horrocks - reasoning with expressive description logics
Post on 10-Apr-2018
241 Views
Preview:
TRANSCRIPT
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
1/186
Reasoning with Expressive Description Logics
Logical Foundations for the Semantic Web
Ian Horrocks
horrocks@cs.man.ac.uk
University of Manchester
Manchester, UK
Reasoning with Expressive Description Logics p. 1/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
2/186
Talk Outline
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
3/186
Talk Outline
Introduction to Description Logics
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
4/186
Talk Outline
Introduction to Description Logics
The Semantic Web: Killer App for (DL) Reasoning?Web Ontology Languages
DAML+OIL Language
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
5/186
Talk Outline
Introduction to Description Logics
The Semantic Web: Killer App for (DL) Reasoning?Web Ontology Languages
DAML+OIL Language
Reasoning with DAML+OIL
OilEd Demo
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
6/186
Talk Outline
Introduction to Description Logics
The Semantic Web: Killer App for (DL) Reasoning?Web Ontology Languages
DAML+OIL Language
Reasoning with DAML+OIL
OilEd Demo
Description Logic Reasoning
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
7/186
Talk Outline
Introduction to Description Logics
The Semantic Web: Killer App for (DL) Reasoning?Web Ontology Languages
DAML+OIL Language
Reasoning with DAML+OIL
OilEd Demo
Description Logic Reasoning
Research Challenges
Reasoning with Expressive Description Logics p. 2/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
8/186
Introduction to Description Logics
Reasoning with Expressive Description Logics p. 3/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
9/186
What are Description Logics?
Reasoning with Expressive Description Logics p. 4/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
10/186
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
Reasoning with Expressive Description Logics p. 4/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
11/186
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)
Reasoning with Expressive Description Logics p. 4/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
12/186
DL Architecture
Tbox (schema)
Abox (data)
Knowledge Base
InferenceSy
stem
Interface
Man.
= Human Male
Happy-Father.
= Man has-child.Female . . ..
.
.
.
.
.
John : Happy-Father
John, Mary : has-child
Reasoning with Expressive Description Logics p. 5/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
13/186
Short History of Description Logics
Reasoning with Expressive Description Logics p. 6/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
14/186
Short History of Description Logics
Phase 1:
Incomplete systems (Back, Classic, Loom, . . . )
Based on structural algorithms
Reasoning with Expressive Description Logics p. 6/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
15/186
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 for Pspace logics (e.g., Kris, Crack)
Investigation of optimisation techniques
Reasoning with Expressive Description Logics p. 6/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
16/186
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 for Pspace logics (e.g., Kris, Crack)
Investigation of optimisation techniquesPhase 3:
Tableau algorithms for very expressive DLs
Highly optimised tableau systems for ExpTime logics (e.g.,
FaCT, DLP, Racer)
Relationship to modal logic and decidable fragments of FOL
Reasoning with Expressive Description Logics p. 6/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
17/186
Latest Developments
Phase 4:
Reasoning with Expressive Description Logics p. 7/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
18/186
Latest Developments
Phase 4:
Mature implementations
Reasoning with Expressive Description Logics p. 7/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
19/186
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
Reasoning with Expressive Description Logics p. 7/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
20/186
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
Reasoning with Expressive Description Logics p. 7/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
21/186
The Semantic Web
Reasoning with Expressive Description Logics p. 8/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
22/186
The Semantic Web Vision
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
23/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
24/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
25/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
26/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
27/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
28/186
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
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
29/186
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 toautomated processes
To be achieved via semantic markup
Metadata annotations that describe content/function
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
30/186
