Logical Foundations for the Semantic Web

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1 Logical Foundations for the Semantic Web Reasoning with Expressive Description Logics: Theory and Practice Ian Horrocks University of Manchester Manchester, UK Logical Foundations for the Semantic Web p. 1/37

2 Talk Outline Logical Foundations for the Semantic Web p. 2/37

3 Talk Outline Introduction to Description Logics Logical Foundations for the Semantic Web p. 2/37

4 Talk Outline Introduction to Description Logics The Semantic Web Logical Foundations for the Semantic Web p. 2/37

5 Talk Outline Introduction to Description Logics The Semantic Web Web Ontology Languages Logical Foundations for the Semantic Web p. 2/37

6 Talk Outline Introduction to Description Logics The Semantic Web Web Ontology Languages DAML+OIL and OWL Languages Logical Foundations for the Semantic Web p. 2/37

7 Talk Outline Introduction to Description Logics The Semantic Web Web Ontology Languages DAML+OIL and OWL Languages Reasoning with OWL OilEd Demo Logical Foundations for the Semantic Web p. 2/37

8 Talk Outline Introduction to Description Logics The Semantic Web Web Ontology Languages DAML+OIL and OWL Languages Reasoning with OWL OilEd Demo Research Challenges Logical Foundations for the Semantic Web p. 2/37

9 Introduction to Description Logics Logical Foundations for the Semantic Web p. 3/37

10 What are Description Logics? Logical Foundations for the Semantic Web p. 4/37

11 What are Description Logics? A family of logic based Knowledge Representation formalisms Descendants of semantic networks and KL-ONE Describe domain in terms of concepts (classes), roles (relationships) and individuals Logical Foundations for the Semantic Web p. 4/37

12 What are Description Logics? A family of logic based Knowledge Representation formalisms Descendants of semantic networks and KL-ONE Describe domain in terms of concepts (classes), roles (relationships) and individuals Distinguished by: Formal semantics (model theoretic) Decidable fragments of FOL Closely related to Propositional Modal & Dynamic Logics Provision of inference services Sound and complete decision procedures for key problems Implemented systems (highly optimised) Logical Foundations for the Semantic Web p. 4/37

13 Short History of Description Logics Logical Foundations for the Semantic Web p. 5/37

14 Short History of Description Logics Phase 1: Incomplete systems (Back, Classic, Loom,... ) Based on structural algorithms Logical Foundations for the Semantic Web p. 5/37

15 Short History of Description Logics Phase 1: Incomplete systems (Back, Classic, Loom,... ) Based on structural algorithms Phase 2: Development of tableau algorithms and complexity results Tableau-based systems (Kris, Crack) Investigation of optimisation techniques Logical Foundations for the Semantic Web p. 5/37

16 Short History of Description Logics Phase 1: Incomplete systems (Back, Classic, Loom,... ) Based on structural algorithms Phase 2: Development of tableau algorithms and complexity results Tableau-based systems (Kris, Crack) Investigation of optimisation techniques Phase 3: Tableau algorithms for very expressive DLs Highly optimised tableau systems (FaCT, DLP, Racer) Relationship to modal logic and decidable fragments of FOL Logical Foundations for the Semantic Web p. 5/37

17 Latest Developments Phase 4: Logical Foundations for the Semantic Web p. 6/37

18 Latest Developments Phase 4: Mature implementations Logical Foundations for the Semantic Web p. 6/37

19 Latest Developments Phase 4: Mature implementations Mainstream applications and Tools Databases Consistency of conceptual schemata (EER, UML etc.) Schema integration Query subsumption (w.r.t. a conceptual schema) Ontologies and Semantic Web (and Grid) Ontology engineering (design, maintenance, integration) Reasoning with ontology-based markup (meta-data) Service description and discovery Logical Foundations for the Semantic Web p. 6/37

20 Latest Developments Phase 4: Mature implementations Mainstream applications and Tools Databases Consistency of conceptual schemata (EER, UML etc.) Schema integration Query subsumption (w.r.t. a conceptual schema) Ontologies and Semantic Web (and Grid) Ontology engineering (design, maintenance, integration) Reasoning with ontology-based markup (meta-data) Service description and discovery Commercial implementations Cerebra system from Network Inference Ltd Logical Foundations for the Semantic Web p. 6/37

21 The Semantic Web Logical Foundations for the Semantic Web p. 7/37

22 The Semantic Web Vision Logical Foundations for the Semantic Web p. 8/37

23 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Logical Foundations for the Semantic Web p. 8/37

24 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it Logical Foundations for the Semantic Web p. 8/37

25 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages Logical Foundations for the Semantic Web p. 8/37

26 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Logical Foundations for the Semantic Web p. 8/37

27 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Both intended for direct human processing/interaction Logical Foundations for the Semantic Web p. 8/37

28 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Both intended for direct human processing/interaction In next generation web, resources should be more accessible to automated processes Logical Foundations for the Semantic Web p. 8/37

