05 Semantic Web Technologies - Ontologies

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05 Semantic Web Technologies - Ontologies

  1. 1. Semantic Web Technologies Lecture Dr. Harald Sack Hasso-Plattner-Institut für IT Systems Engineering University 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
  2. 2. Semantic Web Technologies Content2 1. Introduction 2. Semantic Web - Basic Architecture Languages of the Semantic Web - Part 1 3. Knowledge Representation and Logics Languages of the Semantic Web - Part 2 4. Applications in the ,Web of Data‘ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  3. 3. 3. Knowledge Representation & Logic The Languages of the Semantic Web - Part 23 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  4. 4. Semantic Web Technologien Wiederholung4 e s g i l o to O n Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  5. 5. Semantic Web Technologies Content5 3. Knowledge Representation and Logics The 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  6. 6. 6 „People can‘t share knowledge if they don‘t speak a common language“ Thomas Davenport (1997) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  7. 7. 7 „People can‘t share knowledge if they don‘t speak a common language“ Thomas Davenport (1997) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Turmbau zu Babel, Pieter Brueghel, 1563Dienstag, 13. November 12
  8. 8. Sharing Knowledge8 •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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Turmbau zu Babel, Pieter Brueghel, 1563Dienstag, 13. November 12
  9. 9. Sharing Knowledge9 •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…. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Turmbau zu Babel, Pieter Brueghel, 1563Dienstag, 13. November 12
  10. 10. Sharing Knowledge10 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Turmbau zu Babel, Pieter Brueghel, 1563Dienstag, 13. November 12
  11. 11. What is Knowledge?11 Truths Beliefs Knowledge Traditional Definition: „Knowledge is a subset of all true beliefs“ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  12. 12. 3. Wissensrepräsentation und Logik 3.1 Ontologien in Philosophie und Informatik12 Ontologies as Central Concept in Philosophy Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Raffael: Die Schule von Athen, 1510-11Dienstag, 13. November 12
  13. 13. Definition • ον [greek] participle of „to be“ λογια [greek] science13 „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 Raffael: Die Schule von Athen, 1510-11 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, UniversitätChristian Wolff: Philosophia prima sive Ontologia, 1729 PotsdamDienstag, 13. November 12
  14. 14. Fundamental Questions of Ontology 1.What does it mean for a being to be?14 • 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, Semantic Web Technologies , Dr. Harald Sack, Physices, Metaphysices, seu Ontologiae. Sangalli: Straub, 1606 Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  15. 15. Ontology: where does the term come from?1615 • „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“ Rudolf Goclenius the Elder (1547-1628) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  16. 16. Ontology: where does the term come from?1616 • Christian Wolff named Ontology Ontologya philosophical disciplinespecific in of Metaphysics, more as Part Classic Greek Philosophy of general metaphysics (metaphysica generalis) • Traditional Ontology deals with the relation of the ,being‘ to „existence“ • ontological difference (Heidegger) • Division of „Existenciality“ and Christian Wolff „Categoriality“ (1679-1754) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  17. 17. Ontology in Classical Greek Philosophy1617 • Parmenides (6th-5th Century BC) Parmenides • Fundamental Question: (ca. 535-470 BC) „What are the fundamental categories of existence?“ „...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.“ Parmenides (Peri Physeios, 7.1-7.4) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Raffael: Die Schule von Athen, 1510-11Dienstag, 13. November 12
  18. 18. Ontology in Classical Greek Philosophy1618 • Socrates / Platon (5th-4th Century BC) Socrates „Die Idee/Form (gr. idea, eidos) ist ein wesenhaft eingestaltiges (469-399 BC) 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. Dirk Cürsgen, in: Schäfer (Hrsg.), Platon-Lexikon, 2007, S. 102 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Raffael: Die Schule von Athen, 1510-11Dienstag, 13. November 12