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 toautomated processes
To be achieved via semantic markup
Metadata annotations that describe content/function
Coincides with Tim Berners-Lees vision of a Semantic Web
Reasoning with Expressive Description Logics p. 9/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
31/186
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 toautomated processes
To be achieved via semantic markup
Metadata annotations that describe content/function
Coincides with Tim Berners-Lees vision of a Semantic Web
Reasoning with Expressive Description Logics p. 9/
O
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
32/186
Ontologies
Reasoning with Expressive Description Logics p. 10/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
33/186
O t l i
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
34/186
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)
Reasoning with Expressive Description Logics p. 10/
O t l i
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
35/186
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
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
36/186
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 (NLlogic)
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
37/186
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 (NLlogic)
Increased formality and regularity facilitates machine understanding
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
38/186
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 (NLlogic)
Increased formality and regularity facilitates machine understanding
Ontologies can be used, e.g.: To facilitate buyerseller communication in e-commerce
In semantic based search
To provide richer service descriptions that can be more flexibly
interpreted by intelligent agents
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
39/186
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 (NLlogic)
Increased formality and regularity facilitates machine understanding
Ontologies can be used, e.g.: To facilitate buyerseller communication in e-commerce
In semantic based search
To provide richer service descriptions that can be more flexibly
interpreted by intelligent agents
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
40/186
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 (NLlogic)
Increased formality and regularity facilitates machine understanding
Ontologies can be used, e.g.: To facilitate buyerseller communication in e-commerce
In semantic based search
To provide richer service descriptions that can be more flexibly
interpreted by intelligent agents
Reasoning with Expressive Description Logics p. 10/
Ontologies
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
41/186
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 (NLlogic)
Increased formality and regularity facilitates machine understanding
Ontologies can be used, e.g.: To facilitate buyerseller communication in e-commerce
In semantic based search
To provide richer service descriptions that can be more flexibly
interpreted by intelligent agents
Reasoning with Expressive Description Logics p. 10/
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
42/186
Web Ontology Languages
Reasoning with Expressive Description Logics p. 11/
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
43/186
Web Ontology Languages
OIL and DAML-ONT web ontology languages developed inEuropean and DARPA projects
Reasoning with Expressive Description Logics p. 11/
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
44/186
Web Ontology Languages
OIL and DAML-ONT web ontology languages developed inEuropean and DARPA projects
Efforts merged to produce DAML+OIL
Reasoning with Expressive Description Logics p. 11/
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
45/186
Web Ontology Languages
OIL and DAML-ONT web ontology languages developed inEuropean and DARPA projects
Efforts merged to produce DAML+OIL
Submitted to W3C as basis for standardisation WebOnt working group developing OWL language standard
Reasoning with Expressive Description Logics p. 11/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
46/186
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
47/186
eb O to ogy a guages
OIL and DAML-ONT web ontology languages developed inEuropean and DARPA projects
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, . . . )
Reasoning with Expressive Description Logics p. 11/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
48/186
Web Ontology Languages
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
49/186
gy g g
OIL and DAML-ONT web ontology languages developed inEuropean and DARPA projects
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 class/property structure of domain (Tbox)
E.g., Person subclass of Animal whose parents are all Persons
Uses RDF for class/property membership assertions (Abox)
E.g., john instance of Person; john,mary instance of parent
Reasoning with Expressive Description Logics p. 11/
Logical Foundations of DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
50/186
g
Reasoning with Expressive Description Logics p. 12/
