OpenHPI 4.1 - Ontologies as Central Concept in Philosophy

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Dr. Harald Sack

Hasso Plattner Institute for IT Systems Engineering

University of Potsdam

Spring 2013

Semantic Web Technologies

Lecture 4: Knowledge Representations I01: Ontology as Central Concept in Philosophy

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

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Lecture 4: Knowledge Representations I

Open HPI - Course: Semantic Web Technologies


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01 Ontology as Central Concept in Philosophy

Open HPI - Course: Semantic Web Technologies - Lecture 4: Knowledge Representations I


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

Turmbau zu Babel, Pieter Brueghel, 1563

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

5 To 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


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What is Knowledge?


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What is Knowledge?

Truths


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What is Knowledge?

Truths Beliefs


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What is Knowledge?

Truths Beliefs

Knowledge

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


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Turmbau zu Babel, Pieter Brueghel, 1563

To represent knowledge, we need a formal knowledge representation:

⇒ Ontologies


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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?

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


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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


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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?


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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• Fundamental Question:

„What are the fundamental categories of existence?“

Parmenides(ca. 535-470 BC)


1316Rational/Mind

ideas objects

sensory perception(empeiria)recollection

(anamnesis)

imutableimperishable

Archetypal

mutableperishable

Image

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

Ontology in Classical Greek Philosophy

Platon(427-347 BC)

Socrates(469-399 BC)

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

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

Aristotle(384-322 BC)


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


Syllogisms


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

pattern



Syllogisms


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pattern


major premise All humans are mortal


Syllogisms


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pattern



minor premise All Greeks are humans


Syllogisms


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pattern




conclusion All Greeks are mortal


Syllogisms


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pattern





subject


Syllogisms


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pattern





subject predicate


Syllogisms


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pattern





subject predicate

major term


Syllogisms


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pattern





subject predicate

major termmiddle term


Syllogisms


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pattern





subject predicate

major termminor term middle term


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Ontology in Late Antiquity and Early Middle Ages

Aristotle‘s Categories Revisited


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•Porphyry 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)


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Ontologie in der klassischen griechischen Philosophie

wikipedia.org



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Ontology in Late Antiquity andearly Middle Ages



2016

Ontology in the Middle Ages


2116 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)



2116 Medieval Scholasticism (12th-14th century)

• Thomas Aquinas• Anselm of Canterbury• William of Ockham

Thomas Aquinas(1225-1274)

Anselm of Canterbury(1033-1109)


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

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



2216 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.


„Entia non sunt multiplicanda sine necessitate.“



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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.“



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Arbor naturalis et logicalis, from„Ars Magna“ (~1275)

Ramon Lull(Raimundus Lullus)

(1232-1316


2516 Ontology in the Age of Enlightenment


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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


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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)


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Gottfried Wilhelm Leibniz(1646 – 1716)

• Gottfried Wilhelm Leibniz 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.



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• Immanuel Kant turns himself towards Epistemology (Kritik an der „reinen Vernunft“ eng: Critique of Pure Reason)

•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)



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02 Ontologies in Computer Science Open HPI - Course: Semantic Web Technologies - Lecture 4: Knowledge Representations I

OpenHPI 4.1 - Ontologies as Central Concept in Philosophy

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