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Semantic Web                                               Technologies                                                   ...
Semantic Web Technologies    Content2    1. Introduction    2. Semantic Web - Basic Architecture            Languages of t...
last lect                 ure                                c s                             t i                         a...
Semantic Web Technologies    Content4    3. Knowledge Representation and Logics       The Languages of the Semantic Web - ...
5                                                                                                      g e                ...
3. Knowledge Representation & Logic    3.5 OWL and OWL Semantics6               3.5 OWL and OWL Semantics                 ...
Why OWL and not WOL ...?7           Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamS...
OWL – Web Ontology Language                                     • OWL - W3C Recommendation since 20048                    ...
OWL – Web Ontology Language9                                   • OWL is a semantic fragment of FOL                        ...
OWL – Web Ontology Language10                                  • OWL is a semantic fragment of FOL                        ...
OWL – Web Ontology Language11                                    • OWL Lite SHIF(D)                                      •...
OWL – Web Ontology Language12                                      • Disjunctiveness of classes                           ...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics13               3.5 OWL and OWL Semantics               ...
OWL 1 – Syntax Variants14                           <owl:Class rdf:ID=“Wine“>                            <rdfs:subClassOf ...
OWL 1 – RDF(S) Syntax15                                   • OWL documents are RDF documents                               ...
16                                                              3.5 OWL and OWL Semantics                                 ...
OWL1 Document Header17       <owl:Ontology rdf:about="">         <rdfs:comment rdf:datatype="http://www.w3.org/2001/XMLSch...
OWL Document Header18                           • inherited from rdfs:                       • OWL Versioning:            ...
19     3.5 OWL and OWL Semantics        3.5.1 OWL - Overview        3.5.2 OWL1 Syntax            - OWL1 document header   ...
OWL – Classes, Properties and Individuals20                                        • Ontology axioms consist of the follow...
OWL – Classes                                        • there exist two predefined classes21                                ...
OWL – Individuals22                                    • Definition of individuals via class membership                    ...
OWL – Properties23                                     • there exist two variants:                                      • ...
OWL – Properties                                       • Datatype properties have datatypes as range24                    ...
OWL – Properties and Individuals25                         :Wine a owl:Class .                           :Grapes a owl:Cla...
OWL – Properties and Individuals                                   • Properties in general are not functional26           ...
OWL – Class Hierarchies27                         :Wine a owl:Class ;                                   rdfs:subClassOf :A...
OWL – Class Hierarchies and Disjunctiveness28                  :AlcoholicBeverage a owl:Class .                  :MainDish...
OWL – Class Hierarchies and Equivalence29              :AlcoholicBeverage a owl:Class .                :AlkoholischesGetra...
OWL – Individuals and Class Relationships30                              :WegelerRheingauRiesling a :Wine ;               ...
OWL – Relationships among Individuals31                            :WegelerRheingauRiesling a :Wine ;                     ...
OWL – Relationships among Individuals32                           _:x1 a owl:AllDifferent ;                               ...
OWL – Enumerated Classes (Nominals)                           :Wine a owl:Class ;33                         :ChateauxLatou...
OWL – Class Membership (2)                                   • We define an additional third wine34                        ...
35     3.5 OWL and OWL Semantics        3.5.1 OWL - Overview        3.5.2 OWL1 Syntax           - OWL1 document header    ...
OWL – Logical Class Constructors36                                • logical AND (conjunction): owl:intersectionOf         ...
OWL – Logical Class Constructors37                                    WineInStore ≣ ThingsInStore ⊓ Wine                  ...
OWL – Logical Class Constructors38                                       Wine ≣ DryWine ⊔ MediumWine ⊔ SweetWine          ...
OWL – Logical Class Constructors39                                        Wine ⊑ ¬Pizza                                   ...
OWL – Property Restrictions                                    • are used to describe complex classes via properties40    ...
OWL – Property Restrictions with Constants                                       HaraldsCourses ⊑ isManagedBy.(Harald)41  ...
OWL – Property Restrictions                                    • owl:allValuesFrom42                                      ...
OWL – Property Restrictions                                  • owl:someValuesFrom43                                   desc...
OWL – Cardinality Restrictions                                   • owl:cardinality restricts to an exact number44         ...
45                                                               3.5 OWL and OWL Semantics                                ...
OWL – Property Relationships                                    • Property hierarchies can be created via specializations:...
