owl – open-world semantik und semantische...
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KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Semantic Web Technologies IISS 2009
27.05.2009OWL – Open-World Semantikund Semantische Erweiterungen
Dr. Sudhir AgarwalDr. Stephan GrimmDr. Peter HaasePD Dr. Pascal HitzlerDenny Vrandecic
KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Übersicht
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions - Overview
Autoepistemic DL
Circumscriptive DL
KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Übersicht
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions - Overview
Autoepistemic DL
Circumscriptive DL
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Open-World Assumption
Characteristics No assumptions about incomplete knowledge
Feauture of logics with classical model-theoretic semantics (e.g. DLs)
ExampleKB = { Professor(John), teaches(John,Ben),
Undergraduate(Ben) }
KB⊭ ∀teaches.Undergraduate(John)
KB ∪ { ≤ 1 teaches (John) }⊨ ∀teaches.Undergraduate(John)
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Closed-World Assumption
Characteristics What cannot be proven is assumed to be wrong
Assumption to have full knowledge about instances
ExampleKB = { Professor(John), teaches(John,Ben),
Undergraduate(Ben) }
KB⊨CWA ∀teaches.Undergraduate(John)
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Example DL knowledge base
Intuitive answers to some queries„Is Mary a graduate student?“ → yes„Is Mary an undergraduate student?“ → don‘t know„Is Mary not a graduate student?“ → no
Open world semantics and Queries
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Answering queries by checking for entailmentKB ⊨ α → yes
KB ⊨ ¬α → no
otherwise → don‘t know
Former exampleKB ⊨ Graduate(mary) yes
KB ⊭ Undergrad(mary) ∧ KB ⊭ ¬Undergrad(mary) don‘t know
Open World Semantics and Queries
KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Übersicht
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions – Overview
Autoepistemic DL
Circumscriptive DL
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OWL Matchmaking for Service Discovery
ServiceProviders
ServiceRequester
Service
ServiceServic
eDomainof Value
WS
realises
WS
realises
Interface
WS
OntologySemanticDescription
describes
annotatesSemanticDescription
describes
annotatesSemanticDescription
describes
SemanticAnnotation
. . .
WS
WS
Matchmaking
Discovery
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Service Descriptions in OWL
ServiceDescription
Sp ≡ Shipping ⊓∀ from.EUCity ⊓∀ to.EUCity ⊓∀ item.(∀ weight.≤100)
abstract service
concrete services
S1
LondonFrankfurt
from to
PackageXitem
50 kg
weight
set of accepted concrete services
. . .
describes
S2
HamburgBerlin
from to
BarrelYitem
100 kg
weight
shipping of items with max. 100 kg between EU cities
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Matching OWL Service Descriptions
Matching Service Descriptions of Requesters and Providersby intersection do they specify common concrete services?
Sr
ServiceRequestor
Spi
ServiceProviders
Sp1
Spn
...
( Sr ⊓ Spi ) is satisfiable ?
DomainOntology
Sr
Spi
DLReasoner
KB
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DL Inference for Matching
Satisfiability of Concept Conjunction
(Sr⊓ Sp) is satisfiable w.r.t. KB
(Sr)I1
(Sp)I1
. . .(Sr)I2
(Sp)I2
• (Sr)I ∩ (Sp)I ≠ Ø in some model of KB• Intuitiuon:
– incomplete knowledge issues can be resolved such that request and offer overlap
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Matching in Logistics Scenario
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CargoContainer TankContainer
City
Container
⊕
item
EUCity
UKCity ContinentalEUCity
EnglishCity GermanCity
Plymouth Hamburg
location(from,to) Vehiclevehicle
⊕
OverlandVehicleOverseaVehicle
Aircraft
Ship Train
GroundVehicle ⊕
⊕
MailDelivery
Transportation
Shipping
PostalMail Integer⊕weight
item
geographic ontology
logistics ontology vehicle ontology
Legend: A Bsubsumption
A Bdisjointness
⊕ D Rproperty domain/range
pCinstantiation
I
1(1,1)2
1 1
1
Transportation ⊑ (∃location.UKCity ⊓ ∃location.ContEUCity ⊓ ∀vehicle.OverseaVehicle)⊔ ∀location.UKCity⊔ ∀location.ContEUCity
Axiom
transportation between UK and continental EU requires oversea vehicle
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Matching in Logistics Scenario
request transportation of a cargo container from London to Hamburg by any vehicle but aircrafts
OWL