  19. 19. Platon (427-347 BC) Ontology in Classical Greek Philosophy1619 • Socrates, Platon (5th-4th Century BC) Rational/Mind recollection sensory perception (anamnesis) (empeiria) ideas objects imutable mutable imperishable perishable Archetypal Image nach http://upload.wikimedia.org/wikipedia/commons/7/7d/Platon_Ideenlehre.svg Raffael: Die Schule von Athen, 1510-11 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  20. 20. Platon (427-347 BC) Ontology in Classical Greek Philosophy1620 • 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  21. 21. Platon (427-347 BC) Ontology in Classical Greek Philosophy1621 Platons Cave Parabel • from Platon‘s ,Politeia‘, 7. Book, ca. 370 BC Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam (Abbildung aus: Osborne, Philosophie - Eine Bildergeschichte für Einsteiger)Dienstag, 13. November 12
  22. 22. Aristotle (384-322 BC) Ontology in Classical Greek Philosophy1622 • 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. „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.“ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Aristoteles (De Interpretatione I, 16)Dienstag, 13. November 12
  23. 23. Aristotle (384-322 BC) Ontology in Classical Greek Philosophy Aristotle‘s Categories1623 Aristotle defines a system of general categories for classification of all things about which statements can be made Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  24. 24. Aristotle (384-322 BC) Ontology in Classical Greek Philosophy1624 Aristotle‘s Categories Aristotle defines a system of general categories for classification of all things about which statements can be made wikipedia.org Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  25. 25. Aristotle (384-322 BC) Ontology in Classical Greek Philosophy1625 Syllogisms • συλ-λογισμός [griech.] add up, logical conclusion • Core of Aristotelian logic • Inference rules, all built according to the same pattern minor term middle term major term major premise All humans are mortal minor premise All Greeks are humans conclusion All Greeks are mortal subject predicate Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  26. 26. 1626 Ontology in Late Antiquity and Early Middle Ages Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  27. 27. Ontology in Late Antiquity and early Middle Ages1627 Aristotle‘s Categories Revisited • 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 Porphyry of Tyros (234-?? AD) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  28. 28. Ontologie in der klassischen griechischen Philosophie1628 Porphyry of Tyros (234-?? AD) wikipedia.org Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  29. 29. Ontology in Late Antiquity and early Middle Ages29 Porphyry of Tyros (234-?? AD) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  30. 30. 1630 Ontology in the Middle Ages Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  31. 31. Ontology in the Middle Ages1631 Medieval Scholasticism (12th-14th century) Thomas Aquinas (1225-1274) • Thomas Aquinas • Anselm of Canterbury • William of Ockham • Problem of Universals: „Do Universals (Ideas) possess an ontological Anselm of Canterbury (real) existency?“ (1033-1109) • Realism „Universals are real!“ vs. • Nominalism „Universals are nothing but words and symbols!“ William of Ockham (1288-1349) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  32. 32. Ontology in the Middle Ages1632 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 William of Ockham • it contains as few variables and hypotheses as (1288-1349) possible • that relate clearly logical with each other and • the subject to be explained can be logically deduced. „Entia non sunt multiplicanda sine necessitate.“ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  33. 33. Ontology in the Middle Ages1633 • Christian doctrine of trinity as example for a medieval ontology Tritheism of Roscellin of Compiégne (ca. 1050-1125) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  34. 34. Ontology in the Middle Ages1634 • 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.“ Ramon Lull (Raimundus Lullus) (1232-1316 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  35. 35. 1635 Ramon Lull (Raimundus Lullus) (1232-1316 Arbor naturalis et logicalis, aus „Ars Magna“, um 1275 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  36. 36. 1636 Ontology in the Age of Enlightenment Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  37. 37. Ontology in the Age of Enlightenment1637 • 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. John Wilkins (1614 – 1672) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  38. 38. 1638 John Wilkins (1614 – 1672) ,A Doctor counted very able Designes that all Mankynd converse shall, Spite o th confusion made att Babell, By Character calld Universall. How long this character will be learning, That truly passeth my discerning.‘ (Ballad of Gresham College, 1663) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  39. 39. Ontology in the Age of Enlightenment1639 • 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 Gottfried Wilhelm Leibniz (1646 – 1716) 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. “ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  40. 