05 Semantic Web Technologies - Ontologies

Semantic Web Technologies

LectureDr. Harald Sack

Hasso-Plattner-Institut für IT Systems EngineeringUniversity of Potsdam

Winter Semester 2012/13

Lecture Blog: http://semweb2013.blogspot.com/This file is licensed under the Creative Commons Attribution-NonCommercial 3.0 (CC BY-NC 3.0)

Dienstag, 13. November 12

http://semweb2013.blogspot.com


http://creativecommons.org/licenses/by-nc/3.0/

http://creativecommons.org/licenses/by-nc/3.0/

Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

2 1. Introduction 2. Semantic Web - Basic Architecture

Languages of the Semantic Web - Part 1

3. Knowledge Representation and LogicsLanguages of the Semantic Web - Part 2

4. Applications in the ,Web of Data‘

Semantic Web Technologies Content



3

3. Knowledge Representation & LogicThe Languages of the Semantic Web - Part 2



4

Semantic Web Technologien Wiederholung

Ontolo

gies



5


3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Popositional Logic and First Order Logic

• Description Logics

• RDFS Semantics• OWL and OWL-Semantics• OWL 2 and Rules



6

„People can‘t share knowledge if they don‘t speak a common language“Thomas Davenport (1997)



7

„People can‘t share knowledge if they don‘t speak a common language“Thomas Davenport (1997)

Turmbau zu Babel, Pieter Brueghel, 1563Dienstag, 13. November 12

Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Turmbau zu Babel, Pieter Brueghel, 1563

8 •Information Exchange among heterogeous systems• System A applies Schema A• System B applies Schema B

• same terms might be associated with different meanings (= denote different concepts)

• different terms might have the same meaning

• terms/concepts from System A with Schema A have to be translated into terms/concepts of System B with Schema B

Sharing Knowledge



9 •Information Exchange among heterogeous systems

• Solution (1):• Translator for all possible combinations of

n different systems → needs O(n2) translators….

• Solution (2):• independent representation schema

(Interlingua)•→ needs n translators….

Sharing Knowledge



10

Speak a common language...

• common symbols and concepts (Syntax)

• agreement about their meaning (Semantics)

• classification of concepts (Taxonomy)

• associations and relations of concepts (Thesauri)

• rules and knowledge about which relations are allowed and make sense (Ontologies)

Sharing Knowledge



11

What is Knowledge?

Truths Beliefs

Knowledge

Traditional Definition: „Knowledge is a subset of all true beliefs“



12

3. Wissensrepräsentation und Logik3.1 Ontologien in Philosophie und Informatik

Ontologies as Central Concept in Philosophy

Raffael: Die Schule von Athen, 1510-11Dienstag, 13. November 12


13

Raffael: Die Schule von Athen, 1510-11Christian Wolff: Philosophia prima sive Ontologia, 1729

• ον [greek] participle of „to be“ λογια [greek] science

Definition

„philosophical study of the nature of being, existence, or reality, as well as the basic categories of being and their relations....“ (wikipedia)

• „what does exist or can be said to exist?“

General Metaphysics⇳

Epistemology


http://en.wikipedia.org/wiki/Philosophy

http://en.wikipedia.org/wiki/Philosophy

http://en.wikipedia.org/wiki/Being

http://en.wikipedia.org/wiki/Being

http://en.wikipedia.org/wiki/Existence

http://en.wikipedia.org/wiki/Existence

http://en.wikipedia.org/wiki/Reality

http://en.wikipedia.org/wiki/Reality

http://en.wikipedia.org/wiki/Category_of_being

http://en.wikipedia.org/wiki/Category_of_being


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Fundamental Questions of Ontology

1.What does it mean for a being to be?• When are two things identical?• Is everything that exists also real?• Does something exist, if it is only possible?• Are there non-existing things?

2.What categories of objects do exist?• Do things exist that are only unique or

only multiple (Universalia)?• Do things exist that are unilaterally

dependent of others (Substances)?• Of which sort is this dependency

(Causality)?• Do necessary properties exist

(Essences)?• How do composed things relate to their

components?