Logical Foundations of DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
51/186
g
DAML+OIL equivalent to very expressive Description Logic
Reasoning with Expressive Description Logics p. 12/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
52/186
Logical Foundations of DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
53/186
DAML+OIL equivalent to very expressive Description Logic
More precisely, DAML+OIL is (extension of) SHIQ DL
DAML+OIL benefits from many years of DL research
Well defined semantics Formal properties well understood (complexity, decidability)
Known reasoning algorithms
Implemented systems (highly optimised)
Reasoning with Expressive Description Logics p. 12/
Logical Foundations of DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
54/186
DAML+OIL equivalent to very expressive Description Logic
More precisely, DAML+OIL is (extension of) SHIQ DL
DAML+OIL benefits from many years of DL research
Well defined semantics Formal properties well understood (complexity, decidability)
Known reasoning algorithms
Implemented systems (highly optimised) DAML+OIL classes can be names (URIs) or expressions
Various constructors provided for building class expressions
Reasoning with Expressive Description Logics p. 12/
Logical Foundations of DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
55/186
DAML+OIL equivalent to very expressive Description Logic
More precisely, DAML+OIL is (extension of) SHIQ DL
DAML+OIL benefits from many years of DL research
Well defined semantics Formal properties well understood (complexity, decidability)
Known reasoning algorithms
Implemented systems (highly optimised) DAML+OIL classes can be names (URIs) or expressions
Various constructors provided for building class expressions
Expressive power determined by
Kinds of constructor provided
Kinds of axiom allowed
Reasoning with Expressive Description Logics p. 12/
DAML+OIL Class Constructors
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
56/186
Reasoning with Expressive Description Logics p. 13/
DAML+OIL Class Constructors
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
57/186
Constructor DL Syntax Example (Modal Syntax)
intersectionOf C1 . . . Cn Human Male C1 . . . CnunionOf C1 . . . Cn Doctor Lawyer C1 . . . Cn
complementOf C Male C
oneOf {x1 . . . xn} {john,mary} x1 . . . xntoClass P.C hasChild.Doctor [P]C
hasClass P.C hasChild.Lawyer PCmaxCardinalityQ nP.C 1hasChild.Male [P]n+1C
minCardinalityQ nP.C 2hasChild.Lawyer PnC
Reasoning with Expressive Description Logics p. 13/
DAML+OIL Class Constructors
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
58/186
Constructor DL Syntax Example (Modal Syntax)
intersectionOf C1 . . . Cn Human Male C1 . . . CnunionOf C1 . . . Cn Doctor Lawyer C1 . . . Cn
complementOf C Male C
oneOf {x1 . . . xn} {john,mary} x1 . . . xntoClass P.C hasChild.Doctor [P]C
hasClass P.C hasChild.Lawyer PCmaxCardinalityQ nP.C 1hasChild.Male [P]n+1C
minCardinalityQ nP.C 2hasChild.Lawyer PnC
XMLS datatypes as well as classes in P.C and P.C E.g., hasAge.nonNegativeInteger
Reasoning with Expressive Description Logics p. 13/
DAML+OIL Class Constructors
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
59/186
Constructor DL Syntax Example (Modal Syntax)
intersectionOf C1 . . . Cn Human Male C1 . . . CnunionOf C1 . . . Cn Doctor Lawyer C1 . . . Cn
complementOf C Male C
oneOf {x1 . . . xn} {john,mary} x1 . . . xntoClass P.C hasChild.Doctor [P]C
hasClass P.C hasChild.Lawyer PCmaxCardinalityQ nP.C 1hasChild.Male [P]n+1C
minCardinalityQ nP.C 2hasChild.Lawyer PnC
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)
Reasoning with Expressive Description Logics p. 13/
RDFS Syntax
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
60/186
Reasoning with Expressive Description Logics p. 14/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
61/186
Semantics
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
62/186
Semantics defined by interpretations: I = (I, I)
concepts subsets of I
roles binary relations over I (subsets of I I)
individuals elements of I
Reasoning with Expressive Description Logics p. 15/
Semantics
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
63/186
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 = {xIn, . . . , xIn
}
(R.C)I = {x | y.(x, y) RI y CI}
(R.C)I = {x | y.x, y RI y CI}
(nR.C)I = {x | #{y | x, y RI y CI} n} (nR.C)I = {x | #{y | x, y RI y CI} n}
Reasoning with Expressive Description Logics p. 15/
DAML+OIL Axioms
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
64/186
Reasoning with Expressive Description Logics p. 16/
DAML+OIL Axioms
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
65/186
Axiom DL Syntax Example
subClassOf C1 C2 Human Animal Biped
sameClassAs C1 C2 Man Human Male
disjointWith C1 C2 Male FemalesameIndividualAs {x1} {x2} {President_Bush} {G_W_Bush
differentIndividualFrom {x1} {x2} {john} {peter}
subPropertyOf P1 P2 hasDaughter hasChild
samePropertyAs P1 P2 cost price
inverseOf P1 P
2 hasChild hasParent
transitiveProperty P+ P ancestor+ ancestor
uniqueProperty 1P 1hasMotherunambiguousProperty 1P 1hasSSN
