Representing and Reasoning with Modular Ontologies (2007)
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223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 1/54
Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Representing and Reasoning with Modular Ontologies
Ph.D. Dissertation Defense
Major advisor: Vasant Honavar
Jie Bao
Artificial Intelligence Research LaboratoryComputer Science Department
Iowa State University Ames, IA USA 50011
Email: [email protected]
July 10, 2007
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 2/54
Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• Introduction– Motivation, desiderata and state-of-the-art of
modular ontologies• Representing Modular Ontology
– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology
– Distributed reasoning in P-DL using tableau algorithm
• Privacy-Preserving Reasoning with Hidden Knowledge
• Collaborative Building of Modular Ontologies
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
From Web to Semantic Web
Ontology: a “PhD Candidate” is a “Student”
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantic Web
Figure courtesy of Tim Berners-Lee, AAAI 2006
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
A Very Very Short DL Primer
• Description Logics (DL): – a knowledge representation
formalism to describe ontologies
– the foundation for web ontology languages, e.g., OWL
• Ontology example– A Dog is an Animal– A Dog eats some DogFood– goofy is a Dog
concept
role
individual
axioms
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
DL Families• ALC
– ⊔ (disjunction): Child = Boy ⊔ Girl– ⊓ (conjunction): Mother = Female ⊓ Parent (existential restriction): Parent = hasChild.Human (value restriction): Human ⊑ hasBrother.Man (negation): Boy ⊑ Girl
• SHOIQ– S=ALC+transitive role : Trans(hasSibling)– H (role hierarchy): hasBrother ⊑ hasSibling– O (nominal, i.e., concept that has single instance): Sun, France– I (inverse role): hasChild = hasParent-
– Q (qualified number restriction): Human ⊑ (=2 hasParent.Human)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
From Web Pages to Ontologies
• Web: Network effect
[Diagram: Joanne Luciano, Predictive Medicine; Drug discovery demo using RDF, Sideran Seamark and Oracle 10g]
• Web pages: web Ontologies : semantic web
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Distributed, Modular Ontologies
Distributed ontology modules• Are produced by autonomous participants
– Are limited in their scope – Represent different points of view– Have (potentially) partially overlapping domains
• Lack global semantics– Need contextualized semantics
• Need selective or partial knowledge reuse • Need distributed inference algorithms without forcing
ontology integration• Should facilitate network effect
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Analogy: Paper Writing
Recent development in modular ontologies…
In this paper, we present two algorithms A and B to …
(Alice, 2001)
(Bob, 2007)
Combining Ontologies
Ontology Modularization
Recent development in modular ontologies…
In this paper, we extend the algorithm A proposed by (Alice,2001) …
Same global domain: modular ontologies Multiple independent participants
Possible (partial) reuseContextualized Semantics
Citation is not copy+paste, hence does not result in a single, combined document
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Modular Ontology Languages: State-of-the-art overview
CЄ (SHOIN(D))
OWL
1998 2002 2003 2004 2005 2006 2007
C-OWLC-OWLCTXML
E-Connections
P-DL
DDLDFOL
DDL with Role Concept
Mapping
CЄ(SHIF(D))IHN+s
DL ALCPC SHOIQP
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Ontology Reuse in OWL: Syntactic Importing
• The OWL primitive intended to support ontology reuse is owl:import
• One can use owl:import to copy-and-paste an ontology into another
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Analogy: Paper Writing in OWL fashion
Recent development in modular ontologies…
In this paper, we present two algorithms A and B to …
(Alice, 2001)
(Bob, 2007)
Combining Ontologies
Ontology Modularization
Recent development in modular ontologies…
In this paper, we extend the algorithm A proposed by (Alice,2001) …
copy+paste
• no partial reuse• loss of context
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
DDL
• Distributed Description Logics (DDL) [Borgida & Serafini, 2002]
– Allows “bridge rules” between concepts across ontology modules
– Bridge rules between roles are similar
• Semantics given by “domain relations”
PetAnimal
Dog
(onto)
(into)
I1Dog
Pet I2Animal I1
r12
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
DDL Semantics: Problem with Bridge Rules
DDL bridge rules are not compositional: • r13 cannot be inferred from r12 and r23
• Knowledge is not transitively reusable!