Jacob Lorhard: Ogdoas Scholastica, continens Diagraphen Typicam artium: Grammatices (Latinae, Graecae), Logices, Rhetorices, Astronomices, Ethices, Physices, Metaphysices, seu Ontologiae. Sangalli: Straub, 1606



1516

Rudolf Goclenius the Elder(1547-1628)

•„Ontology“ first turned up in 1606 („ontologia“ in Latin) by Jacob Lorhard in his book „Ogdoas Scholastica“

•In German language the term „Ontologie“ first turns up in 1613 in Rudolf Göckel‘s „Lexicon philosophicum“

Ontology: where does the term come from?



1616

Christian Wolff(1679-1754)

•Christian Wolff named Ontology a philosophical discipline as Part of Metaphysics, more specific of general metaphysics (metaphysica generalis)

•Traditional Ontology deals with the relation of the ,being‘ to „existence“•ontological difference

(Heidegger)•Division of „Existenciality“ and

„Categoriality“

Ontology: where does the term come from?

Ontology in Classic Greek Philosophy



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Raffael: Die Schule von Athen, 1510-11

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Ontology in Classical Greek Philosophy

• Parmenides (6th-5th Century BC)

• Fundamental Question:„What are the fundamental categories of existence?“

Parmenides (Peri Physeios, 7.1-7.4)

Parmenides(ca. 535-470 BC)

„...Denn es ist unmöglich, dass dies zwingend erwiesen wird: es sei Nichtseiendes; Vielmehr halte du von diesem Wege der Forschung den Gedanken fern, Und es soll dich nicht vielerfahrene Gewohnheit auf diesen Weg zwingen, Walten zu lassen das blicklose Auge und das dröhnende Gehör Und die Zunge, nein mit dem Denken bring zur Entscheidung die streitreiche Prüfung, Die von mir genannt wurde.“



18


16

• Socrates / Platon (5th-4th Century BC)

Dirk Cürsgen, in: Schäfer (Hrsg.), Platon-Lexikon, 2007, S. 102


„Die Idee/Form (gr. idea, eidos) ist ein wesenhaft eingestaltiges immer Seiendes, das in den vielen Einzelnen zur Darstellung kommt. Demnach sind bestimmte nur durch die Vernunft zugängliche Entitäten dem Sein und der Erkenntnis nach gegenüber konkreten, sinnlich wahrnehmbaren Einzelgegenständen vorrangig und stehen als seinsbegründende Urbilder in einer bestimmten Beziehung zu diesen. Die Ideen sind wahrhaft seiende, undingliche bloß denkbare reine Einheiten von Bestimmungen, Prinzipien oder Gegenstandsklassen, die allem Einzelnen, das unter sie fällt, das vermitteln, was es als es selbst sein lässt und wodurch es als bestimmt erkennbar ist.

Socrates(469-399 BC)


http://de.wikipedia.org/wiki/Entit%C3%A4t

http://de.wikipedia.org/wiki/Entit%C3%A4t


19


16

Rational/Mind

ideas objects

sensory perception(empeiria)

recollection(anamnesis)

imutableimperishable

Archetypal

mutableperishable

Image

nach http://upload.wikimedia.org/wikipedia/commons/7/7d/Platon_Ideenlehre.svg

• Socrates, Platon (5th-4th Century BC)


Platon(427-347 BC)


http://upload.wikimedia.org/wikipedia/commons/7/7d/Platon_Ideenlehre.svg

http://upload.wikimedia.org/wikipedia/commons/7/7d/Platon_Ideenlehre.svg


2016 • Platon (5th-4th Century BC)

•Division between

• concept / class(idea, ,Noosphere‘, word of idea)

and

• entity (instance)(real world objects, merely „shadows“ of ideas)

•Hierarchy of ideas


Platon(427-347 BC)


Platon(427-347 BC)


2116

(Abbildung aus: Osborne, Philosophie - Eine Bildergeschichte für Einsteiger)

Platons Cave Parabel• from Platon‘s ,Politeia‘, 7. Book, ca. 370 BC




2216

Aristoteles (De Interpretatione I, 16)

• Aristotle (Metaphysics IV, 1)defines a system of general categories for classification of all things about which statements can be made

substance or quantity or qualification or a relative or where or when or being-in-a-position or having or doing or being-affected.