Reasoning with Expressive Description Logics p. 16/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
66/186
DAML+OIL Axioms
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
67/186
Axiom DL Syntax Example
subClassOf C1 C2 Human Animal Biped
sameClassAs C1 C2 Man Human Male
disjointWith C1 C2 Male FemalesameIndividualAs {x1} {x2} {President_Bush} {G_W_Bush
differentIndividualFrom {x1} {x2} {john} {peter}
subPropertyOf P1 P2 hasDaughter hasChild
samePropertyAs P1 P2 cost price
inverseOf P1 P
2 hasChild hasParent
transitiveProperty P+ P ancestor+ ancestor
uniqueProperty 1P 1hasMotherunambiguousProperty 1P 1hasSSN
I satisfies C1 C2 iff CI1 CI2 ; satisfies P1 P2 iff P
I1 P
I2
I satisfies ontology O (is a model of O) iff satisfies every axiom in OReasoning with Expressive Description Logics p. 16/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
68/186
XML Datatypes in DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
69/186
DAML+OIL supports XML Schema datatypes
Primitive (e.g., decimal) and derived (e.g., integer sub-range)
Reasoning with Expressive Description Logics p. 17/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
70/186
XML Datatypes in DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
71/186
DAML+OIL supports XML Schema datatypes
Primitive (e.g., decimal) and derived (e.g., integer sub-range)
Clean separation between object classes and datatypes
Disjoint interpretation domain: dI
D, and D I
= Disjoint datatype properties: PI
D I D
Philosophical reasons:
Datatypes structured by built-in predicates Not appropriate to form new datatypes using ontology language
Reasoning with Expressive Description Logics p. 17/
XML Datatypes in DAML+OIL
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
72/186
DAML+OIL supports XML Schema datatypes
Primitive (e.g., decimal) and derived (e.g., integer sub-range)
Clean separation between object classes and datatypes
Disjoint interpretation domain: dI
D, and D I
= Disjoint datatype properties: PI
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
dI1 . . . dIn
, where di is a (possibly negated) datatype
Reasoning with Expressive Description Logics p. 17/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
73/186
Reasoning with DAML+OIL
Reasoning with Expressive Description Logics p. 18/
Reasoning
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
74/186
Reasoning with Expressive Description Logics p. 19/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
75/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
76/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
77/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
78/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
79/186
Reasoning
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
80/186
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 description more general than another w.r.t.
ontology . . .
Reasoning with Expressive Description Logics p. 19/
Basic Inference Problems
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
81/186
Reasoning with Expressive Description Logics p. 20/
Basic Inference Problems
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
82/186
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
Reasoning with Expressive Description Logics p. 20/
Basic Inference Problems
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
83/186
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
CO D ? CI DI in all models I of O
Reasoning with Expressive Description Logics p. 20/
Basic Inference Problems
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
84/186
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
CO D ? CI DI in all models I of O
Equivalence check if two classes denote same set of instances
CO D ? CI
= DI
in all models I of O
Reasoning with Expressive Description Logics p. 20/
Basic Inference Problems
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
85/186
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
CO D ? CI DI in all models I of O
Equivalence check if two classes denote same set of instances
CO 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
Reasoning with Expressive Description Logics p. 20/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
86/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
87/186
Reasoning Support for Ontology Design: OilEd
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
88/186
Reasoning with Expressive Description Logics p. 21/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
89/186
Tableaux Algorithms Basics
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
90/186
Reasoning with Expressive Description Logics p. 23/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
91/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
92/186
Tableaux Algorithms Basics
T bl l ith d t t t ti fi bilit
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
93/186
Tableaux algorithms used to test satisfiability
Try to build tree-like model I of input concept C
Work on concepts in negation normal form
Push in negation using de Morgans, R.C R.Cetc.