1:Chicken 2:Birdvv
3:Animal
vvChicken Animal ?vv
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
DDL Semantics: Problem with Bridge Rules
1: Fly
1: Bird
2:Penguin
Bird Penguin
~Fly Penguin
DDL bridge rules do not preserve concept unsatisfiability across modules
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
E-Connections
• E-connections allow multiple links between two local domains [Grau, 2005]
• Links can be used to construct local concepts
PetOwner
Pet
PetOwner
Petowns
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
E-Connections [Grau, 2005]
• A concept cannot be declared in an ontology as a subclass of a foreign concept;
• A property cannot be declared as sub-relation of a foreign property;
• An individual cannot be declared as an instance of a foreign concept;
• A pair of individuals cannot instantiate a foreign property;
• The use of E-Connections semantics with owl:imports syntax leads to several difficulties
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Section summary
• OWL – No localized or contextualized semantics, – No partial reuse.
• DDL – Allows inter-module concept inclusions (but not inter-module roles)– In general, does not support transitive knowledge reuse or
preservation of unsatisfiability
• E-Connections– Allows inter-module roles (but not concept inclusions)– Presents strong expressivity limitation
• P-DL aims to overcome these limitations
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• Introduction– Motivation, desiderata and state-of-the-art of
modular ontologies• Representing Modular Ontology
– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology
– Distributed reasoning in P-DL using tableau algorithm
• Privacy-Preserving Reasoning with Hidden Knowledge
• Collaborative Building of Modular Ontologies
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Package-Based Description Logics (P-DL)
• P-DL support semantic importing
O1 (Animal) O2 (Pet)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Syntax of P-DL
• Package and Importing
Pii
Male, Female
Pj
• Contextualized negation– There is no global negation, but only contextualized negation for
each package– Example:
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantics of P-DL
• Localized Semantics
PeopleAnimals
O1 O2
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantics of P-DL
• Semantic importing akin to “citation”
• Package 2 cites package 1 for the definition of ‘1:Dog’– Interpretation of ‘1:Dog’ is the same on the shared
portions of the local domains of packages 1 and 2– The two packages need not agree on the interpretation of
other unrelated concepts (e.g., Cats)
• P-DL supports selective knowledge reuse
P1 P2
1:Dog 2:PetDog 1:Dogvv
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantics of P-DL
• Domain relations are composi-tionally consistent
r13=r23 O
r12
• More requirements are needed when importing of roles and nominals are allowed.
x x’
ΔI1 ΔI2
1:DogI11:DogI2
r12
ΔI3
r13 r23
x’’1:DogI3
• Importing establishes one-to-one domain relations
• (1:Dog)I2 =r12(1:DogI1)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantics of P-DL
²
²importee
importer consequences
• Each package witnesses consequences from its own point of view (using its local and imported knowledge)
importer consequences
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Properties of P-DL
• Exact Reasoning: – extending an ontology in the classic way and in the
modular way will ensure same inferential results.
