The Semantic Web #8 - Ontology

Linked Data &

Semantic Web

Technology

The Semantic Web

Part 8. Ontology

Dr. Myungjin Lee

Linked Data & Semantic Web Technology

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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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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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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Conceptualization

• What is Conceptualization?

– the process of development and clarification of concepts

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Concept

Object

Symbol

“Namdeamun”

symbolize

stand for

refer to

http://www.google.com/url?sa=i&rct=j&q=brain&source=images&cd=&cad=rja&docid=nOE9PIn423TyUM&tbnid=dDcLJI_r8n4DhM:&ved=0CAUQjRw&url=http://www.strokebreakthrough.com/what-we-treat/traumatic-brain-injuries/&ei=fEU9Ua2HEcy8qAGxzYGYDw&bvm=bv.43287494,d.aWM&psig=AFQjCNGTH2W01_OAo8WBmrxgodYsWsnFdw&ust=1363056261535227


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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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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Propositional Logic

• a formal system in which formulas of a formal language may be interpreted as representing propositions

• How to model facts?

• not powerful enough to represent all types of assertions

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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,

then the moon is made of green cheese.

(r ˄ ¬ n) g


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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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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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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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

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FOL DL

class concept

property or predicate role

object individual


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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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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Syntax and Semantics of DL

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Syntax and Semantics of DL

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Naming Convention of Description Logic

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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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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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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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Linked Data & Semantic Web Technology 21 21

Dr. Myungjin Lee

e-Mail : [email protected] Twitter : http://twitter.com/MyungjinLee

Facebook : http://www.facebook.com/mjinlee SlideShare : http://www.slideshare.net/onlyjiny/

The Semantic Web #8 - Ontology

Technology

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