1. Modular Ontologies - A Formal Investigation of Semantics and Expressivity
Jie Bao, Doina Caragea and Vasant G Honavar
Artificial Intelligence Research Laboratory,
Department of Computer Science,
Iowa State University,
Ames, IA , USA.
{baojie,dcaragea,
ASWC, Sept 7, 2006, Beijing, China

2. Outline Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Summary & Conclusion
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3. Modularity
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4. A Modular Semantic Web
Visualising the Semantic Web by Juan C. Dürsteler
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5. Modular Ontologies What is modular ontology? Why modular ontology ?
An ontology that is composed by a set of smaller (semantically) connected component ontologies
Why modular ontology ?
Collaborative Ontology Building
Selective Ontology Reuse
Selective Knowledge Hiding
Distributed Data Management
Large Ontology Storage and Reasoning
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6. OWL Limitations owl:imports: syntactic modularization
No localized semantics
Reasoning is possible only with the integrated ontology
No partial reuse
Reuse all or nothing
E.g. OpenCyc OWL file needs 9 hours to load into Protege
owl:imports
Syntactic import:
“copy and paste”
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7. Modular Ontology Approaches
CTXML
C-OWL
DFOL
DDL
Role<->Concept
Mapping
P-DL
OWL
P-OWL
(Planning)
E-Connections
CЄ(SHIF(D))
CЄ (SHOIN(D))
IHN+s
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8. Requirements Semantic soundness Needed language features
Reasoning correctness
Module autonomy
Needed language features
Concept relations
Role relations …
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9. Localized Semantics Integrated ontology Modular ontology Local Models
Materialized Global Model
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10. Exact Reasoning Integrated ontology Modular ontology C D C D
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11. Directional Semantic Relations
D E
D E
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12. Transitive Reusability
C D
D E
E F
C F
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13. Decidability C D is answerable in finite steps
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14. Language Features Concept Subsumption
Concept Construction with Foreign Concepts
Concept Construction with Role Restrictions.
Role Inclusion
Role Inversion
Role Construction
Transitive Role
Nominal Correspondence
Trans(1:P), 1:P used in 2
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15. Outline Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Conclusion
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16. Multiple observers of a domain
Local Points of View
agents
agents
The domain
Multiple observers of a domain
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17. Abstract Modular Ontology (AMO)Δ 1 Δ 2
DL1
DL2
r13 2
r23 1
r13 1
DL3 Δ 3
Semantics
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18. (General) Domain Relations
neighbourOf Δ 1 Δ 3
r13
friendOf
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19. Image Domain Relation Δ r13 Δ 1 3
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20. Concept Image
r13
Agent3: "these objects in my mind state correspond to the concept
Leg from agent 1’s mind state"
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21. Role Image Δ 1 Δ 3 P
r13
Agent3: "these object pairs in my mind state correspond to object pairs
P from agent 1’s mind state"
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22. Possible AMO Expressivity Features
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23. Semantic Soundness Definitions
Localized Semantics: local domains {Δi} are not necessarily identical
Decidability (of concept C w.r.t AMO O): there is an algorithm to decide in finite steps whether there is a common model <{mi}, {rij}> of C and O.
Directional Semantic Relations:
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24. Semantic Soundness Definitions (2)
Reusability C D
Transitive Reusability Δ 1 Δ 2 Δ 3
(an agent can infer local constraints based on observing
constraints in other agents’ points of view)
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25. Semantic Soundness Definitions (3)
Exact Reasoning
Compatible beliefs of agents may be combined.
Local models M can be merged into an integrated model M' s.t.
Physical
World
Local
Models
Integrated
Model
(consensus)
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26. Outline Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Conclusion
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27. DDL Semantics 1:Dog into 2:Animal 1:Dog onto 2:Hound
[Borgida and L. Serafini, 2002]
1:Dog into 2:Animal
citation
1:Dog onto 2:Hound
implicit domain disjointness
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28. Subsumption Propagation Problem
Cm1
C into D
Dm2
C into E ?
D into E
Em3
DDL domain relations are not transitively reusable
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29. Inter-module Unsatisfiability Problem
Flym1
Bird onto Penguin
Penguinm2
Birdm1
~Fly onto Penguin
DDL allows arbitrary domain relations: loss of reasoning exactness
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30. DDL: Pros & Cons Pros Cons Localized Semantics Directional Relation
Decidability transfer
Cons
No support for role relations
No general module transitive reusability
No general reasoning exactness
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31. E-Connections Local domains are disjoint
[Grau, 2005]
Local domains are disjoint
It allows multiple “link” relations between two local domains
Links can be used to construct local concepts
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32. E-Connections SemanticsR
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33. E-Connections: Pros & Cons
Localized Semantics
Decidability Transfer
Exact Reasoning (without generalized link)
Cons
Very limited transitive reusability
No support for inter-module concept subsumption
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34. P-DL Semantic Importing [Bao et al., 2006]
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35. P-DL Semantics x x’
ΔI1
ΔI2
CI1
CI2
Domain relation: individual correspondence between local domains
r12
ΔI3
r13
r23
x’’
CI3
Importing establishes one-to-one domain relations
“Copied” individuals are shared
Domain relations are compositionally consistent: r13=r12 O r23
Therefore domain relations are transitively reusable. 35

36. P-DL Semantics (2) r12 r13 r23 ΔI1 ΔI2 ΔI3 CI2 CI1 CI CI3 x x’ x x’’
Global model obtained from local
models by merging shared individuals
ΔI3 36

37. Partially Overlapping Domains
Ensure unambiguous communication between local models
satisfiability transfer
transitive reusability
Overlapped domains represent the consensus of agents
Non-sharing domains are still kept local. x CI 37

38. P-DL: Pros & Cons Pros Cons Localized Semantics Exact Reasoning
Stronger Expressivity
Transitive Reusability
Cons
Directional Semantic Relation does not always hold
Decidable only if all modules use the same decidable DL (e.g. OWL).
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39. Summary: Semantic Soundness
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40. Summary: Expressivity
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41. Outline Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressvity Comparison
Conclusion
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42. Summary
We discussed
Semantic soundness and expressvity requirements for modular ontologies
Comparsion of DDL, E-Connections and P-DL under the AMO framework
Analysis of several semantic difficulties and expressivity limitations of existing approaches
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43. Conclusions
There is still no language or reasoner support for both general inter-module concept and inter-module role correspondence
Local domain disjointedness assumption of DDL and E-Connections may be partially relaxed.
to improve expressivity
to ensure reasoning exactness and transitivity reusability.
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44. Open Problems A consensus on expressive modular ontology language
A OWL-compatible syntax for modular ontologies
A reasoner that supports the expressive modular ontology language
Pellet and DRAGO are complementary to each other
To be discussed at the Modular Ontology Workshop (WoMo) at ISWC 2006 , Athens, Georgia, USA, Nov 2006.
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45. Thanks!
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46. Semantic Soundness
What are the logical consequences in an AMO? What are the possible cause of semantic inconsistencies between two agents? What is the "objective" way to integrate knowledge of agents?
r13 y a b x
friendOf
friendOf ?
r13 y a b x
friendOf
enemyOf
a/x
b/y
friendOf
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