Reasoning with Expressive Description Logics p. 23/
Tableaux Algorithms Basics
T bl l ith d t t t satisfiabilit
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
94/186
Tableaux algorithms used to test satisfiability
Try to build tree-like model I of input concept C
Work on concepts in negation normal form
Push in negation using de Morgans, R.C R.Cetc.
Break down C syntactically, inferring constraints on elements of I
Reasoning with Expressive Description Logics p. 23/
Tableaux Algorithms Basics
Tableaux algorithms used to test satisfiability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
95/186
Tableaux algorithms used to test satisfiability
Try to build tree-like model I of input concept C
Work on concepts in negation normal form
Push in negation using de Morgans, R.C R.Cetc.
Break down C syntactically, inferring constraints on elements of I
Decomposition uses tableau rules corresponding to constructors in
logic (e.g., , ) Some rules are nondeterministic (e.g., , )
In practice, this means search
Reasoning with Expressive Description Logics p. 23/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
96/186
Tableaux Algorithms Basics
Tableaux algorithms used to test satisfiability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
97/186
Tableaux algorithms used to test satisfiability
Try to build tree-like model I of input concept C
Work on concepts in negation normal form
Push in negation using de Morgans, R.C R.Cetc.
Break down C syntactically, inferring constraints on elements of I
Decomposition uses tableau rules corresponding to constructors in
logic (e.g., , ) Some rules are nondeterministic (e.g., , )
In practice, this means search
Stop when clash occurs or when no rules are applicable
Blocking (cycle check) used to guarantee termination
Reasoning with Expressive Description Logics p. 23/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
98/186
Tableaux Algorithms Details
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
99/186
Reasoning with Expressive Description Logics p. 24/
Tableaux Algorithms Details
Work on tree T representing model I of concept C
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
100/186
p g p Nodes represent elements of I; labeled with subconcepts of C
Edges represent role-successorships between elements of I
Reasoning with Expressive Description Logics p. 24/
Tableaux Algorithms Details
Work on tree T representing model I of concept C
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
101/186
p g p Nodes represent elements of I; labeled with subconcepts of C
Edges represent role-successorships between elements of I
T initialised with single root node labeled {C}
Reasoning with Expressive Description Logics p. 24/
Tableaux Algorithms Details
Work on tree T representing model I of concept C
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
102/186
p g p Nodes represent elements of I; labeled with subconcepts of C
Edges represent role-successorships between elements of I
T initialised with single root node labeled {C}
Tableau rules repeatedly applied to node labels
Extend labels or extend/modify T structure
Rules can be blocked, e.g, if predecessor has superset label
Nondeterministic rules search possible extensions
Reasoning with Expressive Description Logics p. 24/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
103/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
104/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
105/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
106/186
Tableaux Rules for ALC
! !
'
'
'
x {C1 C2, C1, C2, . . .}x {C1 C2, . . .}
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
107/186
" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
& & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'
( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
x {R.C,.. .} x
{C}
{R.C,.. .}R
y
x
R
y {C, . . .}y
R
x {R.C,.. .}
{. . .}
{R.C,.. .}
for C {C1, C2}
x {C1 C2, C, . . .}
{ }
x {C1 C2, . . .}
{ }
Reasoning with Expressive Description Logics p. 25/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
108/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
109/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
110/186
Tableaux Rule for Transitive Roles
e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e
f
f
f
i
i
i
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
111/186
W WX X
Y Y` `a ab b
c cd d
f
f
f
f
f
f
f
f
f
g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g gh h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h
i
i
i
i
i
i
i
i
i
p
p
p
p
px
R
yy
R
x {R.C,.. .}
{. . .}
{R.C,.. .}
{R.C, . . .}
+
Where R is a transitive role (i.e., (RI)+ = RI)
No longer naturally terminating (e.g., if C= R.)