40. Ontologie theder Philosophie Ontology in in Age of der Aufklärung Enlightenment1640 • 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  41. 41. Ontology in the Age of Enlightenment1641 • Immanuel Kant turns himself towards Epistemology (Kritik an der „reinen Vernunft“) • Epistemology: Categories are pure concepts of understanding Immanuel Kant (1724-1804) Quantity Quality Relation Modality Substance & Unity Reality Possibility Accident Plurality Negation Cause & Effect Existence Totality Limitation Reciprocity Necessity Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  42. 42. 42 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  43. 43. 1643 The Concept of Ontology in Computer Science Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  44. 44. The Concept of Ontology in Computer Science1644 "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 tomgruber.org Specifications.Knowledge Acquisition, 5(2):199-220, 1993. conceptualization: abstract Model (Domain, identified relevant concepts, relations) explicit: Meaning of all concepts must be defined formal: machine understandable shared: consensus about ontology Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  45. 45. Conceptualization1645 apply shared concept Concept symbolizes refers to Symbol Object stands for „Jaguar“ Ogden, Richards: The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism (1923) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  46. 46. 1646 re present uld we How sho es? Ontol ogi Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  47. 47. How should we represent Ontologies?1647 Ontologies - Components and Models • Classes, Relations and Instances • Classes represent concepts • Classs are described via attributs • Attributs are Name Value pairs Address „The address contains the name, title, • given name <string> and place of residence of the person • family name <string> addressed“ • street <string> • ZIP code <int> Informal Description • city <string> •… Semi informal Description Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  48. 48. How should we represent Ontologies?1648 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. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  49. 49. How should we represent Ontologies?1649 • Classes are related to other classes has an Person Address is subclass of is subclass of Formal Definition: Sets m1,…mn Professor Student Relation R ⊆ m1 x … x mn gives visits Lecture Course is subclass of • Relations are special attributes, whose values are objects of (other) classes Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  50. 50. How should we represent Ontologies?1650 • For Relations and Attributs Rules (Constraints) can be defined that determine allowed values is subclass of Woman has Person Address ≠ is subclass of 1:n Man is subclass of is subclass of 1:1 Professor Student Frau ⋂ Mann = ∅ Constraint Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  51. 51. How should we represent Ontologies?1651 • Classes, relations, and constraints can be put together to form statements / assertions • Special Case: formal Axioms Example: • „it is not possible to give two courses at the same time“ • Axioms describe knowledge that can‘t be expressed simply with the help of other existing components. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  52. 52. How should we represent Ontologies?1652 • Instances describe individuals of an ontology Course is subclass of Seminar Bachelor Seminar is a SW enabled Applications Thursday A-2.1 11.00 pm 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. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  53. 53. 1653 defi ne a H ow d o I ntol ogy? el of an o rmal mod fo - tion and pres enta ages ledg e Re on L angu Know escr ipti O ntology D Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  54. 54. Propositional Logic1654 • 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. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  55. 55. First Order Logic • In First Order Logic (FOL) quantors allow assertions about sets1655 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  56. 56. Description Logics1656 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. TBox terminological knowledge Lecture Knowledge about concepts of a domain (classes, attributes, relations…) Lecture ABox assertional knowlegde „Semantic Web Technologies“ knowledge about instances / entities Knowledge Base Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  57. 57. Description Logics1657 • Concepts (unary predicates), • represent entities / classes • e.g., Person, Course, Student, Lecturer, Seminar, ... Student: { x | Student(x)} • Roles (binary predicates) • represent properties / relations • e.g., participatesAt, givesLecture, isGivenByLecturer, … participatesAt: { (x,y) | participatesAt(x,y)} Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  58. 