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Logical Foundations for the Semantic Web Reasoning with Expressive - - PowerPoint PPT Presentation

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Logical Foundations for the Semantic Web Reasoning with Expressive Description Logics: Theory and Practice Ian Horrocks horrocks@cs.man.ac.uk University of Manchester Manchester, UK Logical Foundations for the Semantic Web p. 1/37 Talk

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SLIDE 1

Logical Foundations for the Semantic Web

Reasoning with Expressive Description Logics: Theory and Practice

Ian Horrocks

horrocks@cs.man.ac.uk

University of Manchester Manchester, UK

Logical Foundations for the Semantic Web – p. 1/37

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Talk Outline

Logical Foundations for the Semantic Web – p. 2/37

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Talk Outline

Introduction to Description Logics

Logical Foundations for the Semantic Web – p. 2/37

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Talk Outline

Introduction to Description Logics The Semantic Web

Logical Foundations for the Semantic Web – p. 2/37

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SLIDE 5

Talk Outline

Introduction to Description Logics The Semantic Web Web Ontology Languages

Logical Foundations for the Semantic Web – p. 2/37

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 9

Introduction to Description Logics

Logical Foundations for the Semantic Web – p. 3/37

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What are Description Logics?

Logical Foundations for the Semantic Web – p. 4/37

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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

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SLIDE 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

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Short History of Description Logics

Logical Foundations for the Semantic Web – p. 5/37

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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

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SLIDE 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

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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

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Latest Developments

Phase 4:

Logical Foundations for the Semantic Web – p. 6/37

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Latest Developments

Phase 4: ☞ Mature implementations

Logical Foundations for the Semantic Web – p. 6/37

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SLIDE 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

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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

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The Semantic Web

Logical Foundations for the Semantic Web – p. 7/37

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The Semantic Web Vision

Logical Foundations for the Semantic Web – p. 8/37

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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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 32

Ontologies

Logical Foundations for the Semantic Web – p. 9/37

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SLIDE 33

Ontologies

☞ Semantic markup must be meaningful to automated processes

Logical Foundations for the Semantic Web – p. 9/37

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 42

Web Ontology Languages

Logical Foundations for the Semantic Web – p. 10/37

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SLIDE 43

Web Languages

Logical Foundations for the Semantic Web – p. 11/37

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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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 48

OIL, DAML-ONT, DAML+OIL and OWL

Logical Foundations for the Semantic Web – p. 12/37

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 56

OWL Language

Logical Foundations for the Semantic Web – p. 13/37

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SLIDE 57

Foundations

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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 62

OWL Class Constructors

Constructor DL Syntax Example (Modal Syntax) intersectionOf C1 ⊓ . . . ⊓ Cn Human ⊓ Male C1 ∧ . . . ∧ Cn unionOf C1 ⊔ . . . ⊔ Cn Doctor ⊔ Lawyer C1 ∨ . . . ∨ Cn complementOf ¬C ¬Male ¬C

  • neOf

{x1 . . . xn} {john, mary} x1 ∨ . . . ∨ xn allValuesFrom ∀P.C ∀hasChild.Doctor [P]C someValuesFrom ∃P.C ∃hasChild.Lawyer PC maxCardinality nP 1hasChild [P]n+1 minCardinality nP 2hasChild Pn

Logical Foundations for the Semantic Web – p. 15/37

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SLIDE 63

OWL Class Constructors

Constructor DL Syntax Example (Modal Syntax) intersectionOf C1 ⊓ . . . ⊓ Cn Human ⊓ Male C1 ∧ . . . ∧ Cn unionOf C1 ⊔ . . . ⊔ Cn Doctor ⊔ Lawyer C1 ∨ . . . ∨ Cn complementOf ¬C ¬Male ¬C

  • neOf

{x1 . . . xn} {john, mary} x1 ∨ . . . ∨ xn allValuesFrom ∀P.C ∀hasChild.Doctor [P]C someValuesFrom ∃P.C ∃hasChild.Lawyer PC maxCardinality nP 1hasChild [P]n+1 minCardinality nP 2hasChild Pn ☞ 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

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SLIDE 64

OWL Class Constructors

Constructor DL Syntax Example (Modal Syntax) intersectionOf C1 ⊓ . . . ⊓ Cn Human ⊓ Male C1 ∧ . . . ∧ Cn unionOf C1 ⊔ . . . ⊔ Cn Doctor ⊔ Lawyer C1 ∨ . . . ∨ Cn complementOf ¬C ¬Male ¬C