29 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Both intended for direct human processing/interaction In next generation web, resources should be more accessible to automated processes To be achieved via semantic markup Metadata annotations that describe content/function Logical Foundations for the Semantic Web p. 8/37

30 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Both intended for direct human processing/interaction In next generation web, resources should be more accessible to automated processes To be achieved via semantic markup Metadata annotations that describe content/function Coincides with Tim Berners-Lee s vision of a Semantic Web Logical Foundations for the Semantic Web p. 8/37

31 The Semantic Web Vision Web made possible through established standards TCP/IP for transporting bits down a wire HTTP & HTML for transporting and rendering hyperlinked text Applications able to exploit this common infrastructure Result is the WWW as we know it 1st generation web mostly handwritten HTML pages 2nd generation (current) web often machine generated/active Both intended for direct human processing/interaction In next generation web, resources should be more accessible to automated processes To be achieved via semantic markup Metadata annotations that describe content/function Coincides with Tim Berners-Lee s vision of a Semantic Web Logical Foundations for the Semantic Web p. 8/37

32 Ontologies Logical Foundations for the Semantic Web p. 9/37

33 Ontologies Semantic markup must be meaningful to automated processes Logical Foundations for the Semantic Web p. 9/37

34 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Logical Foundations for the Semantic Web p. 9/37

35 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Logical Foundations for the Semantic Web p. 9/37

36 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Logical Foundations for the Semantic Web p. 9/37

37 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Increased formality and regularity facilitates machine understanding Logical Foundations for the Semantic Web p. 9/37

38 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Increased formality and regularity facilitates machine understanding Ontologies can be used, e.g.: To facilitate agent-agent communication in e-commerce In semantic based search To provide richer service descriptions that can be more flexibly interpreted by intelligent agents Logical Foundations for the Semantic Web p. 9/37

39 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Increased formality and regularity facilitates machine understanding Ontologies can be used, e.g.: To facilitate agent-agent communication in e-commerce In semantic based search To provide richer service descriptions that can be more flexibly interpreted by intelligent agents Logical Foundations for the Semantic Web p. 9/37

40 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Increased formality and regularity facilitates machine understanding Ontologies can be used, e.g.: To facilitate agent-agent communication in e-commerce In semantic based search To provide richer service descriptions that can be more flexibly interpreted by intelligent agents Logical Foundations for the Semantic Web p. 9/37

41 Ontologies Semantic markup must be meaningful to automated processes Ontologies will play a key role Source of precisely defined terms (vocabulary) Can be shared across applications (and humans) Ontology typically consists of: Hierarchical description of important concepts in domain Descriptions of properties of instances of each concept Degree of formality can be quite variable (NL logic) Increased formality and regularity facilitates machine understanding Ontologies can be used, e.g.: To facilitate agent-agent communication in e-commerce In semantic based search To provide richer service descriptions that can be more flexibly interpreted by intelligent agents Logical Foundations for the Semantic Web p. 9/37

42 Web Ontology Languages Logical Foundations for the Semantic Web p. 10/37

43 Web Languages Logical Foundations for the Semantic Web p. 11/37

44 Web Languages Web languages already extended to facilitate content description XML Schema (XMLS) RDF and RDF Schema (RDFS) Logical Foundations for the Semantic Web p. 11/37

45 Web Languages Web languages already extended to facilitate content description XML Schema (XMLS) RDF and RDF Schema (RDFS) RDFS recognisable as an ontology language Classes and properties Range and domain Sub/super-classes (and properties) Logical Foundations for the Semantic Web p. 11/37

46 Web Languages Web languages already extended to facilitate content description XML Schema (XMLS) RDF and RDF Schema (RDFS) RDFS recognisable as an ontology language Classes and properties Range and domain Sub/super-classes (and properties) But RDFS not a suitable foundation for Semantic Web Too weak to describe resources in sufficient detail Logical Foundations for the Semantic Web p. 11/37

47 Web Languages Web languages already extended to facilitate content description XML Schema (XMLS) RDF and RDF Schema (RDFS) RDFS recognisable as an ontology language Classes and properties Range and domain Sub/super-classes (and properties) But RDFS not a suitable foundation for Semantic Web Too weak to describe resources in sufficient detail Requirements for web ontology language: Compatible with existing Web standards (XML, RDF, RDFS) Easy to understand and use (based on familiar KR idioms) Formally specified and of adequate expressive power Possible to provide automated reasoning support Logical Foundations for the Semantic Web p. 11/37

48 OIL, DAML-ONT, DAML+OIL and OWL Logical Foundations for the Semantic Web p. 12/37

49 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Logical Foundations for the Semantic Web p. 12/37

50 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Logical Foundations for the Semantic Web p. 12/37

51 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard Logical Foundations for the Semantic Web p. 12/37