58. Description Logics1658 • 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  59. 59. Description Logics1659 • Fundamental operators: • Conjunction (⊓), • Disjunction (⊔), • Negation (⌐) • restricted form of Quantification (∀,∃) • represents Basic Description Logic  ALC • Attributive Language with Complement Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  60. 60. Attributive Language with Complement - ALC1660 • 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  61. 61. Attributive Language with Complement - ALC1661 • 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  62. 62. Attributive Language with Complement - ALC1662 • 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  63. 63. Description Logics1663 Operator / Constructor Syntax Language Conjunction A⊓B Value Restriction ∀ R .C FL Existential Quantification ∃R Top (Universal Concept) ⊤ Bottom (Most Special Concept) ⊥ S* Negation (C) ⌐A Disjunction C⊔D AL* Existential Restriction ∃ R .C Cardinality Restriction (N) (≤ n R) (≥ n R) Set of Individuals (O) {a1,…,an} Hierarchy of Relations R⊆S H Inverse Relation R-1 I Qualified Cardinality Restriction (≤ n R.C) (≥ n R.C) Q Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  64. 64. Description Logics1664 • 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} Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  65. 65. How should we represent Ontologies?1665 • Ontologies can also be modelled via database or software modelling technologies, as e.g. • UML, ER-Model, … n n Seminar participatesAt Person - Titel: String - GivenName: String n 1 - Semester: String givesLecture - FamilyName: String - Begin: Date -… - End: Date -… Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  66. 66. How should we represent16 Ontologies?66 • 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. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  67. 67. 1667 y T yp es Ont olog Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  68. 68. Ontology Types and Categories1668 general, cross domain ontologies (represent very general concepts Top-Level Ontology as e.g., Time, Space, Event (Upper Ontology, independent of a specific domain Foundation Ontology) or problem.) Domain Ontology Task Ontology fundamental concepts fundamental concepts according according to a to a general activity or task. generic domain. Application Ontology specialized ontology focussed on a specific task and domain (according to Guarino,1998) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  69. 69. Ontology Types and Categories1669 general, cross domain ontologies (represent very general concepts Top-Level Ontology as e.g., Time, Space, Event (Upper Ontology, independent of a specific domain Foundation Ontology) or problem.) Domain Ontology Task Ontology fundamental concepts according fundamental concepts according to a to a general activity or task. generic domain. Application Ontology specialized ontology focussed on a specific task and domain (according to Guarino,1998) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  70. 70. Ontology Types and Categories1670 general, cross domain ontologies (represent very general concepts Top-Level Ontology as e.g., Time, Space, Event (Upper Ontology, independent of a specific domain Foundation Ontology) or problem.) Domain Ontology Task Ontology fundamental concepts fundamental concepts according according to a to a general activity or task. generic domain. Application Ontology specialized ontology focussed on a specific task and domain (according to Guarino,1998) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  71. 71. Ontology Types and Categories1671 general, cross domain ontologies (represent very general concepts Top-Level Ontology as e.g., Time, Space, Event (Upper Ontology, independent of a specific domain Foundation Ontology) or problem.) Domain Ontology Task Ontology fundamental concepts fundamental concepts according according to a to a general activity or task. generic domain. Application Ontology specialized ontology focussed on a specific task and domain (according to Guarino,1998) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  72. 72. Ontology Types and Categories1672 general, cross domain ontologies (represent very general concepts Top-Level Ontology as e.g., Time, Space, Event (Upper Ontology, independent of a specific domain Foundation Ontology) or problem.) Domain Ontology Task Ontology fundamental concepts fundamental concepts according according to a to a general activity or task. generic domain. Application Ontology specialized ontology focussed on a specific task and domain (according to Guarino,1998) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  73. 