Aristotle(384-322 BC)

„Nun sind die (sprachlichen) Äußerungen unserer Stimme Symbole für das, was (beim Sprechen) unserer Seele widerfährt, und unsere schriftlichen Äußerungen sind wiederum Symbole für die (sprachlichen) Äußerungen unserer Stimme. Und wie nicht alle Menschen mit denselben Buchstaben schreiben, so sprechen sie auch nicht dieselbe Sprache. Die seelischen Widerfahrnisse aber, für welche dieses (Gesprochene und Geschriebene) an erster Stelle ein Zeichen ist, sind bei allen Menschen dieselben; und überdies sind auch schon die Dinge, von denen diese (seelischen Widerfahrnisse) Abbildungen sind, für alle dieselben.“




2316Aristotle defines a system of general categories for classification of all things about which statements can be made

Aristotle‘s Categories





2416

wikipedia.org


Aristotle defines a system of general categories for classification of all things about which statements can be made

Aristotle‘s Categories



Syllogisms


2516

• συλ-λογισμός [griech.] add up, logical conclusion•Core of Aristotelian logic• Inference rules, all built according to the same

pattern


major premise All humans are mortal

minor premise All Greeks are humans

conclusion All Greeks are mortal

subject predicate

major termminor term middle term



2616

Ontology in Late Antiquity and Early Middle Ages


Aristotle‘s Categories Revisited


2716

•Porphy of Tyros explains in his textbook „Isagoge“ the Aristotelian categories for beginners

• In the Late Middle Ages the so-called„arbor porphyriana“ (Tree of Porphyry or „Tree of Knowledge“) is created as visualization of the Aristotelian categories

• classic epistemologic ordering system, according to the semantics of botany

Ontology in Late Antiquity andearly Middle Ages

Porphyry of Tyros(234-?? AD)



2816

Ontologie in der klassischen griechischen Philosophie

wikipedia.org




29


Ontology in Late Antiquity andearly Middle Ages



3016

Ontology in the Middle Ages



3116 Medieval Scholasticism (12th-14th century)

• Thomas Aquinas• Anselm of Canterbury• William of Ockham

Thomas Aquinas(1225-1274)

Anselm of Canterbury(1033-1109)

William of Ockham(1288-1349)

• Problem of Universals: „Do Universals (Ideas) possess an ontological (real) existency?“

• Realism „Universals are real!“ vs.• Nominalism „Universals are nothing but words and symbols!“




3216 Occam‘s Razor

• „Principle of Simplicity“ from Scholasticism• Among competing hypotheses, the one that makes

the fewest assumptions should be selected• A theory is simple, if

• it contains as few variables and hypotheses as possible

• that relate clearly logical with each other and • the subject to be explained can be logically

deduced.

William of Ockham(1288-1349)

„Entia non sunt multiplicanda sine necessitate.“




3316

• Christian doctrine of trinity as example for a medieval ontology


Tritheism of Roscellin of Compiégne (ca. 1050-1125)



3416

Ramon Lull(Raimundus Lullus)

(1232-1316

• Ramon Lull applies ontology in the sense of the Aristotelian system of categories within his „Tree of Nature and Logic“ as first predecessor of a logical machine

• Logic according to Ramon Lull is „the art and the science to distinguish between truth or lie with the help of reason, to accept truth and to reject lie.“




3516

Arbor naturalis et logicalis, aus„Ars Magna“, um 1275

Ramon Lull(Raimundus Lullus)

(1232-1316



3616 Ontology in the Age of Enlightenment



3716

John Wilkins(1614 – 1672)

• John Wilkins finds out, that the inaccuracy of natural language impedes scientific progress

• He developed the idea of a universal philosophical Language with the goal to represent the entire knowledge of the universe.

Ontology in the Age of Enlightenment



3816

John Wilkins(1614 – 1672)

,A Doctor counted very ableDesignes that all Mankynd converse shall,

Spite o' th' confusion made att Babell,By Character call'd Universall.

How long this character will be learning,That truly passeth my discerning.‘

(Ballad of Gresham College, 1663)



3916

Gottfried Wilhelm Leibniz(1646 – 1716)

• Gottfried Wilhelm Leibnitz develops the idea of „characteristic numbers“ as a model for Aristotelian Logic, in the hope to solve logical problems with the help of a calculus.