52 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard DAML+OIL/OWL layered on top of RDFS RDFS based syntax and ontological primitives (subclass etc.) Adds much richer set of primitives (transitivity, cardinality,... ) Logical Foundations for the Semantic Web p. 12/37

53 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard DAML+OIL/OWL layered on top of RDFS RDFS based syntax and ontological primitives (subclass etc.) Adds much richer set of primitives (transitivity, cardinality,... ) Logical Foundations for the Semantic Web p. 12/37

54 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard DAML+OIL/OWL layered on top of RDFS RDFS based syntax and ontological primitives (subclass etc.) Adds much richer set of primitives (transitivity, cardinality,... ) Describes structure of domain in terms of Classes and Properties Ontology is set of axioms describing classes and properties E.g., Person subclass of Animal whose parents are all Persons Logical Foundations for the Semantic Web p. 12/37

55 OIL, DAML-ONT, DAML+OIL and OWL Two languages developed to satisfy above requirements OIL: developed by group of (largely) European researchers DAML-ONT: developed in DARPA DAML programme Efforts merged to produce DAML+OIL Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard DAML+OIL/OWL layered on top of RDFS RDFS based syntax and ontological primitives (subclass etc.) Adds much richer set of primitives (transitivity, cardinality,... ) Describes structure of domain in terms of Classes and Properties Ontology is set of axioms describing classes and properties E.g., Person subclass of Animal whose parents are all Persons Uses RDF for class/property membership assertions (ground facts) E.g., john instance of Person; john, mary instance of parent Logical Foundations for the Semantic Web p. 12/37

56 OWL Language Logical Foundations for the Semantic Web p. 13/37

57 Foundations Logical Foundations for the Semantic Web p. 14/37

58 Foundations Three species of OWL OWL full is union of OWL syntax and RDF OWL DL restricted to FOL fragment ( DAML+OIL) OWL Lite is easier to implement subset of OWL DL Logical Foundations for the Semantic Web p. 14/37

59 Foundations Three species of OWL OWL full is union of OWL syntax and RDF OWL DL restricted to FOL fragment ( DAML+OIL) OWL Lite is easier to implement subset of OWL DL Semantic layering OWL DL OWL full within DL fragment DL semantics officially definitive Logical Foundations for the Semantic Web p. 14/37

60 Foundations Three species of OWL OWL full is union of OWL syntax and RDF OWL DL restricted to FOL fragment ( DAML+OIL) OWL Lite is easier to implement subset of OWL DL Semantic layering OWL DL OWL full within DL fragment DL semantics officially definitive OWL DL based on SHIQ Description Logic Logical Foundations for the Semantic Web p. 14/37

61 Foundations Three species of OWL OWL full is union of OWL syntax and RDF OWL DL restricted to FOL fragment ( DAML+OIL) OWL Lite is easier to implement subset of OWL DL Semantic layering OWL DL OWL full within DL fragment DL semantics officially definitive OWL DL based on SHIQ Description Logic Benefits from many years of DL research Well defined semantics Formal properties well understood (complexity, decidability) Known reasoning algorithms Implemented systems (highly optimised) Logical Foundations for the Semantic Web p. 14/37

62 OWL Class Constructors Constructor DL Syntax Example (Modal Syntax) intersectionof C 1... C n Human Male C 1... C n unionof C 1... C n Doctor Lawyer C 1... C n complementof C Male C oneof {x 1... x n } {john, mary} x 1... x n allvaluesfrom P.C haschild.doctor [P ]C somevaluesfrom P.C haschild.lawyer P C maxcardinality np 1hasChild [P ] n+1 mincardinality np 2hasChild P n Logical Foundations for the Semantic Web p. 15/37

63 OWL Class Constructors Constructor DL Syntax Example (Modal Syntax) intersectionof C 1... C n Human Male C 1... C n unionof C 1... C n Doctor Lawyer C 1... C n complementof C Male C oneof {x 1... x n } {john, mary} x 1... x n allvaluesfrom P.C haschild.doctor [P ]C somevaluesfrom P.C haschild.lawyer P C maxcardinality np 1hasChild [P ] n+1 mincardinality np 2hasChild P n XMLS datatypes as well as classes in P.C and P.C E.g., hasage.nonnegativeinteger Logical Foundations for the Semantic Web p. 15/37

64 OWL Class Constructors Constructor DL Syntax Example (Modal Syntax) intersectionof C 1... C n Human Male C 1... C n unionof C 1... C n Doctor Lawyer C 1... C n complementof C Male C oneof {x 1... x n } {john, mary} x 1... x n allvaluesfrom P.C haschild.doctor [P ]C somevaluesfrom P.C haschild.lawyer P C maxcardinality np 1hasChild [P ] n+1 mincardinality np 2hasChild P n XMLS datatypes as well as classes in P.C and P.C E.g., hasage.nonnegativeinteger Arbitrarily complex nesting of constructors E.g., Person haschild.(doctor haschild.doctor) Logical Foundations for the Semantic Web p. 15/37