Need blocking
Simple blocking suffices for ALC plus transitive roles
I.e., do not expand node label if ancestor has superset label More expressive logics (e.g., with inverse roles) need more
sophisticated blocking strategies
Reasoning with Expressive Description Logics p. 26/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
112/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
113/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
114/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
115/186
w
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
116/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
117/186
w
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
L(x) = {C} x
S
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
118/186
w
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
L(x) = {C} x
S
Reasoning with Expressive Description Logics p. 27/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
119/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
120/186
w
L(x) = {C, C D} x
S
L
(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
121/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
122/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
123/186
w
L(x) = {C, C D} x
S
L
(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
124/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
125/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
126/186
w
x y L(y) = {C}L(x) = {C, (C D), D}
RS
L
(w
) = {S.C,
S.
(C
D
),
R.C,
R.
(R.C
)}
Reasoning with Expressive Description Logics p. 27/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
127/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
128/186
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
129/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
RS
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
130/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
zL(z) = {C}
RS
R
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
131/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
zL(z) = {C}
RS
R
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
132/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
zL(z) = {C, R.C, R.(R.C
RS
R
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
133/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
zL(z) = {C, R.C, R.(R.C
RS
R
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
blocked
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
134/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
zL(z) = {C, R.C, R.(R.C
RS
R
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
blocked
Concept is satisfiable: T corresponds to model
Reasoning with Expressive Description Logics p. 27/
Tableaux Algorithm Example
Test satisfiability of S.C S.(C D) R.C R.(R.C)} where R isa transitive role
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
135/186
w
x y L(y) = {C, R.C, R.(R.CL(x) = {C, (C D), D}
RS
L(w) = {S.C, S.(C D), R.C, R.(R.C)}
R
Concept is satisfiable: T corresponds to model
Reasoning with Expressive Description Logics p. 27/
More Advanced Techniques
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
136/186
Reasoning with Expressive Description Logics p. 28/
More Advanced Techniques
Satisfiability w.r.t. a Terminology For each axiom C D T, add C D to every node label
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
137/186
Reasoning with Expressive Description Logics p. 28/
More Advanced Techniques
Satisfiability w.r.t. a Terminology For each axiom C D T, add C D to every node label
More expressive DLs
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
138/186
p
Reasoning with Expressive Description Logics p. 28/
More Advanced Techniques
Satisfiability w.r.t. a Terminology For each axiom C D T, add C D to every node label
More expressive DLs
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
139/186
Basic technique can be extended to deal with
Role inclusion axioms (role hierarchy) Number restrictions Inverse roles Concrete domains and datatypes
Aboxes etc.
Reasoning with Expressive Description Logics p. 28/
More Advanced Techniques
Satisfiability w.r.t. a Terminology For each axiom C D T, add C D to every node label
More expressive DLs
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
140/186
Basic technique can be extended to deal with
Role inclusion axioms (role hierarchy) Number restrictions Inverse roles Concrete domains and datatypes
Aboxes etc.
Extend expansion rules and use more sophisticated blockingstrategy
Reasoning with Expressive Description Logics p. 28/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
141/186
Highly Optimised Implementation
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
142/186
Reasoning with Expressive Description Logics p. 29/
Highly Optimised Implementation
Naive implementation effective non-termination
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
143/186
Reasoning with Expressive Description Logics p. 29/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
144/186
Highly Optimised Implementation
Naive implementation
effective non-termination
Modern systems include MANY optimisations
Optimised classification (compute partial ordering)
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
145/186
Use enhanced traversal (exploit information from previous tests)
Use structural information to select classification order
Reasoning with Expressive Description Logics p. 29/
Highly Optimised Implementation
Naive implementation
effective non-termination
Modern systems include MANY optimisations
Optimised classification (compute partial ordering)
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
146/186
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
. . .