OWL – Property Relationships47                                       • owl:TransitiveProperty                             ...
OWL – Transitive Properties                                       :isLocatedIn a owl:ObjectProperty ;48                   ...
49                                                                 3.5 OWL and OWL Semantics                              ...
OWL – Web Ontology Language50                                    • OWL Lite SHIF(D)                                      •...
OWL FULL51                                    • Unrestricted Usage of all OWL and RDFS language                           ...
OWL DL52                                      • Only explicitly allowed RDFS language elements are to                     ...
OWL LITE (obsolete...)53                                      • All restrictions as for OWL DL.                           ...
54                 3.5 OWL and OWL Semantics                     3.5.1 OWL - Overview                     3.5.2 OWL1 Synta...
Terminological OWL Queries55                                    • Class Equivalence                                      •...
Assertional OWL Queries56                                       • Class membership:                                       ...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics57               3.5 OWL and OWL Semantics               ...
OWL Tools58                                    • Ontology Editors                                        • Protegé, http:/...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics59               3.5 OWL and OWL Semantics               ...
Description Logics revisited60                         Operator/Constructor                                  Syntax       ...
Description Logics revisited                                          • ALC: Attribute Language with Complement61         ...
OWL1 and ALC62                                      • The following OWL1 DL language elements can be                      ...
OWL1 DL as SHOIN(D)63                                     •owl:sameAs                                       •indicates tha...
OWL1 DL as SHOIN(D)64                                    •Enumerated Classes (Nominals)                                   ...
OWL1 DL as SHOIN(D)                                     • Number Restrictions65                                           ...
OWL1 DL as SHOIN(D)                                   •Property Hierarchies66                                   • rdfs:sub...
OWL1 DL as SHOIN(D)                                     • For OWL DL the following is permitted:67                        ...
OWL1 DL Syntax - Overview68                                                                                       Concept ...
OWL1 DL Syntax - Class Constructors69     Constructor                              DL Syntax                           Exa...
OWL1 DL Syntax - Axioms70     Axioms                                            DL Syntax                                 ...
OWL1 DL Syntax                                    • Nesting of constructors:71                                     • Perso...
OWL1 DL und OWL RDF Syntax                                   • Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)72           ...
OWL1 DL und OWL RDF Syntax                                   • Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)73           ...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics74               3.5 OWL and OWL Semantics               ...
Semantic Web Technologies     Content75     3. Knowledge Representation and Logics        The Languages of the Semantic We...
next L           ecture                                                                                                   ...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics77              Bibliography                           • ...
3. Knowledge Representation & Logic     3.5 OWL and OWL Semantics78                                                       ...
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(09) Semantic Web Technologies - OWL

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(09) Semantic Web Technologies - OWL

  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)Samstag, 15. Dezember 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 PotsdamSamstag, 15. Dezember 12
  3. 3. last lect ure c s t i a n3 em S F(S ) a l D m r R r o F o f Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam Rembrandt van Rijn, Die Anatomie des Dr. Tulp, 1632Samstag, 15. Dezember 12