65 RDFS Syntax <owl:class> <owl:intersectionof rdf:parsetype="collection"> <owl:class rdf:about="#person"/> <owl:restriction> <owl:onproperty rdf:resource="#haschild"/> <owl:toclass> <owl:unionof rdf:parsetype="collection"> <owl:class rdf:about="#doctor"/> <owl:restriction> <owl:onproperty rdf:resource="#haschild"/> <owl:hasclass rdf:resource="#doctor"/> </owl:restriction> </owl:unionof> </owl:toclass> </owl:restriction> </owl:intersectionof> </owl:class> Logical Foundations for the Semantic Web p. 16/37

66 OWL DL Semantics Logical Foundations for the Semantic Web p. 17/37

67 OWL DL Semantics Semantics defined by interpretations: I = ( I, I) concepts subsets of I roles binary relations over I (subsets of I I ) individuals elements of I Logical Foundations for the Semantic Web p. 17/37

68 OWL DL Semantics Semantics defined by interpretations: I = ( I, I) concepts subsets of I roles binary relations over I (subsets of I I ) individuals elements of I Interpretation function I extended to concept expressions (C D) I = C I D I (C D) I = C I D I ( C) I = I \ C I {x n,..., x n } I = {x I n,..., x I n} ( R.C) I = {x y. x, y R I y C I } ( R.C) I = {x y.(x, y) R I y C I } ( nr) I = {x #{y x, y R I } n} ( nr) I = {x #{y x, y R I } n} Logical Foundations for the Semantic Web p. 17/37

69 OWL Axioms Axiom DL Syntax Example subclassof C 1 C 2 Human Animal Biped equivalentclass C 1 C 2 Man Human Male disjointwith C 1 C 2 Male Female sameindividualas {x 1 } {x 2 } {President_Bush} {G_W_Bush} differentfrom {x 1 } {x 2 } {john} {peter} subpropertyof P 1 P 2 hasdaughter haschild equivalentproperty P 1 P 2 cost price inverseof P 1 P2 haschild hasparent transitiveproperty P + P ancestor + ancestor functionalproperty 1P 1hasMother inversefunctionalproperty 1P 1hasSSN Logical Foundations for the Semantic Web p. 18/37

70 OWL Axioms Axiom DL Syntax Example subclassof C 1 C 2 Human Animal Biped equivalentclass C 1 C 2 Man Human Male disjointwith C 1 C 2 Male Female sameindividualas {x 1 } {x 2 } {President_Bush} {G_W_Bush} differentfrom {x 1 } {x 2 } {john} {peter} subpropertyof P 1 P 2 hasdaughter haschild equivalentproperty P 1 P 2 cost price inverseof P 1 P2 haschild hasparent transitiveproperty P + P ancestor + ancestor functionalproperty 1P 1hasMother inversefunctionalproperty 1P 1hasSSN I satisfies C 1 C 2 iff C I 1 C I 2 ; satisfies P 1 P 2 iff P I 1 P I 2 Logical Foundations for the Semantic Web p. 18/37

71 OWL Axioms Axiom DL Syntax Example subclassof C 1 C 2 Human Animal Biped equivalentclass C 1 C 2 Man Human Male disjointwith C 1 C 2 Male Female sameindividualas {x 1 } {x 2 } {President_Bush} {G_W_Bush} differentfrom {x 1 } {x 2 } {john} {peter} subpropertyof P 1 P 2 hasdaughter haschild equivalentproperty P 1 P 2 cost price inverseof P 1 P2 haschild hasparent transitiveproperty P + P ancestor + ancestor functionalproperty 1P 1hasMother inversefunctionalproperty 1P 1hasSSN I satisfies C 1 C 2 iff C I 1 C I 2 ; satisfies P 1 P 2 iff P I 1 P I 2 I satisfies ontology O (is a model of O) iff satisfies every axiom in O Logical Foundations for the Semantic Web p. 18/37

72 XML Datatypes in OWL Logical Foundations for the Semantic Web p. 19/37

73 XML Datatypes in OWL OWL supports XML Schema primitive datatypes Logical Foundations for the Semantic Web p. 19/37

74 XML Datatypes in OWL OWL supports XML Schema primitive datatypes Clean separation between object classes and datatypes Disjoint interpretation domain: d I D, and D I = Disjoint datatype properties: PD I I D Logical Foundations for the Semantic Web p. 19/37

75 XML Datatypes in OWL OWL supports XML Schema primitive datatypes Clean separation between object classes and datatypes Disjoint interpretation domain: d I D, and D I = Disjoint datatype properties: P I D I D Philosophical reasons: Datatypes structured by built-in predicates Not appropriate to form new datatypes using ontology language Logical Foundations for the Semantic Web p. 19/37

