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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
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 50011-1040, USA.
{baojie,dcaragea, honavar}@cs.iastate.edu
ASWC, Sept 7, 2006, Beijing, China
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Outline
•
•
•
•
Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Summary & Conclusion
ASWC, Sept 7, 2006, Beijing, China
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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
Modularity
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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
A Modular Semantic Web
Visualising the Semantic Web by Juan C. Dürsteler
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Modular Ontologies
• What is 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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Department of Computer Science
Artificial Intelligence Research Laboratory
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OWL Limitations
• owl:imports: syntactic
modularization
• No localized semantics
owl:imports
– 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
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Syntactic import:
“copy and paste”
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Modular Ontology Approaches
1998
2002
CTXML
DFOL
2003
2004
2005
2006
C-OWL
Role<->Concept
Mapping
DDL
P-DL
OWL
P-OWL
(Planning)
E-Connections
CЄ(SHIF(D))
ASWC, Sept 7, 2006, Beijing, China
Є
CIHN
(SHOIN(D))
s
+
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Department of Computer Science
Artificial Intelligence Research Laboratory
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Requirements
• Semantic soundness
– Reasoning correctness
– Module autonomy
• Needed language features
– Concept relations
– Role relations
–…
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Localized Semantics
Integrated ontology
Modular ontology
Materialized Global Model
Local Models
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Department of Computer Science
Artificial Intelligence Research Laboratory
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Exact Reasoning
Integrated ontology
Modular ontology
Cv D
Cv D
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Artificial Intelligence Research Laboratory
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Directional Semantic Relations
Dv E
Dv E
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Artificial Intelligence Research Laboratory
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Transitive Reusability
Cv D
Dv E
Ev F
Cv F
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Department of Computer Science
Artificial Intelligence Research Laboratory
Decidability
C v D is answerable in
finite steps
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Department of Computer Science
Artificial Intelligence Research Laboratory
Language Features
• Concept Subsumption
• Concept Construction with
Foreign Concepts
• Concept Construction with Role
Restrictions.
• Role Inclusion
• Role Inversion
• Role Construction
• Transitive Role
• Nominal Correspondence
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1:C v 2 : D
1:C u2 : D
9(1 : R):(2 : D )
1:P v 2 : R
1:P = 2:R¡
1:P u2 : R
Trans(1:P), 1:P used in 2
1:x= 2:y
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Outline
•
•
•
•
Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Conclusion
ASWC, Sept 7, 2006, Beijing, China
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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
Local Points of View
agents
agents
The domain
Multiple observers of a domain
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Abstract Modular Ontology (AMO)
Δ1
DL1
Δ2
DL2
2
r13
1
r23
1
r13
DL3
Semantics
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Δ3
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Artificial Intelligence Research Laboratory
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(General) Domain Relations
Δ1
neighbourOf
r13
Δ3
friendOf
r13
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Department of Computer Science
Artificial Intelligence Research Laboratory
Image Domain Relation
Δ1
r13
Δ3
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Department of Computer Science
Artificial Intelligence Research Laboratory
Concept Image
Legm 1
r13
Agent3: "these objects in my mind state
correspond to the concept
Leg1!
Leg from agent 1’s mind state"
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!
: r 13
(L egm 1 )
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Department of Computer Science
Artificial Intelligence Research Laboratory
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Role Image
Δ1
Δ3
P1!
P
3
r13
Agent3: "these object pairs in my mind
state correspond to object pairs
P from agent 1’s mind state"
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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
Possible AMO Expressivity Features
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Department of Computer Science
Artificial Intelligence Research Laboratory
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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:
mj ² C m j µ D m j
mi ² C i à j µ D i Ã
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j
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Artificial Intelligence Research Laboratory
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Semantic Soundness Definitions (2)
• Reusability
C
D
Cm i µ D m i
Ci !
j
µ Di!
j
• Transitive Reusability
Δ1
Δ2
Δ3
(an agent can infer local constraints based on observing
constraints in other agents’ points of view)
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Department of Computer Science
Artificial Intelligence Research Laboratory
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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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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Outline
•
•
•
•
Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressivity Comparison
Conclusion
ASWC, Sept 7, 2006, Beijing, China
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
DDL Semantics
[Borgida and L. Serafini, 2002]
(R.D)I
DI
CI
-
r(CI)= (R .C)I
1:Dog into 2:Animal
DDL : C into D r(CI) DI
-
r(CI)= (R .C)I
CI
DI
C onto D
1:Dog onto 2:Hound
r(CI) DI
implicit domain disjointness
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Artificial Intelligence Research Laboratory
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Subsumption Propagation Problem
Cm1
Dm2
C into D
C into E ?
D into E
Em3
DDL domain relations are not transitively reusable
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Artificial Intelligence Research Laboratory
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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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
DDL: Pros & Cons
• Pros
– 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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Department of Computer Science
Artificial Intelligence Research Laboratory
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E-Connections
• Local domains are
disjoint
• It allows multiple “link”
relations between two
local domains
• Links can be used to
construct local concepts
[Grau, 2005]
owns
Pet
PetOwner
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Department of Computer Science
Artificial Intelligence Research Laboratory
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E-Connections Semantics
-
(R.D)I = r (DI)
(R.D)I=Δ1\r-(Δ2\DI)
R
DI
R
DI
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Department of Computer Science
Artificial Intelligence Research Laboratory
E-Connections: Pros & Cons
• Pros
– 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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Artificial Intelligence Research Laboratory
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P-DL
[Bao et al., 2006]
• Semantic Importing
O1 (General Animal)
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O2 (Pet)
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Artificial Intelligence Research Laboratory
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P-DL Semantics
ΔI
• Domain relation:
individual correspondence
between local domains
• Importing establishes oneto-one domain relations
– “Copied” individuals are
shared
• Domain relations are
compositionally consistent:
r13=r12 r23
O
ΔI
1
r12
2
x’
x
C I2
C I1
r13
r23
x’’
C I3
– Therefore domain relations are
transitively reusable.
ΔI
3
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Department of Computer Science
Artificial Intelligence Research Laboratory
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P-DL Semantics (2)
ΔI
ΔI
1
r12
2
x’
x
C I2
C I1
x
r13
r23
x’’
ΔI
C I3
CI
Global model obtained from local
models by merging shared individuals
3
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Department of Computer Science
Artificial Intelligence Research Laboratory
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
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Department of Computer Science
Artificial Intelligence Research Laboratory
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P-DL: Pros & Cons
• Pros
– 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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Department of Computer Science
Artificial Intelligence Research Laboratory
Summary: Semantic Soundness
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Department of Computer Science
Artificial Intelligence Research Laboratory
Summary: Expressivity
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Outline
•
•
•
•
Desiderata of Modular Ontologies
Abstract Modular Ontology (AMO)
Semantics & Expressvity Comparison
Conclusion
ASWC, Sept 7, 2006, Beijing, China
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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
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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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
Conclusions
• There is still no language or reasoner support for
both general inter-module concept and intermodule 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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Iowa State University
Department of Computer Science
Artificial Intelligence Research Laboratory
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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Department of Computer Science
Artificial Intelligence Research Laboratory
Thanks!
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Department of Computer Science
Artificial Intelligence Research Laboratory
Iowa State University
Semantic Soundness
What are the logical consequences in an AMO?
a
b
r13
y
x
friendOf
friendOf ?
What are the possible cause of semantic
inconsistencies between two agents?
a
b
r13
friendOf
y
x
enemyOf
What is the "objective" way to integrate knowledge of
agents?
a/x
b/y
friendOf
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