Privacy-Preserving Reasoning on the Semantic Web (Poster)
Represent Modular Ontologies with Package-based Description Loigcs -A Short Primer
1. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Represent Modular Ontologies with Package-based
Description Loigcs
-A Short Primer
Jie Bao
The Tetherless World Constellation
Department of Computer Science
Rensselaer Polytechnic Institute
baojie@cs.rpi.edu
http://www.cs.rpi.edu/~baojie
tw.rpi.edu
With contributions by Vasant Honavar, Giora Slutzki, George Voutsadakis,
and Doina Caragea
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 1
2. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
What this talk is about
• Ontologies on the semantic web are distributed
– No a single monolithic ontology
– Multiple, independently developed, ontology
fragments
• P-DL: a framework for representation and
distributed reasoning with description logic
ontology modules
– Local ontologies in the form of DL modules
– Knowledge reuse via semantic importing
– Distributed scalable reasoning tools
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 2
3. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Semantic Technology Research at Iowa State University
• Artificial Intelligence Research Laboratory: The INDUS
project
– Modular ontologies (this talk)
– Federated, Ontology-Based Information Integration
• Handling semantic heterogeneity in data schema and
data content
• Support for statistical queries
• Applications in bioinformatics
– Privacy-Preserving Reasoning
• On graphs and description logics
– Semantic Web Service
• Service Composition
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 3
4. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Modular Ontologies Research Group
Vasant Honavar Jie Bao Giora Slutzki
George Voutsadakis Doina Caragea Harris Lin
(now at KSU)
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 4
6. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Background and Motivation
• Ontologies : semantic web :: Web pages: web
• Autonomous participants
• Network effect
Diet
Pharmacology
Genetics
Physiology
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 6
7. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
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
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 7
8. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
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
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 8
9. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Analogy: Paper Writing in OWL fashion
In this paper, we present
two algorithms A and B to
…
Recent development in
modular ontologies… In this paper, we extend the
copy+paste algorithm A proposed by
(Alice,2001) …
(Alice, 2001)
Recent development in
modular ontologies…
• no partial reuse
• loss of context (Bob, 2007)
July 25,2007, AAAI 2007, Vancouver, British Columbia, Canada . Research supported by NSF IIS-0639230 9/21
10. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Modular ontology languages: Localized Semantics
Major Proposals:
• Distributed description logics (DDL)
• E-connections
• Package-based description logics (P-DL)
Shared features:
• More or less independent ontology modules
• Denotational semantics does not assume the same domain
of interpretation for all ontology modules
Differences:
• What can you import?
• What can you do with the imported names syntactically?
• What is the result semantically?
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 10
11. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Desideratum: Localized Semantics
Animals People
O1 O2
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 11
12. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Desideratum: Directionality of importing relationships
Av B
Av B Dv E
X
Dv E
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 12
13. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Desideratum: Transitive Reuse
v v
Dog Pet Animal
O1 O2 O3
Dog v Animal
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 13
14. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Desideratum: Distributed Inference
Integrated ontology Modular ontology
Dog v Animal Dog v Animal
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 14
15. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Representing Modular Ontology
16. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Package-Based Description Logics (P-DL)
• Motivation:
– Support partial reuse
– Support preservation of context
– Provide “sufficient” modeling ability
– Avoid known problems in existing proposals
• Lack of support for transitive reuse of knowledge
• Non-preservation of concept unsatisfiability
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 16
17. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
P-DL: Semantic Importing
• Each module is called a package
• A package can reuse a subset of names defined in other packages
O1 (Animal) O2 (Pet)
July 25,2007, AAAI 2007, Vancouver, British Columbia, Canada . Research supported by NSF IIS-0639230 17/21
18. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
P-DL: Importing akin to Citation
1:Dog 1:Animal
1:Cat 1:Animal
P1 2:PetOwner 2:owns.1:Dog
P2
July 25,2007, AAAI 2007, Vancouver, British Columbia, Canada . Research supported by NSF IIS-0639230 18/21
19. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
P-DL: Contextualized Negation
Black, White
1 White = Black 2 White = Black ⊔ Red
1 = White 2 = White Black Red
Black
July 25,2007, AAAI 2007, Vancouver, British Columbia, Canada . Research supported by NSF IIS-0639230 19/21
20. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Semantics of P-DL
• Each package has a local ΔI1 ΔI2
interpretation
• Importing establishes domain
r12
x x’
relations
– Partial, One-to-one, Directional 1:DogI2
1:DogI1
• (1:Dog)I2 =r12(1:DogI1)
• It also holds for any complex
concept r13 r23
• Domain relations are compositionally
consistent: r13 = r23 O r12
• More requirements are needed when x’’
importing of roles and nominals is 1:DogI3
allowed.