76 XML Datatypes in OWL OWL supports XML Schema primitive datatypes Clean separation between object classes and datatypes Disjoint interpretation domain: d I D, and D I = Disjoint datatype properties: P I D I D Philosophical reasons: Datatypes structured by built-in predicates Not appropriate to form new datatypes using ontology language Practical reasons: Ontology language remains simple and compact Semantic integrity of ontology language not compromised Implementability not compromised can use hybrid reasoner Only need sound and complete decision procedure for d I 1... d I n, where d i is a (possibly negated) datatype Logical Foundations for the Semantic Web p. 19/37

77 Reasoning with OWL DL Logical Foundations for the Semantic Web p. 20/37

78 Reasoning Logical Foundations for the Semantic Web p. 21/37

79 Reasoning Why do we want it? Logical Foundations for the Semantic Web p. 21/37

80 Reasoning Why do we want it? Semantic Web aims at machine understanding Understanding closely related to reasoning Logical Foundations for the Semantic Web p. 21/37

81 Reasoning Why do we want it? Semantic Web aims at machine understanding Understanding closely related to reasoning What can we do with it? Logical Foundations for the Semantic Web p. 21/37

82 Reasoning Why do we want it? Semantic Web aims at machine understanding Understanding closely related to reasoning What can we do with it? Design and maintenance of ontologies Check class consistency and compute class hierarchy Particularly important with large ontologies/multiple authors Logical Foundations for the Semantic Web p. 21/37

83 Reasoning Why do we want it? Semantic Web aims at machine understanding Understanding closely related to reasoning What can we do with it? Design and maintenance of ontologies Check class consistency and compute class hierarchy Particularly important with large ontologies/multiple authors Integration of ontologies Assert inter-ontology relationships Reasoner computes integrated class hierarchy/consistency Logical Foundations for the Semantic Web p. 21/37

84 Reasoning Why do we want it? Semantic Web aims at machine understanding Understanding closely related to reasoning What can we do with it? Design and maintenance of ontologies Check class consistency and compute class hierarchy Particularly important with large ontologies/multiple authors Integration of ontologies Assert inter-ontology relationships Reasoner computes integrated class hierarchy/consistency Querying class and instance data w.r.t. ontologies Determine if set of facts are consistent w.r.t. ontologies Determine if individuals are instances of ontology classes Retrieve individuals/tuples satisfying a query expression Check if one class subsumes (is more general than) another w.r.t. ontology... Logical Foundations for the Semantic Web p. 21/37

85 Why Decidable Reasoning? Logical Foundations for the Semantic Web p. 22/37

86 Why Decidable Reasoning? OWL DL constructors/axioms restricted so reasoning is decidable Logical Foundations for the Semantic Web p. 22/37

87 Why Decidable Reasoning? OWL DL constructors/axioms restricted so reasoning is decidable Consistent with Semantic Web s layered architecture XML provides syntax transport layer RDF(S) provides basic relational language and simple ontological primitives OWL DL provides powerful but still decidable ontology language Further layers may (will) extend OWL Will almost certainly be undecidable Logical Foundations for the Semantic Web p. 22/37

88 Why Decidable Reasoning? OWL DL constructors/axioms restricted so reasoning is decidable Consistent with Semantic Web s layered architecture XML provides syntax transport layer RDF(S) provides basic relational language and simple ontological primitives OWL DL provides powerful but still decidable ontology language Further layers may (will) extend OWL Will almost certainly be undecidable Facilitates provision of reasoning services Known practical algorithms Several implemented systems Evidence of empirical tractability Logical Foundations for the Semantic Web p. 22/37

89 Why Decidable Reasoning? OWL DL constructors/axioms restricted so reasoning is decidable Consistent with Semantic Web s layered architecture XML provides syntax transport layer RDF(S) provides basic relational language and simple ontological primitives OWL DL provides powerful but still decidable ontology language Further layers may (will) extend OWL Will almost certainly be undecidable Facilitates provision of reasoning services Known practical algorithms Several implemented systems Evidence of empirical tractability Understanding dependent on reliable & consistent reasoning Logical Foundations for the Semantic Web p. 22/37

90 Basic Inference Problems Logical Foundations for the Semantic Web p. 23/37

91 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? There exists some model I of O Is C consistent? C I in some model I of O Logical Foundations for the Semantic Web p. 23/37

92 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? There exists some model I of O Is C consistent? C I in some model I of O Subsumption structure knowledge, compute taxonomy C O D? C I D I in all models I of O Logical Foundations for the Semantic Web p. 23/37

93 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? There exists some model I of O Is C consistent? C I in some model I of O Subsumption structure knowledge, compute taxonomy C O D? C I D I in all models I of O Equivalence check if two classes denote same set of instances C O D? C I = D I in all models I of O Logical Foundations for the Semantic Web p. 23/37

94 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? Is C consistent? There exists some model I of O C I in some model I of O Subsumption structure knowledge, compute taxonomy C O D? C I D I in all models I of O Equivalence check if two classes denote same set of instances C O D? C I = D I in all models I of O Instantiation check if individual i instance of class C i O C? i C I in all models I of O Logical Foundations for the Semantic Web p. 23/37

