Axioms
• C1 ⊑ C2 (Ci complex concepts)
favorite.Brewery ⊑ drinks.Beer
• restrict your models
• For assertional knowledge: ABox contains
– Concept assertions
• a : C (a an individual name, C a complex concept)
John : Man ⊓ has-child.(Male ⊓ Happy)
– Role assertions
• <a1, a2> : R (ai individual names, R a role)
• <John, Bill> : has-child
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20. References
• http://en.wikipedia.org/wiki/Ontology
• http://en.wikipedia.org/wiki/Ontology_(information_science)
• http://en.wikipedia.org/wiki/Ontology_components
• http://en.wikipedia.org/wiki/Logic
• http://en.wikipedia.org/wiki/Propositional_logic
• http://www.cs.odu.edu/~toida/nerzic/content/logic/pred_logic/intr_to_pred_logic.html
• http://en.wikipedia.org/wiki/Predicate_logic
• http://saltlux.tistory.com/15
• http://saltlux.com/wp-content/uploads/2012/12/2011WP_4_semanticweb2_2010_3.pdf
• http://www.slideshare.net/lysander07/05-semantic-web-technologies-ontologies
• http://www.slideshare.net/lysander07/06-semantic-web-technologies-logics
• http://www.slideshare.net/lysander07/07-semantic-web-technologies-description-logics
• http://en.wikipedia.org/wiki/Description_logic
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21. Dr. Myungjin Lee
e-Mail : mjlee@li-st.com
Twitter : http://twitter.com/MyungjinLee
Facebook : http://www.facebook.com/mjinlee
SlideShare : http://www.slideshare.net/onlyjiny/
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