Reasoning with Expressive Description Logics p. 29/
Research Challenges
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
147/186
Research Challenges
Reasoning with Expressive Description Logics p. 30/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
148/186
Challenges
Increased expressive power
Existing DL systems implement (at most) SHIQ
DAML+OIL extends SHIQ with datatypes and nominals
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
149/186
Reasoning with Expressive Description Logics p. 31/
Challenges
Increased expressive power
Existing DL systems implement (at most) SHIQ
DAML+OIL extends SHIQ with datatypes and nominals
Scalability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
150/186
Scalability
Very large KBs Reasoning with (very large numbers of) individuals
Reasoning with Expressive Description Logics p. 31/
Challenges
Increased expressive power
Existing DL systems implement (at most) SHIQ
DAML+OIL extends SHIQ with datatypes and nominals
Scalability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
151/186
Scalability
Very large KBs Reasoning with (very large numbers of) individuals
Other reasoning tasks
Querying Matching
Least common subsumer
. . .
Reasoning with Expressive Description Logics p. 31/
Challenges
Increased expressive power
Existing DL systems implement (at most) SHIQ
DAML+OIL extends SHIQ with datatypes and nominals
Scalability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
152/186
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
Reasoning with Expressive Description Logics p. 31/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
153/186
Increased Expressive Power: Datatypes
DAML+OIL has simple form of datatypes
Unary predicates plus disjoint object-class/datatype domains
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
154/186
Reasoning with Expressive Description Logics p. 32/
Increased Expressive Power: Datatypes
DAML+OIL has simple form of datatypes
Unary predicates plus disjoint object-class/datatype domains
Well understood theoretically
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
155/186
y
Existing work on concrete domains [Baader & Hanschke, Lutz] Algorithm already known for SHOQ(D) [Horrocks & Sattler]
Can use hybrid reasoning (DL reasoner + datatype oracle)
Reasoning with Expressive Description Logics p. 32/
Increased Expressive Power: Datatypes
DAML+OIL has simple form of datatypes
Unary predicates plus disjoint object-class/datatype domains
Well understood theoretically
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
156/186
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
All XMLS datatypes supported (?)
Reasoning with Expressive Description Logics p. 32/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
157/186
Increased Expressive Power: Nominals
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
158/186
Reasoning with Expressive Description Logics p. 33/
Increased Expressive Power: Nominals
DAML+OIL oneOf constructor equivalent to hybrid logic nominals
Extensionally defined concepts, e.g., EU {France, Italy, . . .}
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
159/186
Reasoning with Expressive Description Logics p. 33/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
160/186
Increased Expressive Power: Nominals
DAML+OIL 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)
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
161/186
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 ??
Reasoning with Expressive Description Logics p. 33/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
162/186
Scalability
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
163/186
Reasoning with Expressive Description Logics p. 34/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
164/186
Scalability
Reasoning hard (ExpTime) even without nominals (i.e., SHIQ)
Web ontologies may grow very large
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
165/186
Reasoning with Expressive Description Logics p. 34/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
166/186
Scalability
Reasoning hard (ExpTime) 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
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
167/186
But evidence mostly w.r.t. SHF (no inverse)
Reasoning with Expressive Description Logics p. 34/
Scalability
Reasoning hard (ExpTime) 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
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
168/186
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 Expressive Description Logics p. 34/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
169/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
170/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
171/186
Other Reasoning Tasks
Querying
Retrieval and instantiation wont be sufficient
Minimum requirement will be DB style query language
M l d h t I b t ? t l f
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
172/186