„Wenn man Charaktere oder Zeichen finden könnte, die alle unsere Gedanken genauso rein und klar ausdrücken könnten wie die Arithmetik Zahlen oder die Analytische Geometrie Linien ausdrückt, dann könnte man in allen Angelegenheiten, soweit sie dem rationalen Denken zugänglich sind, das tun, was man in der Arithmetik und Geometrie tut. “




4016

Ontologie in der Philosophie der Aufklärung

• Immanuel Kant turns himself towards Epistemology (Critique of „Pure Reason“)

• Fundamental Question: „How can our mind perceive the world?“

Immanuel Kant(1724-1804)

„Kategorien sind nach Kant apriorisch und unmittelbar gegeben. Sie sind Werkzeuge des Urteilens und Werkzeuge des Wahrnehmens. Als solche dienen sie nur der Anwendung und haben keine Existenz. Sie bestehen somit nur im menschlichen Verstand. Sie sind nicht an Erfahrung gebunden. Durch ihre Unmittelbarkeit sind sie auch nicht an Zeichen gebunden. Kants erkenntnistheoretisches Ziel ist es, über die Bedingungen der Geltungskraft von Urteilen Auskunft zu geben.“

R. Eisler. Kant-Lexikon : Nachschlagewerk zu Kants samtlichen Schriften / Briefen und handschriftlichem Nachlass.. Olms, Hildesheim, 1961



http://www.bibsonomy.org/bibtex/2de58388f1ea97810eab9912baa377300/lysander07





4116

• Immanuel Kant turns himself towards Epistemology (Kritik an der „reinen Vernunft“)

• Epistemology: Categories are pure concepts of understanding

Quantity Quality Relation Modality

Unity RealitySubstance &

AccidentPossibility

Plurality Negation Cause & Effect Existence

Totality Limitation Reciprocity Necessity

Immanuel Kant(1724-1804)




42



4316

The Concept of Ontologyin Computer Science



4416 "An ontology is an explicit, formal specification of a shared conceptualization. The term is borrowed from philosophy, where an Ontology is a systematic account of Existence. For AI systems, what ‘exists’ is that which can be represented.“

Thomas R. Gruber: A Translation Approach to Portable Ontology Specifications.Knowledge Acquisition, 5(2):199-220, 1993.

conceptualization: abstract Model (Domain, identified relevant concepts, relations)explicit: Meaning of all concepts must be definedformal: machine understandableshared: consensus about ontology

tomgruber.org

The Concept of Ontology in Computer Science



4516

Conceptualization

Symbol Object

Ogden, Richards: The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism (1923)

„Jaguar“

Concept

apply sharedconcept

stands for

refers tosymbolizes



4616

How should we represent

Ontologies?



4716 Ontologies - Components and Models

• Classes, Relations and Instances

• Classes represent concepts• Classs are described via attributs• Attributs are Name Value pairs

Address• given name <string>• family name <string>• street <string>• ZIP code <int>• city <string>• …

„The address contains the name, title, and place of residence of the person addressed“

Informal Description

Semi informal Description

How should we represent Ontologies?



4816

Forms of Modelling

• informal Description in natural language

• semi informal structured description in controlled batural language

• semi formal description in artificial formal defined language

• formal description in well-defined terms with given formal semantics, incl. proof of correctness and completeness.




4916

• Classes are related to other classes

• Relations are special attributes, whose values are objects of (other) classes

AddressPerson

Professor Student

is subclass of

Lecture

gives visits

Course

Formal Definition: Sets m1,…mn Relation R ⊆ m1 x … x mn

has an


is subclass of

is subclass of



5016

• For Relations and Attributs Rules (Constraints) can be defined that determine allowed values

AddressPersonhas

Professor Student

1:n

1:1

Woman

Man

≠

Frau ⋂ Mann = ∅


Constraint

is subclass of

is subclass of

is subclass of is subclass of



5116

• Classes, relations, and constraints can be put together to form statements / assertions

• Special Case: formal Axioms

• Axioms describe knowledge that can‘t be expressed simply with the help of other existing components.

Example: • „it is not possible to give two courses at the

same time“




5216

• Instances describe individuals of an ontology

Course

Seminar

is subclass of

Bachelor SeminarSW enabled Applications

Thursday11.00 pm A-2.1

Individuals (instances) are the basic components of an ontology. The individuals in an ontology may include concrete objects such as people, animals, tables, automobiles, molecules, and planets, as well as abstract individuals such as numbers and words.

is a




5316

How do I define a

formal model o

f an ontology?