95 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? Is C consistent? There exists some model I of O C I in some model I of O Subsumption structure knowledge, compute taxonomy C O D? C I D I in all models I of O Equivalence check if two classes denote same set of instances C O D? C I = D I in all models I of O Instantiation check if individual i instance of class C i O C? i C I in all models I of O Retrieval retrieve set of individuals that instantiate C set of i s.t. i C I in all models I of O Logical Foundations for the Semantic Web p. 23/37

96 Basic Inference Problems Consistency check if knowledge is meaningful Is O consistent? Is C consistent? There exists some model I of O C I in some model I of O Subsumption structure knowledge, compute taxonomy C O D? C I D I in all models I of O Equivalence check if two classes denote same set of instances C O D? C I = D I in all models I of O Instantiation check if individual i instance of class C i O C? i C I in all models I of O Retrieval retrieve set of individuals that instantiate C set of i s.t. i C I in all models I of O Problems all reducible to consistency (satisfiability): C O D iff C D not consistent w.r.t. O i O C iff O {i C} is not consistent Logical Foundations for the Semantic Web p. 23/37

97 Reasoning Support for Ontology Design: OilEd Logical Foundations for the Semantic Web p. 24/37

98 Description Logic Reasoning Logical Foundations for the Semantic Web p. 25/37

99 Highly Optimised Implementation Logical Foundations for the Semantic Web p. 26/37

100 Highly Optimised Implementation DL reasoning based on tableaux algorithms Logical Foundations for the Semantic Web p. 26/37

101 Highly Optimised Implementation DL reasoning based on tableaux algorithms Naive implementation effective non-termination Logical Foundations for the Semantic Web p. 26/37

102 Highly Optimised Implementation DL reasoning based on tableaux algorithms Naive implementation effective non-termination Modern systems include MANY optimisations Logical Foundations for the Semantic Web p. 26/37

103 Highly Optimised Implementation DL reasoning based on tableaux algorithms Naive implementation effective non-termination Modern systems include MANY optimisations Optimised classification (compute partial ordering) Use enhanced traversal (exploit information from previous tests) Use structural information to select classification order Logical Foundations for the Semantic Web p. 26/37

104 Highly Optimised Implementation DL reasoning based on tableaux algorithms Naive implementation effective non-termination Modern systems include MANY optimisations Optimised classification (compute partial ordering) Use enhanced traversal (exploit information from previous tests) Use structural information to select classification order Optimised subsumption testing (search for models) Normalisation and simplification of concepts Absorption (simplification) of general axioms Davis-Putnam style semantic branching search Dependency directed backtracking Caching of satisfiability results and (partial) models Heuristic ordering of propositional and modal expansion... Logical Foundations for the Semantic Web p. 26/37

105 Research and Implementation Challenges Logical Foundations for the Semantic Web p. 27/37

106 Challenges Logical Foundations for the Semantic Web p. 28/37

107 Challenges Increased expressive power Existing DL systems implement (at most) SHIQ OWL extends SHIQ with datatypes and nominals Logical Foundations for the Semantic Web p. 28/37

108 Challenges Increased expressive power Existing DL systems implement (at most) SHIQ OWL extends SHIQ with datatypes and nominals Scalability Very large KBs Reasoning with (very large numbers of) individuals Logical Foundations for the Semantic Web p. 28/37

109 Challenges Increased expressive power Existing DL systems implement (at most) SHIQ OWL extends SHIQ with datatypes and nominals Scalability Very large KBs Reasoning with (very large numbers of) individuals Other reasoning tasks Querying Matching Least common subsumer... Logical Foundations for the Semantic Web p. 28/37

110 Challenges Increased expressive power Existing DL systems implement (at most) SHIQ OWL extends SHIQ with datatypes and nominals Scalability Very large KBs Reasoning with (very large numbers of) individuals Other reasoning tasks Querying Matching Least common subsumer... Tools and Infrastructure Support for large scale ontological engineering and deployment Logical Foundations for the Semantic Web p. 28/37

111 Increased Expressive Power: Datatypes Logical Foundations for the Semantic Web p. 29/37

112 Increased Expressive Power: Datatypes OWL has simple form of datatypes Unary predicates plus disjoint object-class/datatype domains Logical Foundations for the Semantic Web p. 29/37

113 Increased Expressive Power: Datatypes OWL has simple form of datatypes Unary predicates plus disjoint object-class/datatype domains Well understood theoretically Existing work on concrete domains [Baader & Hanschke, Lutz] Algorithm already known for SHOQ(D) [Horrocks & Sattler] Can use hybrid reasoning (DL reasoner + datatype oracle ) Logical Foundations for the Semantic Web p. 29/37