Sr ≡ Shipping ⊓∃ from . {London} ⊓∃ to . {Hamburg} ⊓∃ item . CargoContainer ⊓∃ vehicle . ¬Aircraft
R
CargoContainer TankContainer
City
Container
⊕
item
EUCity
UKCity ContinentalEUCity
EnglishCity GermanCity
Plymouth Hamburg
location(from,to) Vehiclevehicle
⊕
OverlandVehicleOverseaVehicle
Aircraft
Ship Train
GroundVehicle ⊕
⊕
MailDelivery
Transportation
Shipping
PostalMail Integer⊕weight
item
geographic ontology
logistics ontology vehicle ontology
Legend: A Bsubsumption
A Bdisjointness
⊕ D Rproperty domain/range
pCinstantiation
I
1(1,1)2
1 1
1
OWL
SpA ≡ Shipping ⊓∀ location . EUCity ⊓∃ item . Container∃ vehicle . Ship
PA
provide shipping of containersbetween EU cities by Ship
OWL
SpB ≡ Shipping ⊓∀ location . EUCity ⊓∃ item . Container ⊓∀ vehicle . ¬Ship
PB
provide shipping of containers between EU cities by any vehicle but ships
transportation between UK and continental EU requires oversea vehicle
London
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Problematic Matching under OWA
USCity I
UKCity I
Requester
Provider B
EUCity I
Provider A
DomainOntology
request
offer A
offer B
Sr ≡ Shipping u ∀from.UKCity
SpA ≡ Shipping u ∀from.EUCitySpB ≡ Shipping u ∀from.USCity
KB = { UKCity ⊑ EUCity , Shipping⊑ ∃from.T
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Problematic Matching under OWA
DomainOntology
DomainOntology
request
offer A
offer B
Sr ≡ Shipping u ∀from.UKCity
SpA ≡ Shipping u ∀from.EUCitySpB ≡ Shipping u ∀from.UKCity
KB = { UKCity ⊑ EUCity , UKCity ⊑ ∃from.T
KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Übersicht
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Some patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions – Overview
Autoepistemic DL
Circumscriptive DL
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negative matchrequires disjointness
Modelling Patterns for Proper Matching
Disjoint Partitioning subsumption + disjointness + coverage
default for taxonomies
OverseaVehicle
AircraftShip⊔⊕
OWL
Sr ⊑ ∃ vehicle . Ship
require shipas vehicle
OWL
Sp ⊑ ∀ vehicle . Aircraft
allow only aircraftas vehicle
R P
OWL
Sr ⊑ ∃ vehicle . OverseaVehicle
use oversea vehicle
OWL
Sp ⊑ ∀ vehicle . ¬Ship ⊓ ¬Aircraft
prohibit aircraft andship as vehicle
R P negative matchrequires coverage
Ship ⊓ Aircraft ⊑ ⊥OverseaVehicle ⊑ Ship ⊔ Aircraft
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Modelling Patterns for Proper Matching
Disjoint Partitioning subsumption + disjointness + coverage
default for taxonomies
Mandatory Properties existential restriction or minimum cardinality
explicit restriction of properties by default,if not explicitly optional
OverseaVehicle
AircraftShip⊔⊕
OWL
Sr ⊑ ∀ vehicle . Ship
allow only ship as vehicle
OWL
Sp ⊑ ∀ vehicle . Aircraft
allow only aircraft as vehicle
R P
VehiclevehicleShipping1..*
enforce use ofsome vehicle
Shipping ⊑ ∃ vehicle .⊤
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Modelling Patterns for Proper Matching
Disjoint Partitioning subsumption + disjointness + coverage
default for taxonomies
Mandatory Properties existential restriction or minimum cardinality
explicit restriction of properties by default,if not explicitly otional
Quantitative Property Closure maximum cardinality restrictions
explicit restriction of properties with natural bound
OverseaVehicle
AircraftShip⊔⊕
VehiclevehicleShipping1..*
VehiclevehicleShipping0..n
OWL
Sr ⊑ ∀ vehicle . Ship
OWL
Sp ⊑ ∀ vehicle . Aircraft
R Pprevent useof two vehicles
Shipping ⊑ ≤ 1 vehicle
KIT – die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH)
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Overview
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions – Overview
Autoepistemic DL
Circumscriptive DL
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Nonstandard Semantics
Uncertainty and Vagueness Probabilistic DL (uncertainty)
– „Any Professor lectures some course with a probability of at least 0.9“Professor ⊑ ∃lectures.Course [0.9;1]
Fuzzy DL (vagueness)
– „Logics is a difficult course to degree 0.8“⟨DifficultCourse(Logics) , 0.8⟩
Paraconsistent Reasoning Reasoning despite inconsistencies in the knowledge base
One Approach: four-valued logics (e.g. ALC4)
Nonmonotonic Reasoning
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Agent collects knowledge in the web
Reasoning allows to derive implicit knowledge
Reasoning is monotonic if the derived knowledge monotonically grows
tKB⊨ {fa,fb}
KB ∪ {fc}⊨ {fa,fb,fc,fd}
KB ∪ {fc,fd}⊨ {fa,fb,fc,fd}
SemanticWeb
AgentKB ∪ {fa,fb} ∪ {fc} ∪ . . .