  4. 4. Semantic Web Technologies Content4 3. Knowledge Representation and Logics The Languages of the Semantic Web - Part 2 • Excursion: Ontologies in Philosophy and Computer Science • Recapitulation: Propositional Logic and First Order Logic • Description Logics • RDF(S) Semantics • OWL and OWL-Semantics • OWL 2 and Rules Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  5. 5. 5 g e u a W LL ang O g y ol o n t b O W e Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  6. 6. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics6 3.5 OWL and OWL Semantics 3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax 3.5.3 OWL 1 - Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  7. 7. Why OWL and not WOL ...?7 Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12 Turmbau zu Babel, Pieter Brueghel, 1563
  8. 8. OWL – Web Ontology Language • OWL - W3C Recommendation since 20048 • OWL 2 - W3C Recommendation since 2009 • OWL Ontology consists of • Classes / properties / individuals (instances of Classes) • Open World Assumption • „Absence of information must not be valued as negative information.“ • E.g.: sitsNextTo(PersonA, PersonB) PersonA my also sit next to another person… • No Unique Name Assumption • „Difference must be expressed explicitly“ • E.g.: PersonA might denote the same individual as PersonB Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12 Turmbau zu Babel, Pieter Brueghel, 1563
  9. 9. OWL – Web Ontology Language9 • OWL is a semantic fragment of FOL • OWL existists in different flavours • OWL Lite ⊆ OWL DL ⊆ OWL Full OWL1 FOL OWL1 SWRL/RIF OWL Full OWL DL OWL EL OWL Lite RDFS OWL RL OWL QL Concept Hierarchies Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12 Turmbau zu Babel, Pieter Brueghel, 1563
  10. 10. OWL – Web Ontology Language10 • OWL is a semantic fragment of FOL • OWL existists in different flavours • OWL Lite ⊆ OWL DL ⊆ OWL Full • for OWL2: FOL • OWL EL, OWL RL, OWL QL OWL2 ⊆ OWL DL ⊆ OWL Full SWRL/RIF OWL Full OWL DL OWL2 OWL EL OWL Lite RDFS OWL RL OWL QL Concept Hierarchies Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12 Turmbau zu Babel, Pieter Brueghel, 1563
  11. 11. OWL – Web Ontology Language11 • OWL Lite SHIF(D) • Subset of OWL DL , rather restricted (no nominal classes, no cardinality, no disjunctiveness) • Complexity ExpTime (worst case) • OWL DL (Description Logic) SHOIN (D) or SHROIQ (D) [OWL2] Full • formally sound semantics DL • decidable, complete, sound • Complexity NExpTime (worst case) Lite • OWL Full • Union of OWL Syntax and RDF(S) • Meta modeling (Nesting) • undecidable (is not a descrtion logic) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  12. 12. OWL – Web Ontology Language12 • Disjunctiveness of classes • E.g.: Classes Person and Beverage are disjunctive • Inverse properties • E.g.: likes isLikedBy Full • Difference of individuals DL • E.g.: PersonA != PersonB Lite • Class descriptions • E.g.: Class CoffeeLover consists of members of class Person, who for the Property likes have the value “Coffee“ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  13. 13. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics13 3.5 OWL and OWL Semantics 3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax 3.5.3 OWL 1 - Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  14. 14. OWL 1 – Syntax Variants14 <owl:Class rdf:ID=“Wine“> <rdfs:subClassOf rdf:resource=“#Beverage“/> RDF(S) Syntax </owl:Class> class(a:Wine partial a:Beverage) abstract Syntax Wine ⊆ Beverage DL Syntax :Beverage a owl:Class . :Wine a owl:Class ; Turtle rdfs:subClassOf :Beverage . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  15. 15. OWL 1 – RDF(S) Syntax15 • OWL documents are RDF documents (at least according to the standard syntax) • OWL documents (in RDF(S) syntax) consist of • Header with general information • Body with the actual ontology <rdf:RDF xmlns ="http://www.semanticweb-fundamentals.de/exampleontology#" xmlns:rdf ="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:xsd ="http://www.w3.org/2001/XMLSchema#" xmlns:rdfs ="http://www.w3.org/2000/01/rdf-schema#" xmlns:owl ="http://www.w3.org/2002/07/owl#“ > ... </rdf:RDF> Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  16. 16. 16 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  17. 