73. Ontology Types and Categories1673 informal formal - Expressivity + general controlled formal Frames logical Thesauri Vocabulary IS-A Constraints Disjunctness, Glossaries informal formal Value Inversiveness, IS-A Instance Restrictions Part-of… Logic First Order Terms Folksonomies Data formal Programming Description Logics Dictionaries Taxonomies Logics lightweight ontologies heavyweight ontologies (according to Lassila/McGuinnes, 2001) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  74. 74. Ontology Types and Categories1674 • 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) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  75. 75. Ontology Types and Categories1675 Thesaurus narrower concept Panties broader concept Briefs Underwear Underpants Bloomers Synonyms Boxershorts Knickers Association Undershirt Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  76. 76. Ontology Types and Categories1676 Taxonomies Taxonomy: Definition of a hierarchical system of groups (from [greek] τασσεῖν (tassein) = to arrange and νόµος (nomos) = method) ... • 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  77. 77. • Carl v. Linné (ca. 1740) created a simple classification schema for organisms that is still used today1677 Carl v. Linné (1707-1778) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Des Ritters Carl von Linné vollständiges Natursystem, 1778Dienstag, 13. November 12
  78. 78. Ontology Types and Categories1678 - Expressivity + general controlled formal Frames logical Thesauri Vocabulary is-a Constraints Disjunctness, Terms/ informal formal Value Inversiveness, Glossary is-a Instance Restrictions Part-of… lightweight ontologies heavyweight ontologies (according to Lassila/McGuinnes, 2001) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  79. 79. Ontology Types and Categories1679 • 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  80. 80. Ontologies as Interpretation of Reality16 various categories of animals from "a certain chinese encyclopedia"80 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 Jorge Luis Borges • Those that, at a distance, resemble flies (1899-1986) Jorge Luis Borges: The Analytical Language of John Wilkins (1942) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  81. 81. 1681 les of Ex amp to log ies On Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  82. 82. Examples of Ontologies1682 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  83. 83. Examples of Ontologies1683 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  84. 84. Examples of Ontologies1684 • Top-Level Ontology for Cyc (Knowledge Base with ca. 200,000 entities and 1 Mio. axioms) • 6,000 concepts in 43 groups resp. relations (OpenCyc, Douglas Lenat ) http://www.opencyc.org/ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  85. 85. Examples of Ontologies1685 • Standard Upper Merged Ontology • IEEE SUO Working Group • integrates various resources to form a Top-Level Ontology (SUMO, IEEE SUOWG ) http://www.ontologyportal.org/ Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  86. 86. Examples of Ontologies1686 Domain Ontology NP-complete is special/general variant is weaker / stronger NP P is a is a can be reduced to is a member of decision problem has member complexity class is a is a … problem graph problem logic problem set problem is a is a Colorability SAT 3-SAT (NP-Ontologie, Sack, Niedermeier, Vogel, 2006 ) Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  87. 87. Semantic Web Technologies Content87 3. Knowledge Representation and Logics The 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 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  88. 88. 3. Knowledge Representation & Logic The Languages of the Semantic Web - Part 288 Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  89. 89. next Lecture die nächste Vorlesung....89 Pro p osi tio nal Fir and Log st ic Ord er Log ic Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  90. 90. 3. Knowledge Representation & Logic 3.1 Ontologies in Philosophy and Computer Science90 Bibliography • S. Staab, R. Studer (Eds.): Handbook on Ontologies, 2nd ed., Springer (2009) • L. De Crescenzo: Geschichte der griechischen Philosophie, diogenes. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  91. 91. 3. Knowledge Representation & Logic 3.1 Ontologies in Philosophy and Computer Science91 Bibliography • P. Hitzler, M. Krötzsch, S. Rudolph: Foundations of Semantic Web Technologies, CRC Press, 2009. Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12
  92. 92. 3. Knowledge Representation & Logic 3.2 Ontologies in Philosophy and Computer Science92 □Blog http://semweb2013.blogspot.com/ □Webseite http://www.hpi.uni-potsdam.de/studium/ lehrangebot/itse/veranstaltung/ semantic_web_technologien-3.html □bibsonomy - Bookmarks http://www.bibsonomy.org/user/lysander07/ swt1213_05 Lecture Semantic Web Technologies, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamDienstag, 13. November 12

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