  • neOf

{x1 . . . xn} {john, mary} x1 ∨ . . . ∨ xn allValuesFrom ∀P.C ∀hasChild.Doctor [P]C someValuesFrom ∃P.C ∃hasChild.Lawyer PC maxCardinality nP 1hasChild [P]n+1 minCardinality nP 2hasChild Pn ☞ 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

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SLIDE 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

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SLIDE 66

OWL DL Semantics

Logical Foundations for the Semantic Web – p. 17/37

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SLIDE 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

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SLIDE 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 = CI ∩ DI

(C ⊔ D)I = CI ∪ DI (¬C)I = ∆I \ CI

  • {xn, . . . , xn}I = {xI

n, . . . , xI n}

  • (∃R.C)I = {x | ∃y.x, y ∈ RI ∧ y ∈ CI}
  • (∀R.C)I = {x | ∀y.(x, y) ∈ RI ⇒ y ∈ CI}
  • (nR)I = {x | #{y | x, y ∈ RI} n}
  • (nR)I = {x | #{y | x, y ∈ RI} n}

Logical Foundations for the Semantic Web – p. 17/37

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SLIDE 69

OWL Axioms

Axiom DL Syntax Example subClassOf C1 ⊑ C2 Human ⊑ Animal ⊓ Biped equivalentClass C1 ≡ C2 Man ≡ Human ⊓ Male disjointWith C1 ⊑ ¬C2 Male ⊑ ¬Female sameIndividualAs {x1} ≡ {x2} {President_Bush} ≡ {G_W_Bush} differentFrom {x1} ⊑ ¬{x2} {john} ⊑ ¬{peter} subPropertyOf P1 ⊑ P2 hasDaughter ⊑ hasChild equivalentProperty P1 ≡ P2 cost ≡ price inverseOf P1 ≡ P −

2

hasChild ≡ hasParent− transitiveProperty P + ⊑ P ancestor+ ⊑ ancestor functionalProperty ⊤ ⊑ 1P ⊤ ⊑ 1hasMother inverseFunctionalProperty ⊤ ⊑ 1P − ⊤ ⊑ 1hasSSN−

Logical Foundations for the Semantic Web – p. 18/37

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SLIDE 70

OWL Axioms

Axiom DL Syntax Example subClassOf C1 ⊑ C2 Human ⊑ Animal ⊓ Biped equivalentClass C1 ≡ C2 Man ≡ Human ⊓ Male disjointWith C1 ⊑ ¬C2 Male ⊑ ¬Female sameIndividualAs {x1} ≡ {x2} {President_Bush} ≡ {G_W_Bush} differentFrom {x1} ⊑ ¬{x2} {john} ⊑ ¬{peter} subPropertyOf P1 ⊑ P2 hasDaughter ⊑ hasChild equivalentProperty P1 ≡ P2 cost ≡ price inverseOf P1 ≡ P −

2

hasChild ≡ hasParent− transitiveProperty P + ⊑ P ancestor+ ⊑ ancestor functionalProperty ⊤ ⊑ 1P ⊤ ⊑ 1hasMother inverseFunctionalProperty ⊤ ⊑ 1P − ⊤ ⊑ 1hasSSN− ☞ I satisfies C1 ⊑ C2 iff CI

1 ⊆ CI 2 ; satisfies P1 ⊑ P2 iff P I 1 ⊆ P I 2

Logical Foundations for the Semantic Web – p. 18/37

slide-71
SLIDE 71

OWL Axioms

Axiom DL Syntax Example subClassOf C1 ⊑ C2 Human ⊑ Animal ⊓ Biped equivalentClass C1 ≡ C2 Man ≡ Human ⊓ Male disjointWith C1 ⊑ ¬C2 Male ⊑ ¬Female sameIndividualAs {x1} ≡ {x2} {President_Bush} ≡ {G_W_Bush} differentFrom {x1} ⊑ ¬{x2} {john} ⊑ ¬{peter} subPropertyOf P1 ⊑ P2 hasDaughter ⊑ hasChild equivalentProperty P1 ≡ P2 cost ≡ price inverseOf P1 ≡ P −