17. OWL1 Document Header17 <owl:Ontology rdf:about=""> <rdfs:comment rdf:datatype="http://www.w3.org/2001/XMLSchema#string“> SWRC Ontology in the version of january 2012 </rdfs:comment> <owl:versionInfo>v0.5</owl:versionInfo> <owl:imports rdf:resource="http://www.hpi.uni-potsdam.de/foo"/> <owl:priorVersion rdf:resource="http://www.semweb.de/swrc"/> </owl:Ontology> Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  18. 18. OWL Document Header18 • inherited from rdfs: • OWL Versioning: • rdfs:comment • owl:versionInfo • rdfs:label • owl:priorVersion • rdfs:seeAlso • owl:backwardCompatibleWith • rdfs:isDefinedBy • owl:incompatibleWith • owl:DeprecatedClass • other: • owl:DeprecatedProperty • owl:imports Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  19. 19. 19 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  20. 20. OWL – Classes, Properties and Individuals20 • Ontology axioms consist of the following three building blocks: • Classes •comparable with classes in RDFS • Individuals •comparable with objects in RDFS • Properties •comparable with properties in RDFS Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  21. 21. OWL – Classes • there exist two predefined classes21 • owl:Thing (class that contains all individuals) ⊤ • owl:Nothing (empty class) ⊥ • Definition of a class :Wine a owl:Class . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  22. 22. OWL – Individuals22 • Definition of individuals via class membership :WegelerRheingauRiesling a :Wine . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  23. 23. OWL – Properties23 • there exist two variants: • object properties • datatype properties • Object properties are defined like classes :isMadeFrom a owl:ObjectProperty . • Domain and Range of object properties :isMadeOf a owl:ObjectProperty ; rdfs:domain :Wine ; rdfs:range :Grapes . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  24. 24. OWL – Properties • Datatype properties have datatypes as range24 :hasQuality a owl:DatatypeProperty . • Domain and range of datatype properties :hasQuality a owl:DatatypeProperty ; rdfs:domain :Wine ; rdfs:range xsd:string . • Many XML datatypes can be used. The standard provides integer and string. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  25. 25. OWL – Properties and Individuals25 :Wine a owl:Class . :Grapes a owl:Class . :Riesling a :Grapes . :isMadeOf a owl:ObjectProperty ; rdfs:domain :Wine ; rdfs:range :Grapes . :hasQuality a owl:DatatypeProperty ; rdfs:domain :Wine ; rdfs:range xsd:string . :WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spätlese“ . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  26. 26. OWL – Properties and Individuals • Properties in general are not functional26 :Tempranillo a :Grapes . :Garnacha a :Grapes . :Mazuelo a :Grapes . :Graciano a :Grapes . :MarquesDeRiscal a :Wine ; :isMadeOf :Tempranillo ; :isMadeOf :Garnacha ; :isMadeOf :Mazuelo ; :isMadeOf :Graciano . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  27. 27. OWL – Class Hierarchies27 :Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage . :AlcoholicBeverage a owl:Class ; rdfs:subClassOf :Beverage . :Beverage a owl:Class . • via inference it can be entailed that „Wine“ is also a subclass of „Beverage“ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  28. 28. OWL – Class Hierarchies and Disjunctiveness28 :AlcoholicBeverage a owl:Class . :MainDish a owl:Class . :Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage . :Pizza a owl:Class ; rdfs:subClassOf :MainDish . :AlcoholicBeverage owl:disjointWith :MainDish . • via inference it can be entailed that „Wine“ and „Pizza“ are also disjoint classes. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  29. 29. OWL – Class Hierarchies and Equivalence29 :AlcoholicBeverage a owl:Class . :AlkoholischesGetraenk a owl:Class . :Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage . :AlcoholicBeverage owl:equivalentWith :AlkoholischesGetraenk . • via inference it can be entailed that „Wine“ is also an „AlkoholischesGetraenk“ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  30. 30. OWL – Individuals and Class Relationships30 :WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spaetlese“ . :Wine a owl:Class ; rdfs:subClassOf AlcoholicBeverage . :AlcoholicBeverage a owl:Class. • via inference it can be entailed that „WegelerRheingauRiesling“ is an „AlcoholicBeverage“ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  31. 