vv
Integrated ontology Modular ontology
Dog Animal vvDog Animal
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Properties of P-DL
• Directional Relation
vvD EvvA B
vvA B
vvD EX
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Properties of P-DL
• The preservation of unsatisfiability
• Transitive Reusability
Dogvv
vvDog Animal
Pet Animalvv
P1 P2 P3
(Pj imports Pi)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
P-DL Families
• P – package extension with importing of any type of names (concept, role and nominal)– P- - acyclic importing: if P (directly or indirectly) imports
Q, then Q cannot (directly or indirectly) import P– PC – importing of concept names only
• Examples: – ALCPC
[Bao et al,CRR 2006] – ALCPC
-[Bao et al,WI 2006] – SHIQP[Bao et al,ISWC 2007]
– SHOIQP[Bao et al,AAAI 2007]
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
DDL and E-connections vs P-DL• P-DL can simulate
– DDL with bridge rules using subsumption between • imported concepts and local concepts • imported roles and local roles
– (one-way binary) E-Connections using roles that relate a local concept with an imported concept
• DDL, E-Connection or their combination cannot simulate P-DL– One-to-one domain relations cannot be simulated by
DDL or E-Connections– P-DL, unlike DDL and E-connections, supports transitive
reuse of knowledge
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Section Summary
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Section Summary
(Details in dissertation Table 4.4)
1,4 Limited Support 2,3 May be simulated using syntactical encoding
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• Introduction– Motivation, desiderata and state-of-the-art of
modular ontologies• Representing Modular Ontology
– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology
– Distributed reasoning in P-DL using tableau algorithm
• Privacy-Preserving Reasoning with Hidden Knowledge
• Collaborative Building of Modular Ontologies
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Tableau Algorithm
• Description Logics usually uses the Tableau Algorithm [Baader & Sattler 2001] for reasoning tasks.
• A tableau is a representation of a model– A model for an ontology represents a world which satisfies
assertions in the ontology.
– Decidable DLs typically have tree models [Vardi,1996]
• Tableau algorithms try to check concept satisfiability w.r.t. a KB by constructing a tree that is the model of the concept and the KB
Ontology: Man ⊑ Human Model:Man
Human
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Tableau Algorithm: Example
goofyL(goofy)={Dog, Animal, eats.DogFood }
foo L(foo)={DogFood }
{eats}
Completion Tree (Tableau)
Note: the tableau is simplified for demonstration purpose
Dog Animal⊑Dog ⊑ eats.DogFood
DogFood ⊑ hasTM.Brand
DogFood ⊑ soldBy.Supermarket
If “Dog” is satisfiable? pedigreeL(pedigree)={Brand }
{hasTM}
walmartL(walmart)={Supermarket}
{soldBy}
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Reasoning for Modular Ontology
• Major Considerations: – Avoid integrating ontology modules– Minimize local memory cost– Respect module autonomy, e.g., privacy
• Question: can we reason with P-DL without – (syntactic level) an integrated ontology ?– (semantic level) a (materialized) global tableau ?
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Federated Reasoning
• There are multiple local reasoners, one for each package– Each local reasoner only knows and uses local knowledge – A reasoner may ask another reasoner (by messages) about the
meaning of imported names .
What is a “Dog”?
“Dog” is a type of “Animal”
Dog
Dog ⊑ AnimalP2 P1
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Distributed Tableau
(Virtual) combined tableau for the (conceptual) integrated ontology from all packages
Distributed tableau • each local tableau is a fragment of the virtual global tree• thus, each local tableau is a forest• a node may be “shared” among local tableaux (indicated by domain relations)
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Construction of Distributed Tableau
• Developed algorithms ALCPC, ALCPC-, SHIQP
• Basics of the algorithm: – Intra-tableau expansion rules: e.g., if C⊓D L(x), then
{C,D} <= L(x)– Inter-tableau expansion rules: e.g., if C L(x), C
is defined in another package P, then send a reporting message r(x,C) to the reasoner of P.
– Termination: is guaranteed using suitable blocking rules.
– The algorithm is proven to be sound and complete.