2

hasChild ≡ hasParent− transitiveProperty P + ⊑ P ancestor+ ⊑ ancestor functionalProperty ⊤ ⊑ 1P ⊤ ⊑ 1hasMother inverseFunctionalProperty ⊤ ⊑ 1P − ⊤ ⊑ 1hasSSN− ☞ I satisfies C1 ⊑ C2 iff CI

1 ⊆ CI 2 ; satisfies P1 ⊑ P2 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

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SLIDE 72

XML Datatypes in OWL

Logical Foundations for the Semantic Web – p. 19/37

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SLIDE 73

XML Datatypes in OWL

☞ OWL supports XML Schema primitive datatypes

Logical Foundations for the Semantic Web – p. 19/37

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SLIDE 74

XML Datatypes in OWL

☞ OWL supports XML Schema primitive datatypes ☞ Clean separation between “object” classes and datatypes

  • Disjoint interpretation domain: dI ⊆ ∆D, and ∆D ∩ ∆I = ∅
  • Disjoint datatype properties: P I

D ⊆ ∆I × ∆D

Logical Foundations for the Semantic Web – p. 19/37

slide-75
SLIDE 75

XML Datatypes in OWL

☞ OWL supports XML Schema primitive datatypes ☞ Clean separation between “object” classes and datatypes

  • Disjoint interpretation domain: dI ⊆ ∆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

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SLIDE 76

XML Datatypes in OWL

☞ OWL supports XML Schema primitive datatypes ☞ Clean separation between “object” classes and datatypes

  • Disjoint interpretation domain: dI ⊆ ∆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 dI

1 ∩ . . . ∩ dI n, where di is a (possibly negated) datatype

Logical Foundations for the Semantic Web – p. 19/37

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SLIDE 77

Reasoning with OWL DL

Logical Foundations for the Semantic Web – p. 20/37

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SLIDE 78

Reasoning

Logical Foundations for the Semantic Web – p. 21/37

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SLIDE 79

Reasoning

☞ Why do we want it?

Logical Foundations for the Semantic Web – p. 21/37

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SLIDE 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

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SLIDE 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

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SLIDE 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

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SLIDE 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

slide-84
SLIDE 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

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SLIDE 85

Why Decidable Reasoning?

Logical Foundations for the Semantic Web – p. 22/37

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SLIDE 86

Why Decidable Reasoning?

☞ OWL DL constructors/axioms restricted so reasoning is decidable

Logical Foundations for the Semantic Web – p. 22/37

slide-87
SLIDE 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
  • ntological 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

slide-88
SLIDE 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
  • ntological 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

slide-89
SLIDE 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
  • ntological 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

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SLIDE 90

Basic Inference Problems

Logical Foundations for the Semantic Web – p. 23/37

slide-91
SLIDE 91

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O

Logical Foundations for the Semantic Web – p. 23/37

slide-92
SLIDE 92

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O ☞ Subsumption — structure knowledge, compute taxonomy

  • C ⊑O D ?

CI ⊆ DI in all models I of O

Logical Foundations for the Semantic Web – p. 23/37

slide-93
SLIDE 93

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O ☞ Subsumption — structure knowledge, compute taxonomy

  • C ⊑O D ?

CI ⊆ DI in all models I of O ☞ Equivalence — check if two classes denote same set of instances

  • C ≡O D ?

CI = DI in all models I of O

Logical Foundations for the Semantic Web – p. 23/37

slide-94
SLIDE 94

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O ☞ Subsumption — structure knowledge, compute taxonomy

  • C ⊑O D ?

CI ⊆ DI in all models I of O ☞ Equivalence — check if two classes denote same set of instances

  • C ≡O D ?

CI = DI in all models I of O ☞ Instantiation — check if individual i instance of class C

  • i ∈O C?

i ∈ CI in all models I of O

Logical Foundations for the Semantic Web – p. 23/37

slide-95
SLIDE 95

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O ☞ Subsumption — structure knowledge, compute taxonomy

  • C ⊑O D ?

CI ⊆ DI in all models I of O ☞ Equivalence — check if two classes denote same set of instances

  • C ≡O D ?

CI = DI in all models I of O ☞ Instantiation — check if individual i instance of class C

  • i ∈O C?

i ∈ CI in all models I of O ☞ Retrieval — retrieve set of individuals that instantiate C

  • set of i s.t. i ∈ CI in all models I of O

Logical Foundations for the Semantic Web – p. 23/37

slide-96
SLIDE 96

Basic Inference Problems

☞ Consistency — check if knowledge is meaningful

  • Is O consistent?