31. OWL – Relationships among Individuals31 :WegelerRheingauRiesling a :Wine ; :isMadeOf :Riesling ; :hasQuality “Spaetlese“ ; owl:sameAs :WRR012345 . :Wine a owl:Class ; rdfs:subClassOf :AlcoholicBeverage . :AlcoholicBeverage a owl:Class. • via inference it can be entailed that „WRR012345“ is an „AlcoholicBeverage“ • Difference of Individuals via owl:differentFrom :WRR012346 a :Wine ; owl:differentFrom :WRR012345 . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  32. 32. OWL – Relationships among Individuals32 _:x1 a owl:AllDifferent ; owl:distinctMembers (:WegelerRheingauRiesling :AltoAdigeChardonnay :ChateauxLafiteRothschild :MarquesDeRiscal) . • Abbreviation instead of writing many times owl:differentFrom. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  33. 33. OWL – Enumerated Classes (Nominals) :Wine a owl:Class ;33 :ChateauxLatourPauillac a :Wine . :ChateauxLafiteRothschild a :Wine . :RedwinesInStore a owl:Class ; owl:oneOf (:ChateauxLatourPauillac, :ChateauxLafiteRothschild) . • This says that there are only exactly two redwines available in the store. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  34. 34. OWL – Class Membership (2) • We define an additional third wine34 :AltoAdigeSauvignonBlanc a :Wine . _:x1 rdf:type owl:AllDifferent ; owl:distinctMembers (:ChateauxLatourPauillac :ChateauxLafiteRothschild :AltoAdigeSauvignonBlanc) . • this entails that “AltoAdigeSauvignonBlanc“ is not available in the store. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  35. 35. 35 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  36. 36. OWL – Logical Class Constructors36 • logical AND (conjunction): owl:intersectionOf ⊓ • logical OR (disjunction): owl:unionOf ⊔ • logical negation: owl:complementOf ¬ • Logical constructors are applied to create complex class descriptions from atomic classes. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  37. 37. OWL – Logical Class Constructors37 WineInStore ≣ ThingsInStore ⊓ Wine :Wine a owl:Class . :ThingsInStore a owl:Class . :WineInStore a owl:Class ; owl:intersectionOf (:Wine :ThingsInStore) . • The class “WineInStore“ results from the intersection of all individuals of the classes “ThingsInStore“ and “Wine“ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  38. 38. OWL – Logical Class Constructors38 Wine ≣ DryWine ⊔ MediumWine ⊔ SweetWine :Wine a owl:Class ; owl:equivalentClass [ owl:unionOf ( :DryWine :MediumWine :SweetWine) ] . • Dry, medium and sweet wines are also wines Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  39. 39. OWL – Logical Class Constructors39 Wine ⊑ ¬Pizza :Wine a owl:Class ; rdfs:subClassOf [ owl:complementOf :Pizza ] . • semantically equivalent assertion: :Wine a owl:Class ; owl:disjointWith :Pizza . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  40. 40. OWL – Property Restrictions • are used to describe complex classes via properties40 • restrictions on values: • owl:hasValue! ! ! • owl:allValuesFrom • owl:someValuesFrom • restrictions on cardinality: • owl:cardinality • owl:minCardinality • owl:maxCardinality Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  41. 41. OWL – Property Restrictions with Constants HaraldsCourses ⊑ isManagedBy.(Harald)41 :HaraldsCourses a owl:Class ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :isManagedBy ; owl:hasValue :Harald ] . • Class „HaraldsCourses“ is described via fixed value assignment (=constant) of the individual „Harald“ to the property „isManagedBy“ :Person a owl:Class . :Course a owl:Class . :Harald a :Person . :isManagedBy a owl:ObjectProperty ; rdfs:domain :Course ; rdfs:range :Person . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  42. 42. OWL – Property Restrictions • owl:allValuesFrom42 fixes all instances of a specific class C as allowed range for a property P → (Universal Quantification) ∀P.C Wine ⊑ ∀hasProducer.Winemaker :Wine a owl:Class ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :hasProducer ; owl:allValuesFrom :Winemaker ] . :Producer a owl:Class . :Product a owl:Class . :Winemaker owl:subClassOf :Producer . :hasProducer a owl:ObjectProperty ; rdfs:domain :Product ; rdfs:range :Producer . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  43. 43. OWL – Property Restrictions • owl:someValuesFrom43 describes that there must exist an individual for property P and fixes its range to class C → (existential quantification) ∃P.C Animals ⊑ ∃feedsOn.Vegetables :Animals a owl:Class ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :feedsOn ; owl:somelValuesFrom :Vegetables ] . :Animal a owl:Class . :Food a owl:Class . :Vegetables owl:subClassOf :Food . :feedsOn a owl:ObjectProperty ; rdfs:domain :Animal ; rdfs:range :Food . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  44. 44. OWL – Cardinality Restrictions • owl:cardinality restricts to an exact number44 (for OWL Lite only 1/0) • owl:minCardinality, owl:maxCardinality restricts to upper / lower bounds Stringquartett ⊑ (=4)hasMembers :Stringquartett a owl:Class ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :hasMembers ; owl:cardinality 4 ] . :hasMembers a owl:DatatypeProperty ; rdfs:domain :Thing ; rdfs:range xsd:integer . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  45. 45. 45 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  46. 46. OWL – Property Relationships • Property hierarchies can be created via specializations:46 rdfs:subPropertyOf • Inverse properties are defined via owl:inverseOf • Identical properties are defined via owl:equivalentProperty :isMadeOf a owl:ObjectProperty ; rdfs:subPropertyOf :consistsOf . :isProcessedTo a owl:ObjectProperty ; owl:inverseOf :isMadeOf . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  47. 47. OWL – Property Relationships47 • owl:TransitiveProperty • E.g.: A isPartOf B, B isPartOf C A isPartOf C • owl:SymmetricProperty • E.g.: A isNeighborOf B B isNeighborOf A • owl:FunctionalProperty • E.g.: A hasMother B, A hasMother C B=C • owl:InverseFunctionalProperty • Bsp.: B isMotherOf A, C isMotherOf A B=C Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  48. 48. OWL – Transitive Properties :isLocatedIn a owl:ObjectProperty ;48 a owl:TransitiveProperty ; rdfs:domain owl:Thing ; rdfs:range :Region . :Rheinhessen a :Region ; :isLocatedIn :Hessen . :Hessen a :Region ; :isLocatedIn :Germany . • via inference it can be entailed that „Rheinhessen“ is located in „Germany“ . :Region a owl:Class . :Germany a :Region . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  49. 49. 49 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  50. 50. OWL – Web Ontology Language50 • OWL Lite SHIF(D) • Subset of OWL DL , rather... t e restricted (no nominalbs ole cardinality, no disjunctiveness) o classes, no • Complexity ExpTime (worst case) • OWL DL (Description Logic) SHOIN (D) or SHROIQ (D) [OWL2] • formally sound semantics Full • decidable, complete, sound DL • Complexity NExpTime (worst case) Lite • OWL Full • Union of OWL Syntax and RDF(S) • Meta modeling (Nesting) • undecidable (is not a description logic) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  51. 51. OWL FULL51 • Unrestricted Usage of all OWL and RDFS language elements (...must be valid RDFS). • Problems: no strict type separation (classes, properties, individuals), therefore: • owl:Thing is the same as rdfs:Resource • owl:Class is the same as rdfs:Class • owl:DatatypeProperty becomes subclass of owl:ObjectProperty • owl:ObjectProperty is the same as rdfs:Property Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  52. 52. OWL DL52 • Only explicitly allowed RDFS language elements are to be used (as e.g. in our examples). • not allowed: rdfs:Class, rdfs:Property • type separation: • Classes and Properties must be explicitly declared. • Datatype properties must not be transitive, symmetric, invers, or invers-functional. • Number restrictions must not be applied with transitive properties, their subproperties, or their inverse properties. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  53. 53. OWL LITE (obsolete...)53 • All restrictions as for OWL DL. • Not allowed: • oneOf, • unionOf, e... obs olet • complementOf, • hasValue, • disjointWith • Number restrictions only with 0 and 1. • Some restrictions according anonymous (complex) classes, i.e. in some cases the usage of class names or property names is mandatory. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  54. 54. 54 3.5 OWL and OWL Semantics 3.5.1 OWL - Overview 3.5.2 OWL1 Syntax - OWL1 document header - OWL1 classes, properties and individuals - OWL1 - complex classes - OWL1 - properties - OWL1 variants - Querying OWL1 3.5.3 OWL1 Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  55. 55. Terminological OWL Queries55 • Class Equivalence • Subclass relationships • Disjunctiveness of classes • Global consistency (satisfiability) • Class consistency: a class is inconsistent, if it is equivalent to owl:Nothing • indicates often a modeling failure :Wine a owl:Class; owl:subClassOf :Beverage; owl:disjointWith :Beverage . Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  56. 