114 Increased Expressive Power: Datatypes OWL has simple form of datatypes Unary predicates plus disjoint object-class/datatype domains Well understood theoretically Existing work on concrete domains [Baader & Hanschke, Lutz] Algorithm already known for SHOQ(D) [Horrocks & Sattler] Can use hybrid reasoning (DL reasoner + datatype oracle ) May be practically challenging Large number of XMLS datatypes may be supported Logical Foundations for the Semantic Web p. 29/37

115 Increased Expressive Power: Datatypes OWL has simple form of datatypes Unary predicates plus disjoint object-class/datatype domains Well understood theoretically Existing work on concrete domains [Baader & Hanschke, Lutz] Algorithm already known for SHOQ(D) [Horrocks & Sattler] Can use hybrid reasoning (DL reasoner + datatype oracle ) May be practically challenging Large number of XMLS datatypes may be supported Already seeing some (partial) implementations Cerebra system (Network Inference), Racer system (Hamburg) Logical Foundations for the Semantic Web p. 29/37

116 Increased Expressive Power: Nominals Logical Foundations for the Semantic Web p. 30/37

117 Increased Expressive Power: Nominals OWL oneof constructor equivalent to hybrid logic nominals Extensionally defined concepts, e.g., EU {France, Italy,...} Logical Foundations for the Semantic Web p. 30/37

118 Increased Expressive Power: Nominals OWL oneof constructor equivalent to hybrid logic nominals Extensionally defined concepts, e.g., EU {France, Italy,...} Theoretically very challenging Resulting logic has known high complexity (NExpTime) No known practical algorithm Not obvious how to extend tableaux techniques in this direction Loss of tree model property Spy-points: R.{Spy} Finite domains: {Spy} nr Logical Foundations for the Semantic Web p. 30/37

119 Increased Expressive Power: Nominals OWL oneof constructor equivalent to hybrid logic nominals Extensionally defined concepts, e.g., EU {France, Italy,...} Theoretically very challenging Resulting logic has known high complexity (NExpTime) No known practical algorithm Not obvious how to extend tableaux techniques in this direction Loss of tree model property Spy-points: R.{Spy} Finite domains: {Spy} nr?? automata based algorithms?? Logical Foundations for the Semantic Web p. 30/37

120 Increased Expressive Power: Nominals OWL oneof constructor equivalent to hybrid logic nominals Extensionally defined concepts, e.g., EU {France, Italy,...} Theoretically very challenging Resulting logic has known high complexity (NExpTime) No known practical algorithm Not obvious how to extend tableaux techniques in this direction Loss of tree model property Spy-points: R.{Spy} Finite domains: {Spy} nr?? automata based algorithms?? Standard solution is weaker semantics for nominals Treat nominals as (disjoint) primitive classes Loose some inferential power, e.g., w.r.t. max cardinality Logical Foundations for the Semantic Web p. 30/37

121 Scalability Logical Foundations for the Semantic Web p. 31/37

122 Scalability Reasoning hard even without nominals (i.e., SHIQ) Logical Foundations for the Semantic Web p. 31/37

123 Scalability Reasoning hard even without nominals (i.e., SHIQ) Web ontologies may grow very large Logical Foundations for the Semantic Web p. 31/37

124 Scalability Reasoning hard even without nominals (i.e., SHIQ) Web ontologies may grow very large Good empirical evidence of scalability/tractability for DL systems E.g., 5,000 (complex) classes 100,000+ (simple) classes Logical Foundations for the Semantic Web p. 31/37

125 Scalability Reasoning hard even without nominals (i.e., SHIQ) Web ontologies may grow very large Good empirical evidence of scalability/tractability for DL systems E.g., 5,000 (complex) classes 100,000+ (simple) classes But evidence mostly w.r.t. SHF (no inverse) Logical Foundations for the Semantic Web p. 31/37

126 Scalability Reasoning hard even without nominals (i.e., SHIQ) Web ontologies may grow very large Good empirical evidence of scalability/tractability for DL systems E.g., 5,000 (complex) classes 100,000+ (simple) classes But evidence mostly w.r.t. SHF (no inverse) Problems can arise when SHF extended to SHIQ Important optimisations no longer (fully) work Logical Foundations for the Semantic Web p. 31/37

127 Scalability Reasoning hard even without nominals (i.e., SHIQ) Web ontologies may grow very large Good empirical evidence of scalability/tractability for DL systems E.g., 5,000 (complex) classes 100,000+ (simple) classes But evidence mostly w.r.t. SHF (no inverse) Problems can arise when SHF extended to SHIQ Important optimisations no longer (fully) work Reasoning with individuals Deployment of web ontologies will mean reasoning with (possibly very large numbers of) individuals/tuples Unlikely that standard Abox techniques will be able to cope Logical Foundations for the Semantic Web p. 31/37

128 Other Reasoning Tasks Logical Foundations for the Semantic Web p. 32/37

129 Other Reasoning Tasks Querying Retrieval and instantiation wont be sufficient Minimum requirement will be DB style query language May also need what can I say about x? style of query Logical Foundations for the Semantic Web p. 32/37