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Example
• Check if PetDog is satisfiable as witnessed by O2
O1 (Animal) O2 (Pet)
{ other axioms … }
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Example• Each local reasoner maintains a local tableau. • Connections between local tableaux is created by a set of messages.
x1
{PetDog}
Local Reasoner 2(for package Pet)
R12(x1,Dog)
R12(x1,Animal)
{Animal}{DogFood}
x2
{eats}
R12(x2,Animal)
{eats}x2’
x1
{Dog,Carnirvore,Animal}’
Local Reasoner 1(for package Animal)
R12(<x1,x2>,eats)Expansion for other axioms in PAnimal
Note: the tableau is simplified for demonstration purpose
PetDog Dog⊑PetDog ⊑ eats.DogFood
Dog Carnivore⊑Carnivore Animal⊑
Carnivore ⊑ eats.Animal
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Section Summary• Distributed reasoning algorithms have been
designed for P-DL:– Federated: no integration of all ontology modules is
required;– Peer-to-peer: each local reasoner only requires local
knowledge;– Parallel: subtasks in reasoning can be explored
concurrently by multiple reasoners;– Message-based: the overall reasoning process is
enabled by messages exchanged between local reasoners.
• Algorithms available for ALCPC-, ALCPC, SHIQP
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• Introduction– Motivation, desiderata and state-of-the-art of
modular ontologies• Representing Modular Ontology
– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology
– Distributed reasoning in P-DL using tableau algorithm
• Privacy-Preserving Reasoning with Hidden Knowledge
• Collaborative Building of Modular Ontologies
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Partially Hidden Knowledge
Locally visible:Has date
Globally visible:Has activity
Bob’ schedule ontology
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Privacy-Preserving Reasoning
• A reasoner should not expose hidden knowledge
• However, such hidden knowledge may still be (indirectly) used in safe queries.
QueriesYes
Unknown
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Privacy-Preserving Reasoning
• Practical algorithms designed for– Hierarchical ontologies. (e.g. biological ontologies)– Description Logics (e.g. SHIQ)– Open for P-DL
• Applications– Privacy protection in medical information system– Secure web service – Query answering in p2p applications– …
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• Introduction– Motivation, desiderata and state-of-the-art of
modular ontologies• Representing Modular Ontology
– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology
– Distributed reasoning in P-DL using tableau algorithm
• Privacy-Preserving Reasoning with Hidden Knowledge
• Collaborative Building of Modular Ontologies
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Collaborative Ontology Building
Ontology modularity facilitates collaborative building• Each package can be independently developed• Different curators can concurrently edit the ontology on
different packages• Ontology can be only partially loaded• Unwanted interactions are minimized by limiting term and
axiom visibility
Prototypes• COB-Editor [Bao et al, BIDM 2006]
• WikiOnt [Bao & Honavar, EON 2004]
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Iowa State University Department of Computer ScienceArtificial Intelligence Research LaboratoryThe COB Editor
Pig Package
Cattle Package
Chicken Package
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
WikiOnt 2 (Ongoing)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Contributions
Figure courtesy of Tim Berners-Lee, AAAI 2006
• Formal investigation on requirements of modular ontologies • The specification of Package-based Description Logics (P-DL) which overcomes many semantic problems and expressivity limitations of existing approaches
Chapter 3,4
Distributed reasoning algorithms for modular ontologies• federated, no integration required• peer-to-peer• parallel reasoning, scalable for large ontologies• message-based
Chapter 5Privacy-preserving inference with hidden knowledge• general framework• practical algorithms for hierarchies and DL
Chapter 6
Collaborative Building of Modular Ontologies• Software prototypes: WikiOnt and COB-Editor
Chapter 7
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Results
• Presentations– Academic Conferences: AAAI-07, RR-07 (Web Reasoning and Rule System), WI-
06 (Web Intelligence), ISWC-06(International Semantic Web Conference), ASWC-06 (Asian Semantic Web Conference, Best Paper)
– Industrial Conferences: SemGrail (Microsoft) 2007, Semantic Technology Conference 2007
• Funding– Results of this study formed the basis of proposals on modular
ontologies that were funded by NSF (IIS-0639230) and ISU CIAG (Center for Integrated Animal Genomics)
• Community Involvement– 4 workshop organization efforts on related topics (SWeCka
2006,2007, Modular Ontologies (WoMo) 2006,2007)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Future Work
• Modular Ontology Framework– Understanding modular ontology using DL + rules; RDF
modularity
• Extending P-DL– ABox, Query, Syntax, Interfaces and Views
• Distributed Reasoning– Implementation, SHOIQ reasoning, optimization
• Privacy-Preserving Reasoning – P-DL, RDF, medical ontologies
• Applications– WikiOnt2, Semantic Data Integration (INDUS project)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Acknowledgement• Major advisor: Vasant Honavar• Modular Ontology Group: Giora Slutzki, Doina Caragea, George
Voutsadakis• COB-Editor Group: LaRon Hughes, Zhiliang Hu, Peter Wong, James
Reecy, • Medical Ontology Building: Yu Cao, Wallapak Tavanapong, • INDUS Group: Doina Caragea, Jyotishman Pathak, Neeraj Koul, Jaime
Reinoso-Castillo• Discussion: Gary Leavens, Dae-ki Kang, Rafael-Armando Jordan,
Adrian Silvescu, Kewei Tu, Jun Zhang, Feihong Wu, Changhui Yan, Hua Pei, Hua Ming, and other members of the AI Lab.
