The Semantic Web #8 - Ontology

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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.

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The Semantic Web #8 - Ontology

  1. 1. Linked Data &Semantic WebTechnology The Semantic Web Part 8. Ontology Dr. Myungjin Lee
  2. 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 2Linked Data & Semantic Web Technology
  3. 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 3Linked Data & Semantic Web Technology
  4. 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 4Linked Data & Semantic Web Technology
  5. 5. Conceptualization • What is Conceptualization? – the process of development and clarification of concepts Object refer to stand for Concept symbolize “Namdeamun” Symbol 5Linked Data & Semantic Web Technology
  6. 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 6Linked Data & Semantic Web Technology
  7. 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 – … 7Linked Data & Semantic Web Technology
  8. 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 8Linked Data & Semantic Web Technology
  9. 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… 9Linked Data & Semantic Web Technology
  10. 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)) 10Linked Data & Semantic Web Technology
  11. 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) 11Linked Data & Semantic Web Technology
  12. 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 12Linked Data & Semantic Web Technology
  13. 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 … 13Linked Data & Semantic Web Technology
  14. 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 14Linked Data & Semantic Web Technology
  15. 15. Syntax and Semantics of DL 15Linked Data & Semantic Web Technology
  16. 16. Syntax and Semantics of DL 16Linked Data & Semantic Web Technology
  17. 17. Naming Convention of Description Logic 17Linked Data & Semantic Web Technology
  18. 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 18Linked Data & Semantic Web Technology
  19. 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 19Linked Data & Semantic Web Technology
  20. 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 20Linked Data & Semantic Web Technology
  21. 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/ 21 21Linked Data & Semantic Web Technology

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