56. Assertional OWL Queries56 • Class membership: • Does a given individual belong to a specific class? • Class extension: • Search for all individuals that are contained in a specific class. • Property checking: • Are two given individuals connected via a given property? • Property extension: • Search or all pairs of individuals that are connected via a specific property. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  57. 57. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics57 3.5 OWL and OWL Semantics 3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax 3.5.3 OWL 1 - Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  58. 58. OWL Tools58 • Ontology Editors • Protegé, http://protege.stanford.edu • SWOOP, http://www.mindswap.org/2004/SWOOP/ • KAON(2) OWL Tools, http://owltools.ontoware.org/ • Inference engines (Reasoner) • Pellet, http://clarkparsia.com/pellet • KAON2, http://kaon2.semanticweb.org • FACT++, http://owl.man.ac.uk/factplusplus/ • Racer, http://www.racer-systems.com/ • HermiT, http://hermit-reasoner.com/ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  59. 59. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics59 3.5 OWL and OWL Semantics 3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax 3.5.3 OWL 1 - Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  60. 60. Description Logics revisited60 Operator/Constructor Syntax Language Conjunction A⊓B Universal (Range) Restriction ∀R.C FL Existential Quantification ∃R Top ⊤ Bottom ⊥ S* Negation ¬A Disjunction A⊔B AL* Existential (Range) Restriction ∃R.C Number Restriction (≤nR) (≥nR) Enumerated Classes (Nominals) {a1,...,a2} Property Hierarchy R⊑S H Inverse Property R-1 I Qualified Number Restriction (≤nR.C) (≥nR.C) Q Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  61. 61. Description Logics revisited • ALC: Attribute Language with Complement61 • S: ALC + transitive Properties • H: Property Hierarchies • O: Nominals (enumerated classes) • I: inverse Properties • N: Number Restrictions ≤n R etc. • Q: Qualified Number Restrictions ≤n R.C etc. • (D): Datentype • F: functional Properties • R: Property Constructor • OWL 1 DL is SHOIN(D) / OWL 2 DL is SHROIQ(D) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  62. 62. OWL1 and ALC62 • The following OWL1 DL language elements can be represented in ALC: • classes, properties, individuals • class membership, property instances • owl:Thing and owl:Nothing • Class subsumption, equivalence, disjunctiveness • owl:intersectionOf, owl:unionOf • owl:complementOf • owl:allValuesFrom, owl:someValuesFrom • rdfs:range and rdfs:domain Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  63. 63. OWL1 DL as SHOIN(D)63 •owl:sameAs •indicates that two individuals denote the same element •DL: a=b •FOL: extension via equality predicate •owl:differentFrom •indicates that two individuals denote the different elements •DL: a≠b •FOL: ¬(a=b) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  64. 64. OWL1 DL as SHOIN(D)64 •Enumerated Classes (Nominals) •owl:oneOf •defines a class by extension of all its members •DL: C ≡ {a,b,c} •FOL: (∀x) (C(x) (x=a ∨ x=b ∨ x=c)) •owl:hasValue •„forces“ property to a specific individual •can be represented via owl:someValuesFrom and owl:oneOf Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  65. 65. OWL1 DL as SHOIN(D) • Number Restrictions65 :Examination a owl:Class; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty :hasExaminer; owl:maxCardinality 2 ] . • An examination has at most 2 examiners. • DL: Examination ⊑ ≤2hasExaminer • FOL: (E… Examination, h…hasExaminer) • (∀x)(E(x) ! ¬((∃x1)(∃x2)(∃x3) (x1 ≠ x2 Λ x2 ≠ x3 Λ x1 ≠ x3 Λ h(x,x1) Λ h(x,x2) Λ h(x,x3)))) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  66. 66. OWL1 DL as SHOIN(D) •Property Hierarchies66 • rdfs:subPropertyOf • DL: R ⊑ S • FOL: (∀x)∀(y)(R(x,y) ! S(x,y)) • Property equivalency likewise • owl:inverseOf • DL: R ≡ S- • FOL: (∀x)(∀y)(R(x,y) S(y,x)) • owl:TransitiveProperty • DL: R ⊑+ R • FOL: (∀x)(∀y)(∀z)(R(x,y)ΛR(y,z)!R(x,z)) • Symmetric Properties: R ≡ R- • Functional Properties: ⊤ ⊑ ≤1R • Inverse Functionality: ⊤ ⊑ ≤1R- Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  67. 67. OWL1 DL as SHOIN(D) • For OWL DL the following is permitted:67 • ALC • Equality and Inequality of individuals • Enumerated classes • Number restrictions • Property hierarchies and property equivalences • Inverse and transitive properties • Datatypes • Datatypes are allowed to use as 2nd argument of datatype properties in the ABox. • A set of specific typed data might form an enumerated class. • Datatypes cannot simply be expressed in FOL. But FOL semantics can be extended accordingly. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  68. 68. OWL1 DL Syntax - Overview68 Concept Axioms (TBox) Concepts Atomic A, B Subclass C⊑D Not ¬C Equivalent C≡D And C⊓D ALC Or C⊔D Property Axioms (TBox) Exists Subproperty R⊑S H ∃R.C For all ∀R.C Transitivity R+ S At least ≥n R.C (≥n R) Q(N) At most ≤n R.C (≤n R) Assertional Axioms (ABox) Instance C(a) Nominal {i1,...in} O Property R(a,b) Properties Same a=b Atomic Properties Different a≠b Inverse R- I Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  69. 69. OWL1 DL Syntax - Class Constructors69 Constructor DL Syntax Example FOL Syntax intersectionOf C1 ⊓… ⊓ Cn Person ⊓ Male C1(x)∧…∧Cn(x) unionOf C1 ⊔… ⊔ Cn Student ⊔ Professor C1(x)⋁…⋁Cn(x) complementOf ⌐C ⌐ Male ⌐C(x) oneOf {x1} ⊔… ⊔ {xn} {john} ⊔ {mary} x=x1 ⋁…⋁ x=xn allValuesFrom ∀P.C ∀attends.Seminar ∀y,P(x,y)→C(y) someValuesFrom ∃P.C ∃attends.Seminar ∃y,P(x,y)→C(y) maxCardinality ≤nP ≤2 attends ∃≤n y,P(x,y) minCardinality ≥nP ≥1 attends ∃≥n y,P(x,y) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  70. 70. OWL1 DL Syntax - Axioms70 Axioms DL Syntax Example subClassOf C1 ⊑ C2 Human ⊑ Animal ⊓ Biped equivalentClass C1 ≡ C2 Woman ≡ Human ⊓ Female disjointWith C1 ⊑ ⌐C2 Male ⊑ ⌐ Female sameAs {x1} ≡ {x2} {JamesBond} ≡ {007} differentFrom {x1} ⊑ ⌐{x2} {John} ⊑ ⌐{Mary} subPropertyOf P1 ⊑ P2 hasDaughter ⊑ hasChild equivalentProperty P1 ≡ P2 cost ≡ price inverseOf P1 ≡ P2- hasChild ≡ hasParent_ dsdsd TransitiveProperty P1 ⊑+ P2 hasAncester ⊑+ hasAncester FunctionalProperty ⊤ ⊑ ≤1P ⊤ ⊑ ≤1hasMother InverseFunctionalProperty ⊤ ⊑ ≤1P_ ⊤ ⊑ ≤1isMotherOf_ Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  71. 71. OWL1 DL Syntax • Nesting of constructors:71 • Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor) • General Class Inclusion (⊑) is sufficient: • C ≡ D iff (C ⊑ D and D ⊑ C) • Obvious FOL Equivalences • C ≡ D corresponds to (∀x)(C(x)⟺D(x)) • C ⊑ D corresponds to (∀x)(C(x) D(x)) Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  72. 72. OWL1 DL und OWL RDF Syntax • Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)72 <owl:Class> <owl:intersectionOf rdf:parseType="collection"> <owl:Class rdf:about="Person"/> <owl:Restriction> <owl:onProperty rdf:resource="hasChild"/> <owl:allValuesFrom> <owl:unionOf rdf:parseType="collection"> <owl:Class rdf:about="Doctor"/> <owl:Restriction> <owl:onProperty rdf:resource="hasChild"/> <owl:someValuesFrom rdf:resource="Doctor"/> </owl:Restriction> </owl:unionOf> </owl:allValuesFrom> </owl:Restriction> </owl:intersectionOf> </owl:Class> Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  73. 73. OWL1 DL und OWL RDF Syntax • Person ⊓ ∀hasChild.(Doctor ⊔ ∃hasChild.Doctor)73 [ a owl:Class; owl:IntersectionOf ( :person [ a owl:Restriction ; owl:onProperty :hasChild ; owl:allValuesFrom [ owl:unionOf ( :Doctor [ a owl:Restriction ; owl:onProperty :hasChild ; owl:someValuesFrom :Doctor ] ) ] ] ) ]. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  74. 74. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics74 3.5 OWL and OWL Semantics 3.5.1 OWL 1 - Overview 3.5.2 OWL 1 - Syntax 3.5.3 OWL 1 - Tools 3.5.4 OWL Semantics Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  75. 75. Semantic Web Technologies Content75 3. Knowledge Representation and Logics The Languages of the Semantic Web - Part 2 • Excursion: Ontologies in Philosophy and Computer Science • Recapitulation: Propositional Logic and First Order Logic • Description Logics • RDF(S) Semantics • OWL and OWL-Semantics • OWL 2 and Rules Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  76. 76. next L ecture OWL 276 OWL SHROIQ(D) SHOIN(D) Extension Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  77. 77. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics77 Bibliography • P. Hitzler, S. Roschke, Y. Sure: Semantic Web Grundlagen, Springer, 2007. • P. Hitzler, M. Krötzsch, S. Rudolph: Foundations of Semantic Web Technologies, CRC Press, 2009. Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12
  78. 78. 3. Knowledge Representation & Logic 3.5 OWL and OWL Semantics78 □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_09 Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamSamstag, 15. Dezember 12

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