• Non-ISU collaboration: Jeff Pan, Yimin Wang, Luciano Serafini, Andrei Tamilin, Zhengxiang Pan and Jing Mei.
• Research supported by funding from National Science Foundation (IIS 0219699,0639230),National Institutes of Health (GM 066387), and Center for Integrated Animal Genomics, Iowa State University, and grants from USDA NAGRP Bioinformatics Coordination Project.
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Backup
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Why not owl:imports?
• owl:imports does not preserve semantics of imported concepts or roles as defined in the source ontology (loss of
context) • owl:imports does not support partial reuse
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Hidden Knowledge vs. Incomplete Knowledge
• Open World Assumption (OWA)
• An ontology may have only incomplete knowledge about a domain– KB: Dog is Animal– Query: if Cat is Animal ? Unknown
if Cat is not Animal ? Also unknown
• Hidden knowledge can be protected as if it is incomplete knowledge
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Privacy-Preserving Reasoner• A privacy-preserving reasoner should be
– History independent: it answers in the same way regardless the history of past queries
– Honest: it never “lies”
– History safe: answers and visible knowledge combined cannot be used to infer hidden knowledge
q R A {Y,N,U}
KB
q R
KBfalse
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Example: Hierarchies
unknownYES
a
b
c
d
OWA: there may be another path that connects a and d but is not included in the visible graph (thus a→d does not imply b→c )
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Example: Hierarchies
a
b
c
d
e
Y
Y
a
b
c
d
e
“unsafe” graph “safe” graph
Reasoning Strategy:
Safety Scope:
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Privacy-preserving reasoning with DL
• Critical visible knowledge (Kvc) contains existing knowledge about Sig(Kh)• If we can ensure Kv + QY will not give extra information about Sig(Kh), other than
that Kvc, then the reasoner is safe• Conservative Extension[Grau etal, 2006]: α of Sig(Kvc), Kvc|= α iff Kv+QY |= α• Practical algorithm exists for SHIQ (using “local ontologies”[Grau et al, IJCAI 2007])
Hidden knowledge (Kh)
Visible knowledge (Kv)
Critical visible knowledge (Kvc)
C ⊑ D
C ⊑ R.D
G ⊑ H
axioms that contain names in Sig(Kh)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Privacy-preserving reasoning with P-DL
• Still an open problem
• Key issue: message safety
r(x,Dog), r(x,Animal)
Dog ⊑ Animal P1
Dog ⊑ Animal inferred!
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Section Summary
• Selective knowledge reuse using partially hidden knowledge
• Privacy-preserving reasoning based on the open world assumption
• Practical algorithms available for hierarchies and DL SHIQ.
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
WikiOnt
• A web browser based ontology editor
• Using Wiki script to store ontologies
• With features to support team work, version control, page locking, and navigation.