ΔI3
July 25,2007, AAAI 2007, Vancouver, British Columbia, Canada . Research supported by NSF IIS-0639230 20/21
21. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Semantics of P-DL
• Each package witnesses consequences of its local or
imported) knowledge from its own point of view
|=
importer consequences
importee
|=
importer consequences
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 21
22. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Properties of P-DL Semantics
• Transitive Reusability
(Pj imports Pi)
• The preservation of unsatisfiability
(Pj imports Pi)
• Reasoning Exactness
Let # be a reduction from P-DL to DL[Bao et al. AAAI 2007]
O |= a iff #(O) |= #(a)
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 22/54
23. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Modular ontology languages
Major Proposals:
• Distributed description logics (DDL)
• E-connections
• Package-based description logics (P-DL)
Shared features:
• More or less independent ontology modules
• Denotational semantics does not assume the same domain
of interpretation for all ontology modules
Differences:
• What can you import?
• What can you do with the imported names syntactically?
• What is the result semantically?
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 23
24. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Modular ontology languages: Comparison
DDL E-Connection P-DL
What can you Nothing Concept name, Concept, Role, and
import? Nominal name Nominal name
What can you do (bridge rules Use it in the Free use except that
with the imported between concepts range of a (link) imported roles can
names and between role not be used in role
syntactically? roles) inclusions
What is the result Decidability with Decidability Decidability ,
semantically? BR between Transitive
concepts. Reusability,
Preservation of
Unsatisfiability
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 24
25. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Modular ontology languages: Comparison
1,4 Limited Support 2,3 May be simulated using syntactical encoding
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 25
26. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Reasoning with Modular Ontology
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 26
27. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Tableau Algorithm: Example
goofy
L(goofy)={Dog, Animal,
eats.DogFood }
Dog Animal {eats}
Dog eats.DogFood
foo L(foo)={DogFood }
DogFood hasTM.Brand
DogFood soldBy.Supermarket {hasTM} {soldBy}
If “Dog” is satisfiable? pedigree walmart
L(pedigree)={Brand } L(walmart)={Supermarket}
Completion Tree (Tableau)
Note: the tableau is simplified for demonstration purpose
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 27/54
28. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
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 modular
ontologies without
– (syntactic level) an integrated ontology ?
– (semantic level) a (materialized) global tableau ?
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 28/54
29. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
P-DL 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
P2 Dog ⊑ Animal P1
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 29/54
30. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
P-DL 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)
223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 30/54
32. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Summary
• Ontologies : semantic web :: Web pages: web
• Needed
– A theoretical sound, practically useful, framework for
representation and reasoning with description logic
ontology modules
• Our solution: Package-Based Description Logics (P-DL)
– Support for selective, transitive knowledge reuse via
semantic importing
– Contextualized semantics
– Sound distributed inference from the point of view of a
witness module
– OWL-compatible syntax
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 32
33. Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation
Ongoing Work at ISU
• Developing a distributed reasoner
• More expressive modular ontology language?
– Catch up with OWL 1.1
– Modular ontology under the framework of rule+DL
• OWL syntax extension to support modular ontology
• Modularity in Abox
• Applying ontology modularity in privacy-preserving
reasoning
Talk presented at Semantic Technology Conference, May 23, 2007, San Jose, CA, USA. Research Supported by NSF award IIS 0639230. 33