130 Other Reasoning Tasks Querying Retrieval and instantiation wont be sufficient Minimum requirement will be DB style query language May also need what can I say about x? style of query Explanation To support ontology design Justifications and proofs (e.g., of query results) Logical Foundations for the Semantic Web p. 32/37

131 Other Reasoning Tasks Querying Retrieval and instantiation wont be sufficient Minimum requirement will be DB style query language May also need what can I say about x? style of query Explanation To support ontology design Justifications and proofs (e.g., of query results) Non-Standard Inferences, e.g., LCS, matching To support ontology integration To support bottom up design of ontologies Logical Foundations for the Semantic Web p. 32/37

132 Summary Logical Foundations for the Semantic Web p. 33/37

133 Summary Semantic Web aims to make web resources accessible to automated processes Logical Foundations for the Semantic Web p. 33/37

134 Summary Semantic Web aims to make web resources accessible to automated processes Ontologies will play key role by providing vocabulary for semantic markup Logical Foundations for the Semantic Web p. 33/37

135 Summary Semantic Web aims to make web resources accessible to automated processes Ontologies will play key role by providing vocabulary for semantic markup OWL is an ontology language designed for the web Exploits existing standards: XML, RDF(S) Adds KR idioms from object oriented and frame systems Formal rigor of a logic Facilitates provision of reasoning support Logical Foundations for the Semantic Web p. 33/37

136 Summary Semantic Web aims to make web resources accessible to automated processes Ontologies will play key role by providing vocabulary for semantic markup OWL is an ontology language designed for the web Exploits existing standards: XML, RDF(S) Adds KR idioms from object oriented and frame systems Formal rigor of a logic Facilitates provision of reasoning support Challenges remain Reasoning with nominals (Convincing) demonstration(s) of scalability New reasoning tasks Logical Foundations for the Semantic Web p. 33/37

137 Acknowledgements Logical Foundations for the Semantic Web p. 34/37

138 Acknowledgements Members of the OIL, DAML+OIL and OWL development teams, in particular Dieter Fensel and Frank van Harmelen (Amsterdam) and Peter Patel-Schneider (Bell Labs) Logical Foundations for the Semantic Web p. 34/37

139 Acknowledgements Members of the OIL, DAML+OIL and OWL development teams, in particular Dieter Fensel and Frank van Harmelen (Amsterdam) and Peter Patel-Schneider (Bell Labs) Franz Baader, Uli Sattler and Stefan Tobies (Dresden) Logical Foundations for the Semantic Web p. 34/37

140 Acknowledgements Members of the OIL, DAML+OIL and OWL development teams, in particular Dieter Fensel and Frank van Harmelen (Amsterdam) and Peter Patel-Schneider (Bell Labs) Franz Baader, Uli Sattler and Stefan Tobies (Dresden) Members of the Information Management, Medical Informatics and Formal Methods Groups at the University of Manchester Logical Foundations for the Semantic Web p. 34/37

141 Resources Slides from this talk FaCT system (open source) OilEd (open source) DAML+OIL W3C Web-Ontology (WebOnt) working group (OWL) Description Logic Handbook Cambridge University Press Logical Foundations for the Semantic Web p. 35/37

142 Select Bibliography I. Horrocks. DAML+OIL: a reason-able web ontology language. In Proc. of EDBT 2002, number 2287 in Lecture Notes in Computer Science, pages Springer-Verlag, Mar I. Horrocks, P. F. Patel-Schneider, and F. van Harmelen. Reviewing the design of DAML+OIL: An ontology language for the semantic web. In Proc. of AAAI 2002, To appear. I. Horrocks and S. Tessaris. Querying the semantic web: a formal approach. In I. Horrocks and J. Hendler, editors, Proc. of the 2002 International Semantic Web Conference (ISWC 2002), number 2342 in Lecture Notes in Computer Science. Springer-Verlag, C. Lutz. The Complexity of Reasoning with Concrete Domains. PhD thesis, Teaching and Research Area for Theoretical Computer Science, RWTH Aachen, Logical Foundations for the Semantic Web p. 36/37

143 Select Bibliography I. Horrocks and U. Sattler. Ontology reasoning in the SHOQ(D) description logic. In B. Nebel, editor, Proc. of IJCAI-01, pages Morgan Kaufmann, F. Baader, S. Brandt, and R. Küsters. Matching under side conditions in description logics. In B. Nebel, editor, Proc. of IJCAI-01, pages , Seattle, Washington, Morgan Kaufmann. A. Borgida, E. Franconi, and I. Horrocks. Explaining ALC subsumption. In Proc. of ECAI 2000, pages IOS Press, D. Calvanese, G. De Giacomo, M. Lenzerini, D. Nardi, and R. Rosati. A principled approach to data integration and reconciliation in data warehousing. In Proceedings of the International Workshop on Design and Management of Data Warehouses (DWDM 99), Logical Foundations for the Semantic Web p. 37/37

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