-

Knowledge Represen

tation and

Ontology Descript

ion Languages



5416 • in propositional logic the world consists simply of facts and nothing else (statements of assertions)

• Example for propositional logic assertions and deductions:

• If it rains, the road will get wet.• If the moon is made out of green cheese, then cows can fly.• If Oliver is in love, then he will be happy.

• The world consists out of objects and properties that distinguish one objectr from another.

• Between objects are relations. Some relations are unique, i.e. functions.

Propositional Logic



5516• In First Order Logic (FOL) quantors allow assertions about sets

of objects, without naming the objects explicitely.

• All humans are mortal.• Socrates is a human.• Socrates is mortal.

• FOL is perfectly suited for the description of ontologies, but...• FOL is rather expressive,• therefore also rather bulky for modelling,• difficult to achieve consense in modelling and• rather complex to proof (correctness and completeness of

assertions)

First Order Logic



5616

Description Logics

Description Logics are a family of languages for knowledge representation. Most description logics are a subset of First Order Logic, but in difference to FOL most description logics decidable. Therefore, it is possible to make logical deductions based on description logics, i.e. to create new knowledge from existing knowledge.

Lecture

Lecture„Semantic Web Technologies“

TBox terminological knowledge Knowledge about concepts of a domain (classes, attributes, relations…)

ABox assertional knowlegde knowledge about instances / entities

Knowledge Base



5716 • Concepts (unary predicates),

• represent entities / classes

• e.g., Person, Course, Student, Lecturer, Seminar, ...

• Roles (binary predicates)

• represent properties / relations

• e.g., participatesAt, givesLecture, isGivenByLecturer, …

Student: { x | Student(x)}

participatesAt: { (x,y) | participatesAt(x,y)}

Description Logics



5816 • Individuals (constants, individual entities, concept assertion)

• e.g., Alice, Bob, SemanticWeb

• Syntax: Student(Alice)

• Operators / Constructors (to construct complex representations of concepts / roles)

• Expressivity is limited:• Satisfiability and Subsumption is decidable and • (preferably) of low complexity• Syntax: participatesAt(Alice, SemanticWeb)

Description Logics



5916 • Fundamental operators:

• Conjunction (⊓),

• Disjunction (⊔),

• Negation (⌐)

• restricted form of Quantification (∀,∃)

• represents Basic Description Logic ALC• Attributive Language with Complement

Description Logics



6016

Attributive Language with Complement - ALC• Atomic Types• concept names A, B, ... • special concepts

• ⊤ - Top (universal concept)• ⊥ - Bottom concept

• role names R,S, ...

• Constructors • Negation: ¬C • Conjunction: C ⊓ D• Disjunction: C ⊔ D• Existential Quantor: ∃R.C• Universal Quantor: ∀R.C



6116 • Class Relations• Inclusion C ⊑ D

• E.g., Man ⊑ Human• Equality C ≣ D

• E.g., Frau ≣ Woman

• Class Constructors

• E.g., Seminarist ≡ Person ⊓ (∃participatesAt.Seminar ⊔ ∃givesLecture.Seminar)

Attributive Language with Complement - ALC



6216 • Terminological Knowledge (TBox)• Axioms describing the structure of the represented domain

(conceptional schema)• Human ⊑ ∃hasParents.Human

Orphan ≣ Human ⊓ ¬∃hasParents.Alive

• Assertional Knowledge (ABox)• Axioms describing specific situations (data)

• Orphan(harrypotter)hasParent(harrypotter, jamespotter)

Attributive Language with Complement - ALC



6316 Operator / Constructor Syntax LanguageLanguage

Conjunction A ⊓ B

FL

S*

Value Restriction ∀ R .C FL

S*

Existential Quantification ∃ R

FL

S*

Top (Universal Concept) ⊤

AL*

S*Bottom (Most Special Concept) ⊥

AL*

S*Negation (C) ⌐ A

AL*

S*

Disjunction C ⊔ D AL*

S*

Existential Restriction ∃ R .C

AL*

S*

Cardinality Restriction (N) (≤ n R) (≥ n R)