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)
Reasoning with Expressive Description Logics p. 35/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
173/186
Summary
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
174/186
Reasoning with Expressive Description Logics p. 36/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
175/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
176/186
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
177/186
Summary
Description Logics are family of logical KR formalisms
Applications of DLs include DataBases and Semantic Web
Ontologies will provide vocabulary for semantic markup
DAML+OIL web ontology language based on SHIQ DL
Set to become W3C standard (OWL) & already widely adopted
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
178/186
Set to become W3C standard (OWL) & already widely adopted Use of DL provides formal foundations and reasoning support
DL Reasoning based on tableau algorithms
Highly Optimised implementations used in DL systems
Reasoning with Expressive Description Logics p. 36/
Summary
Description Logics are family of logical KR formalisms
Applications of DLs include DataBases and Semantic Web
Ontologies will provide vocabulary for semantic markup
DAML+OIL web ontology language based on SHIQ DL
Set to become W3C standard (OWL) & already widely adopted
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
179/186
Set to become W3C standard (OWL) & already widely adopted Use of DL provides formal foundations and reasoning support
DL Reasoning based on tableau algorithms
Highly Optimised implementations used in DL systems Challenges remain
Reasoning with full DAML+OIL/OWL language
(Convincing) demonstration(s) of scalability
New reasoning tasks
Development of (high quality) tools and infrastructure
Reasoning with Expressive Description Logics p. 36/
Acknowledgements
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
180/186
Reasoning with Expressive Description Logics p. 37/
Acknowledgements
Members of the OIL and DAML+OIL development teams, in
particular Dieter Fensel and Frank van Harmelen (Amsterdam) andPeter Patel-Schneider (Bell Labs)
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
181/186
Reasoning with Expressive Description Logics p. 37/
Acknowledgements
Members of the OIL and DAML+OIL development teams, in
particular Dieter Fensel and Frank van Harmelen (Amsterdam) andPeter Patel-Schneider (Bell Labs)
Franz Baader, Uli Sattler and Stefan Tobies (Dresden)
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
182/186
Reasoning with Expressive Description Logics p. 37/
Acknowledgements
Members of the OIL and DAML+OIL development teams, in
particular Dieter Fensel and Frank van Harmelen (Amsterdam) andPeter Patel-Schneider (Bell Labs)
Franz Baader, Uli Sattler and Stefan Tobies (Dresden)
Members of the Information Management, Medical Informatics andFormal Methods Groups at the University of Manchester
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
183/186
e be s o t e o at o a age e t, ed ca o at cs a dFormal Methods Groups at the University of Manchester
Reasoning with Expressive Description Logics p. 37/
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
184/186
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, pages213. Springer-Verlag, Mar. 2002.
I. Horrocks, P. F. Patel-Schneider, and F. van Harmelen. Reviewing thedesign of DAML+OIL: An ontology language for the semantic web. In Proc.of AAAI 2002, 2002. To appear.
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
185/186
of AAAI 2002, 2002. To appear.
I. Horrocks and S. Tessaris. Querying the semantic web: a formalapproach. In I. Horrocks and J. Hendler, editors, Proc. of the 2002
International Semantic Web Conference (ISWC 2002), number 2342 inLecture Notes in Computer Science. Springer-Verlag, 2002.
C. Lutz. The Complexity of Reasoning with Concrete Domains. PhDthesis, Teaching and Research Area for Theoretical Computer Science,
RWTH Aachen, 2001.
Reasoning with Expressive Description Logics p. 39/
Select Bibliography
I. Horrocks and U. Sattler. Ontology reasoning in the SHOQ(D)
description logic. In B. Nebel, editor, Proc. of IJCAI-01, pages 199204.Morgan Kaufmann, 2001.
F. Baader, S. Brandt, and R. Ksters. Matching under side conditions indescription logics. In B. Nebel, editor, Proc. of IJCAI-01, pages 213218,Seattle, Washington, 2001. Morgan Kaufmann.
-
8/8/2019 Horrocks - Reasoning With Expressive Description Logics
186/186
Seattle, Washington, 2001. Morgan Kaufmann.
A. Borgida, E. Franconi, and I. Horrocks. Explaining ALC subsumption. InProc. of ECAI 2000, pages 209213. IOS Press, 2000.
D. Calvanese, G. De Giacomo, M. Lenzerini, D. Nardi, and R. Rosati. Aprincipled approach to data integration and reconciliation in datawarehousing. In Proceedings of the International Workshop on Designand Management of Data Warehouses (DWDM99), 1999.
Reasoning with Expressive Description Logics p. 40/
top related