AgentKB ⊨ {fa, fb, fc, fx, fy, ... }
non-monotonic
KB ∪ {fc,fd,fe}⊨ {fc,fd} . . .
(Non-)Monotonicity of Reasoning
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Defeasible Inference
Inferences in OWL are universally true based on description logics (monotonic)
conclusions only drawn from ensured evidence (OWA)
Defeasible Inferences are based on common-sense conjectures conclusions drawn based on assumptions about what typically holds
retracted in the presence of counter-evidence
Example
Assumption: Pizzas with non-chili toppings only are typically non-spicy
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Information in the web is inherently incomplete NMR provides means to handle situations of incomplete
knowledge
Equip SW agents with common-sense NMR accounts for default assumptions and conjectures
NMR in the Semantic Web
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Autoepistemic Logic belief operator
Default Logic rules with exceptions
Circumscription minimization of abnormality predicates
LP formalisms minimal models and negation-as-failure
∀x : ¬ hasTopping(x,chili) ∧ ¬ B SpicyDish(x) → ¬ SpicyDish(x)
¬ hasTopping(x,chili) : ¬ SpicyDish(x)¬ SpicyDish(x)
∀x : ¬ hasTopping(x,chili) ∧ ¬ min(AbnormalPizza)(x) → ¬ SpicyDish(x)
NonSpicyDish(x) :— ~ SpicyDish(x) ∧ ~ hasTopping(x,chili)
Nonmonotonic Formalisms
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Local Closed-World Reasoning
OWA distinction between negative knowledge and lack of knowledge
– draw conclusions only if there is enough evidence
CWA negative knowledge coincides with lack of knowledge
– draw some (negative) conclusions if there is no counter-evidence
LCWA start from OWA and treat dedicated parts of the domain model under
CWA
Realisation of LCW Reasoning through non-monotinic extensions of DL Autoepistemic DL
Circumscriptive DL
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Overview
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions – Overview
Autoepistemic DL
Circumscriptive DL
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The Autoepistemic Operator K
KC = „known to belong to C“ concept closure by LCW assumption
– assuming full knowledge about instances of C
KCity = „known cities“
{ x : KB ⊨ City(x) }
Syntax of ALCK
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K-Operator - Example
Querying for Cities Knowledge base
Asking for cities in EU or US classically
Asking for cities known to be in EU resp. US
Asking for cities not known to be in EU resp. US
– No classical way of retrieving Tokio
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Model-Theoretic Semantics for K-Operator
interpretation of closed concepts KC as the intersection of extensions over all models
DL interpretation
Models of KB
epistemic interpretation
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Concept Satisfiability with K
USCity I
EUCity I
London I
NewYorkI
Paris I
KUSCity I
KEUCity I
satisfiableunsatisfiable
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Matching with K-Operator
KUSCity IProvider B
KEUCity I
Provider A
Requester
KUKCity I
London I
DomainOntology
request
offer A
offer B
Sr ≡ Shipping u ∀from.KUKCity
SpA ≡ Shipping u ∀from.KEUCitySpB ≡ Shipping u ∀from.KUKCity
KB = { UKCity ⊑ EUCity , UKCity ⊑ ∃from.T , UKCity(London) }
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Overview
Ontology Modelling under OWA Open vs. Closed World Assumption
Application of OWL: Matchmaking
Patterns / best practises in OWA Modelling
Semantic Extensions to OWL Nonmonotonic Extensions – Overview
Autoepistemic DL
Circumscriptive DL
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Circumscription Patterns for DL
DL with circumscription minimising extensions of DL-predicates explicitly
circumscription pattern CP for knowledge base KB
Example:
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Model-Theoretic Semantics for Circumscription
Preference relation <CP on Interpretations
models of a circumscribed KB are minimal w.r.t. <CP
comparing interpretations by their extensions for minimized predicates
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Concept Minimisation
Trade models for conclusions the less models the more conclusion nonmonotonicity: regain models by learning new knowledge
Example
models of KB
. . .
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Matching with Circumscription
DomainOntology
request
offer A
offer B
Sr ≡ Shipping u ∀from.UKCity
SpA ≡ Shipping u ∀from.EUCitySpB ≡ Shipping u ∀from.UKCity
KB = { UKCity ⊑ EUCity , UKCity ⊑ ∃from.T , UKCity(London) }
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Zusammenfassung (Semantik-Block)
OWL – Semantik Interpretationen und Modelle
Logische Konsequenz
Ontologiemodellierung mit OWL Intuition für OWL Modellierungskonstrukte
Modellierung und Inferenz mit Protégé
Typische Patterns / Fallen
Nichtmonotone Erweiterungen Autoepistemischer Operator K
Circumscriptive DL
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