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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Representing and Reasoning with Modular Ontologies
Jie Bao and Vasant G Honavar
1Artificial Intelligence Research Laboratory, Department of Computer Science,
Iowa State University, Ames, IA 50011-1040, USA.
{baojie, honavar}@cs.iastate.edu
AAAI 2006 Fall Symposium on Semantic Web for Collaborative Knowledge Acquisition (SweCka 2006), October 13-15 2006, Hyatt Crystal City, Arlington, VA, USA
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• The need for modular ontologies
• Representing and reasoning with modularity
• Representing and reasoning with hidden knowledge
• Related work and Conclusions
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Modularity
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
The Need for Modular Ontologies(MO)• Modularity
– A large ontology usually contains components covering sub-domains of the domain in question.
– Ontologies need fine-grained organizational structure to enable partial reuse.
– Ontologies on the semantic web are distributed and connected to each other.
• Selective Knowledge Hiding– Ontology modules are usually autonomous– Security, Privacy, Copyright concerns.
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Modular Ontology Example
Computer Science Dept Ontology Registrar’s Office Ontology
GraduateOK v : 9f ails:CoreCourseGraduateOK v PrelimOKPrelimOK(J ie)
CsCoreCourse(cs511)fails(3304,cs511)SSN(3304,123456789)
Semantic Relations
CsCoreCourse v CoreCourseJ ie= 3304
Hidden Knowledge
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• The need for modular ontologies
• Representing and reasoning with modularity
• Representing and reasoning with hidden knowledge
• Related work and Conclusions
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Package-based Description Logics• A package is an ontology
module that captures a sub-domain;
• Each term has a home package• A package can import terms
from other packages• Package extension is denoted as
P– PC :Package extension with only
concept name importing
– E.g., ALCPC = ALC + PC
General Pet
Wild Livestock
Animal ontology
PetDogPet
DogGeneral
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Package: Example
O1 (General Animal) O2 (Pet)
It uses ALCP, but not ALCPC
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
P-DL Semantics
• Clear and unambiguous semantics is a prerequisite for reasoning
• Semantics: meaning of language forms. • Description Logics (DL) usually has model-theoretical semantics
Syntax Semantics
Man Human
In every world (interpretation), anybody who is a Man is also a Human
{x|Man(x)} {x|Human(x)}
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Interpretations
Interpretation: In every world that conforms to the ontology
Ontology:
Dog I
AnimalI
• For any instance x of Dog, x is also an instance of Animal.
goofyI
• The individual goofy in the world is a Dog.
eatsI
• There is a y in the world, that a Dog x eats y and y is a DogFood
DogFoodI
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Tableau
Dog(goofy)
Animal(goofy)( eats.DogFood)(goofy)
eats(goofy,foo)DogFood(foo)
goofyL(goofy)={Dog, Animal, eats.DogFood }
fooL(foo)={DogFood }
eats
ABox Representation Completion Tree Representation
Note: both representations are simplified for demostration purpose
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Local Interpretations
AnimalI
CarnivoreI
DogI
goofy
fooI
DogI
PetIPetDogI
pluto
eatsI
1
1
1
2
2
2
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DogFoodI 2
AnimalI2
O1 O2
A modular ontology may have multiple (local) interpretations for its modules
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Semantics of Importing
O1 O2importing
AnimalI
CarnivoreI
DogI
fooI
DogI
PetIPetDogI
pluto
eatsI
1
1
1
2
2
2
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DogFoodI 2
AnimalI2
goofy pluto, DogI1 DogI2=
goofy
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Model Projection
x
CI
x
CI1
x’
CI2
x’’CI3
Global model
local models
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Tableau Projection
x1
{A1,B1}
{A2}
{A3,B3}
{B2}x2 x3
x4
x1
{A1}
{A2}
{A3}
x2
x4
x1
{B1}
{B3}
{B2}x3
x4
The (conceptual) global tableau Local Reasoner
for package ALocal Reasonerfor package B
Shared individuals mean partially overlapped local models
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Build Tableau for ALCPC
Tableau Expansion for ALCPC with acyclic importing
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Messages
y y{C?}T1 T2
y y{C}
C(y)T1 T2
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Advantages• Reasoning without the integration of ontology
modules:– (syntactic level) no integrated terminology– (semantic level) no (materialized) global tableau
• Result is always the same as that obtained from an reasoner over the integrated ontology.– Can avoid many reasoning difficulties in other
approaches.
• Supports stronger expressivity: both inter-module subsumption and inter-module role relations
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• The need for modular ontologies
• Representing and reasoning with modularity
• Representing and reasoning with hidden knowledge
• Related work and Conclusions
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Selective Knowledge Hiding
Locally visible:Has date
Globally visible:Has activity
Bob’ schedule ontology
Alice’ schedule ontology
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Scope Limitation Modifier • Defines the visible scope of a term or axiom• SLM of an ontology term or axiom t
– is a boolean function V(t,r), where r is a package – r could access t iff V(t,r) = True.
• Example SLMs– Public (t,r): t is accessible from anywhere
– Private (t,r): t is only available in the home package
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
SLM: exampleA schedule ontology
Hidden: details of the activity
Visible: there is an activity
Kv
Kh
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Concealable 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
Why It Is Possible
• 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 concealed as if it is incomplete knowledge
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Example: Graph Reachability
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
A Concealable Reasoner
Unknown(Hidden knowledge)
Y N
Y N
Unknown(Incomplete knowledge)
Yes
Subsumption query
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Safe Scope Policy
• Hidden knowledge should not be inferred from the visible part of the ontology.– –
• Is it safe enough?– What if an attacker memorizes previous query results?
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
History-safe Scope Policy
a
b
c
d
e
YES
YES
Open problem: history-safe scope policy for expressive P-DL
a
b
c
d
e
• History-safe scope policy for taxonomy ontologies – can be reduced to graph
reachability– hidden knowledge should be
closed: if the hidden part infers x→y, then there is no path in the whole graph from x to y that contains a visible edge (visible knowledge).
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Outline
• The need for modular ontologies
• Representing and reasoning with modularity
• Representing and reasoning with hidden knowledge
• Related work and Conclusions
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Related Work
• Modular ontologies– Distributed Description Logics (DDL) (Borgida &
Serafini 2002) – E-Connections (Grau, Parsia, & Sirin 2004)– Semantic Importing (Pan, Serafini & Zhao 2006)
• Knowledge Hiding– Encryption of ontology (Giereth 2005)– Access control (Godik & Moses 2002)
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
More DetailsP-DL Syntax and Semantics• Bao, J.; Caragea, D.; and Honavar, V. (2006) Towards collaborative
environments for ontology construction and sharing. In International Symposium on Collaborative Technologies and Systems (CTS 2006). IEEE Press. 99–108.
• Bao, J.; Caragea, D.; and Honavar, V.(2006) Modular ontologies - a formal investigation of semantics and expressivity. In R. Mizoguchi, Z. Shi, and F. Giunchiglia (Eds.): Asian Semantic Web Conference 2006, LNCS 4185, 616–631.
• Bao, J.; Caragea, D.; and Honavar, V. (2006) On the semantics of linking and importing in modular ontologies. In I. Cruz et al. (Eds.): ISWC 2006, LNCS 4273. 72–86.
P-DL Reasoning• Bao, J.; Caragea, D.; and Honavar, V. (2006) A tableau-based
federated reasoning algorithm for modular ontologies. Accepted by 2006 IEEE/WIC/ACM International Conference on Web Intelligence (In Press).
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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory
Thanks !