AL*

S*

Set of Individuals (O) {a1,…,an}

AL*

S*

Hierarchy of Relations R ⊆ S HH

Inverse Relation R-1 II

Qualified Cardinality Restriction (≤ n R.C) (≥ n R.C) QQ

Description Logics



6416 • Semantics is determined via Interpretation (ΔI, I)

• ΔI … Domain of Discourse, ΔI ≠ ∅

• Interpretation Function:

• I :A → AI ⊆ ΔI , A ... atomic concept

• I :R → RI ⊆ ΔI x ΔI , R … atomic Relation

┬I = ΔI

⊥I = ∅(¬A)I = ΔI \ AI (C Π D)I = CI ∩ DI (∀ R.C)I = {a ∈ ΔI | ∀ b.<a,b> ∈ RI ⇒ b ∈ CI}(∃ R.┬)I = {a ∈ ΔI | ∃ b.<a,b>∈ RI}

Description Logics



6516

• Ontologies can also be modelled via database or softwaremodelling technologies, as e.g.

• UML, ER-Model, …

Seminar

- Titel: String - Semester: String - Begin: Date - End: Date - …

Person

- GivenName: String - FamilyName: String - …

participatesAtnn

givesLecture1n




6616

• Formalisms and models limit the knowledge that can be represented by them

• e.g. UML, ER, SQL are not able to represent complex logical constraints and logical inference

• AI-based languages (e.g. Ontolingua, LOOM, OCML, FLogic,…) and Ontology Markup Languages (z.B. RDFS, DAML+OIL, OWL, …) are better suited for the represenation of ontologies.




6716

Ontology Types



6816

Ontology Types and Categories

general, cross domain ontologies (represent very general concepts as e.g., Time, Space, Event independent of a specific domain or problem.)

Domain Ontology Task Ontology

specialized ontology focussed on a specific task and domain

Application Ontology

(according to Guarino,1998)

fundamental concepts according to a general activity or task.

fundamental concepts according to ageneric domain.

Top-Level Ontology(Upper Ontology,

Foundation Ontology)



6916







fundamental concepts according to a general activity or task.fundamental concepts according to a

generic domain.





7016













7116













7216













7316

lightweight ontologies heavyweight ontologies

controlledVocabulary

(according to Lassila/McGuinnes, 2001)

Thesauri

Glossaries informalIS-A

formalIS-A

formalInstance

Frames

ValueRestrictions

generallogical

Constraints

Disjunctness,Inversiveness,Part-of…

Expressivity +-


informal formal

Folksonomiesformal

Taxonomies

LogicProgramming Description

Logics

First OrderLogicsData

Dictionaries

Terms



7416 • Controlled Vocabulary:finite list of terms (e.g. catalogue)

• Glossary: finite list of terms including an informal definition of their semantics in natural language

• Thesauri: [greek. „treasure, treasure house“]controlled vocabulary, concepts are connected via relations.• Equivalency (synonyms)• Hierarchies (subclasses, superclasses)• Homographs (Homonyms)• Associations (similar concepts)




7516Thesaurus

Underpants

Knickers

Synonyms

Panties

Bloomers

Briefs

Boxershorts

narrower concept

Underwearbroader concept

Undershirt

Association




7616 Taxonomies

• also classification schema, Nomenclature, …• in science most times classification into (mono-)hierarchical sets

(classes, subclasses, ...)• (also) subject of biology:

• the arrangement of organisms into a classification according to similarities

Taxonomy: Definition of a hierarchical system of groups (from [greek] τασσεῖν (tassein) = to arrange and νόµος (nomos) = method) ...




7716

• Carl v. Linné (ca. 1740) created a simple classification schema for organisms that is still used today

Carl v. Linné(1707-1778)

Des Ritters Carl von Linné vollständiges Natursystem, 1778Dienstag, 13. November 12


7816

lightweight ontologies heavyweight ontologies

controlledVocabulary

(according to Lassila/McGuinnes, 2001)

Thesauri

Terms/Glossary

informalis-a

formalis-a

formalInstance

Frames

ValueRestrictions

generallogical

Constraints

Disjunctness,Inversiveness,Part-of…

Expressivity +-




7916 • informal IS-A-Hierarchy: explicite hierarchy of classes, subclass relations are not strict(e.g. index of a library)

• formal IS-A-Hierarchy: explicite hierarchy of classes, suclass relations are strict

• formale instance: explicite class hierarchy, besides subclass relations also instance-of relations are allowed