There exists some model I of O

  • Is C consistent?

CI = ∅ in some model I of O ☞ Subsumption — structure knowledge, compute taxonomy

  • C ⊑O D ?

CI ⊆ DI in all models I of O ☞ Equivalence — check if two classes denote same set of instances

  • C ≡O D ?

CI = DI in all models I of O ☞ Instantiation — check if individual i instance of class C

  • i ∈O C?

i ∈ CI in all models I of O ☞ Retrieval — retrieve set of individuals that instantiate C

  • set of i s.t. i ∈ CI 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

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SLIDE 97

Reasoning Support for Ontology Design: OilEd

Logical Foundations for the Semantic Web – p. 24/37

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SLIDE 98

Description Logic Reasoning

Logical Foundations for the Semantic Web – p. 25/37

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SLIDE 99

Highly Optimised Implementation

Logical Foundations for the Semantic Web – p. 26/37

slide-100
SLIDE 100

Highly Optimised Implementation

☞ DL reasoning based on tableaux algorithms

Logical Foundations for the Semantic Web – p. 26/37

slide-101
SLIDE 101

Highly Optimised Implementation

☞ DL reasoning based on tableaux algorithms ☞ Naive implementation − → effective non-termination

Logical Foundations for the Semantic Web – p. 26/37

slide-102
SLIDE 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

slide-103
SLIDE 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

slide-104
SLIDE 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

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SLIDE 105

Research and Implementation Challenges

Logical Foundations for the Semantic Web – p. 27/37

slide-106
SLIDE 106

Challenges

Logical Foundations for the Semantic Web – p. 28/37

slide-107
SLIDE 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

slide-108
SLIDE 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

slide-109
SLIDE 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

slide-110
SLIDE 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

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SLIDE 111

Increased Expressive Power: Datatypes

Logical Foundations for the Semantic Web – p. 29/37

slide-112
SLIDE 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

slide-113
SLIDE 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

slide-114
SLIDE 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

slide-115
SLIDE 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

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SLIDE 116

Increased Expressive Power: Nominals

Logical Foundations for the Semantic Web – p. 30/37

slide-117
SLIDE 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

slide-118
SLIDE 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

slide-119
SLIDE 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

slide-120
SLIDE 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

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SLIDE 121

Scalability

Logical Foundations for the Semantic Web – p. 31/37

slide-122
SLIDE 122

Scalability

☞ Reasoning hard — even without nominals (i.e., SHIQ)

Logical Foundations for the Semantic Web – p. 31/37

slide-123
SLIDE 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

slide-124
SLIDE 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

slide-125
SLIDE 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

slide-126
SLIDE 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

slide-127
SLIDE 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

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SLIDE 128

Other Reasoning Tasks

Logical Foundations for the Semantic Web – p. 32/37

slide-129
SLIDE 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

slide-130
SLIDE 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

slide-131
SLIDE 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

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SLIDE 132

Summary

Logical Foundations for the Semantic Web – p. 33/37

slide-133
SLIDE 133

Summary

☞ Semantic Web aims to make web resources accessible to automated processes

Logical Foundations for the Semantic Web – p. 33/37

slide-134
SLIDE 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

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SLIDE 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

slide-136
SLIDE 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

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SLIDE 137

Acknowledgements

Logical Foundations for the Semantic Web – p. 34/37

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SLIDE 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

slide-139
SLIDE 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

slide-140
SLIDE 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

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SLIDE 141

Resources

Slides from this talk http://www.cs.man.ac.uk/~horrocks/Slides/glasgow03.pdf FaCT system (open source) http://www.cs.man.ac.uk/FaCT/ OilEd (open source) http://oiled.man.ac.uk/ DAML+OIL http://www.w3c.org/Submission/2001/12/ W3C Web-Ontology (WebOnt) working group (OWL) http://www.w3.org/2001/sw/WebOnt/ Description Logic Handbook Cambridge University Press

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SLIDE 142

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EDBT 2002, number 2287 in Lecture Notes in Computer Science, pages 2–13. Springer-Verlag, Mar. 2002.

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  • C. Lutz. The Complexity of Reasoning with Concrete Domains. PhD

thesis, Teaching and Research Area for Theoretical Computer Science, RWTH Aachen, 2001.

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SLIDE 143

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