Represent Modular Ontologies with Package-based Description Logics

Rensselaer Polytechnic Institute Department of Computer Science
The Tetherless World Constellation

Represent Modular Ontologies with Package-based
Description Loigcs
-A Short Primer

Jie Bao

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


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


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



Modular Ontologies Research Group

Vasant Honavar Jie Bao Giora Slutzki

George Voutsadakis Doina Caragea Harris Lin
(now at KSU)



Motivation and Background


Background and Motivation
• Ontologies : semantic web :: Web pages: web
• Autonomous participants
• Network effect

Diet

Pharmacology

Genetics

Physiology



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



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



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


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?



Desideratum: Localized Semantics

Animals People

O1 O2



Desideratum: Directionality of importing relationships

Av B

Av B Dv E

X
Dv E



Desideratum: Transitive Reuse

v v
Dog Pet Animal

O1 O2 O3

Dog v Animal



Desideratum: Distributed Inference

Integrated ontology Modular ontology

Dog v Animal Dog v Animal



Representing Modular Ontology


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



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)



P-DL: Importing akin to Citation

1:Dog 1:Animal
1:Cat 1:Animal

P1 2:PetOwner 2:owns.1:Dog

P2



P-DL: Contextualized Negation

Black, White

1 White = Black 2 White = Black ⊔ Red

1 = White 2 = White Black Red
 Black 



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


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


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


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?



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



Modular ontology languages: Comparison

1,4 Limited Support 2,3 May be simulated using syntactical encoding


Reasoning with Modular Ontology



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


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 ?



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



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)



Summary


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



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


Represent Modular Ontologies with Package-based Description Logics

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Ähnlich wie Represent Modular Ontologies with Package-based Description Logics

Ähnlich wie Represent Modular Ontologies with Package-based Description Logics (20)

Mehr von Jie Bao

Mehr von Jie Bao (20)

Represent Modular Ontologies with Package-based Description Logics