8016

Ontologies as Interpretation of Reality

various categories of animals from "a certain chinese encyclopedia" according to Jorge Luis Borges:

• Those that belong to the emperor• Embalmed ones• Those that are trained• Suckling pigs• Mermaids (or Sirens)• Fabulous ones• Stray dogs• Those that are included in this classification• Those that tremble as if they were mad• Innumerable ones• Those drawn with a very fine camel hair brush• Et cetera• Those that have just broken the flower vase• Those that, at a distance, resemble flies Jorge Luis Borges

(1899-1986)

Jorge Luis Borges: The Analytical Language of John Wilkins (1942)


http://en.wikipedia.org/wiki/Embalming

http://en.wikipedia.org/wiki/Embalming

http://en.wikipedia.org/wiki/Siren

http://en.wikipedia.org/wiki/Siren

http://en.wikipedia.org/wiki/Brush#Bristles

http://en.wikipedia.org/wiki/Brush#Bristles

http://en.wikipedia.org/wiki/Et_cetera

http://en.wikipedia.org/wiki/Et_cetera

http://en.wikipedia.org/w/index.php?title=The_Analytical_Language_of_John_Wilkins&action=edit&redlink=1

http://en.wikipedia.org/w/index.php?title=The_Analytical_Language_of_John_Wilkins&action=edit&redlink=1


8116

Examples of

Ontologies



8216

Examples of Ontologies

WordNet• link-based electronic dictionary• Dictionary with semantic relations • organized in 117587 „Synsets“,ordered by

• Nouns (N)• Verbs (V)• Adjektives (Adj)• Adverbs (Av)

http://wordnetweb.princeton.edu/perl/webwn


http://wordnet.princeton.edu/perl/webwn

http://wordnet.princeton.edu/perl/webwn




8316 Top-level Ontologies • describe rather general concepts• concepts independent of specific domain.

e.g. KR Ontology(John F. Sowa )

• contains 27 concepts• organized as lattice

http://www.jfsowa.com/ontology/kronto.htm






8416

(OpenCyc, Douglas Lenat )

• Top-Level Ontology for Cyc (Knowledge Base with ca. 200,000 entities and 1 Mio. axioms)• 6,000 concepts in 43 groups resp. relations

http://www.opencyc.org/



http://www.opencyc.org

http://www.opencyc.org


8516

(SUMO, IEEE SUOWG )

• Standard Upper Merged Ontology• IEEE SUO Working Group• integrates various resources to form a Top-Level Ontology

http://www.ontologyportal.org/



http://www.ontologyportal.org

http://www.ontologyportal.org


8616

Domain Ontology

decision problem complexity classis a member of

has member

can be reduced to

is weaker / stronger

is special/general variant

SAT 3-SATColorability

is a is a

NP P

NP-complete

is a is a

graph problem logic problem set problem… problem

is a is a

(NP-Ontologie, Sack, Niedermeier, Vogel, 2006 )




87


3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Popositional Logic and First Order Logic

• Description Logics

• RDFS Semantics• OWL and OWL-Semantics• OWL 2 and Rules



88

3. Knowledge Representation & LogicThe Languages of the Semantic Web - Part 2



89

die nächste Vorlesung....

Propositional Logicand First Order Logic

next Lecture



90

3. Knowledge Representation & Logic3.1 Ontologies in Philosophy and Computer Science

Bibliography

• S. Staab, R. Studer (Eds.):Handbook on Ontologies, 2nd ed., Springer (2009)

• L. De Crescenzo:Geschichte der griechischen Philosophie,diogenes.


http://www.amazon.de/gp/product/3540709991/ref=as_li_ss_tl?ie=UTF8&camp=1638&creative=19454&creativeASIN=3540709991&linkCode=as2&tag=moresemantic-21


http://www.amazon.de/gp/product/325721913X/ref=as_li_ss_tl?ie=UTF8&camp=1638&creative=19454&creativeASIN=325721913X&linkCode=as2&tag=moresemantic-21
































































































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Bibliography

• P. Hitzler, M. Krötzsch, S. Rudolph:Foundations of Semantic Web Technologies,CRC Press, 2009.


http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X

http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X

Lecture Semantic Web Technologies, Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

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Education

05 Semantic Web Technologies - Ontologies