DRAGO: Distributed Reasoning Architecture for the Semantic Web

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DRAGO Distributed Reasoning Architecture for
the Semantic Web

• Andrei Tamilin and Luciano Serafini

Second European Semantic Web Conferece
(ESWC'05) Heraklion, Greece
1 June 2005
Work is supported by
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Talk outline

• Motivation and vision
• Distributed Description Logics (DDL)
• Distributed tableau for reasoning in DDL
• DRAGO reasoning architecture

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Motivation

• Where we start
• Steady ontology proliferation
• Heterogeneity is inevitable
• How to achieve interoperability
• Interoperability bridge
• Semantic mappings
• Reasoning support
• Goal
• Provide reasoning for ontology space (ontologies
  interrelated by mappings)

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Global reasoning vision

• Compile a global ontology
• and reason with existing DL tools
• Benefits
• Stable theory and tools of DL
• Drawbacks
• (i) non-scalability
• (ii) losing language and reasoning specificity
• (iii) losing privacy and autonomy of ontological
  knowledge

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Distributed reasoning vision

• Reasoning through a combination, via mappings, of
  distributed local reasoners
• Benefits
• (i) scalable
• (ii) respects language specificity
• (iii) supports information hiding
• Revisited goal
• Provide a distributed reasoning for ontology space

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Requirements / Our proposals
Requirements / Our proposals

• Formal framework to represent ontology space
• Distributed Description Logics
• Extension of DL
• Define a suitable decision procedure
• Distributed tableau algorithm
• Extension of DL tableau
• Implement the reasoning procedure
• DRAGO reasoning system
• Extension of Pellet OWL DL reasoner

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Distributed Description Logics
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DDL syntax

• DDL is a family of description logics DLii?I
• A bridge rule from i to j is an expression of the
  form
• where X and Y are concepts of DLi and DLj.
• A distributed T-box (DTB) is a pair ?Tii?I,
  Biji?j?I?
• where Bij is a collection of bridge rules from i
  to j

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Bridge graph

• A bridge graph of a DTB

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DDL semantics

• A distributed interpretation (DI) of a DTB
• ?Iii?I, riji?j?I?
• Ii is a local interpretation of Ti on a local
  domain ?Ii
• T1, T2, T3, T4, T5, T6, T7
• I1, I2, I3, I4, I5, I6, I7
• rij is a domain relations from I to j
• rij??Ii x ?Ij

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DDL satisfiability

• DI?Iii?I,riji?j?I? satisfies
  DTB?Tii?I,Biji?j?I?
• DI DTB
• If
• all Ti are satisfied
• all bridge rules Bij are satisfied

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Into-bridge rule satisfiability
rij(xIi) ? YIj
?Ii
?Ij
Y
X
r12(X)
rij
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Onto-bridge rule satisfiability
rij(xIi) ? YIj
r12(X)
?Ii
?Ij
X
rij
Y
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Subsumption propagation in DDL
DTB ?T1, T2, B12?
T1
T2
A
G
isA
H
B
GI2 ? r12(AI1)
r12(BI1) ? HI2
?
Directionality property Knowledge propagates
ONLY along the direction of bridge rules!
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Generalized subsumption propagation

• DTB?Tii?I,Biji?j?I?

Ti
Tj
A
G
B1
H1
H2
B2


Hn
Bn
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Soundness and completeness
Let DTB12 ?T1, T2, B12? be a distributed
T-box Bridge operator encapsulates propagated
axioms
Theorem
DTB12 2X Y T2 ? B12(T1) X Y
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Distributed tableau algorithm
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Basic reasoning service of DDL

• iX is satisfiable with respect to DTB
• if there exist a DI such that DI DTB
• and XIi?0

Restrictions (1) bridge graph is
cycle-free (2) bridge rules connect atomic
concepts (3) no nominals
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Distributed tableau intuition
D
Tab1(X)
D
Tab7(X)
D
Tab2(X)
D
Tab6(X)
D
Tab3(X)
D
D
Tab4(X)
Tab5(X)
DTabi(X) Tabi(X) lazy computation of bridge
operator
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Distributed tableau intuition
Is jD is satisfiable wrt DTB?
DTabj(D)
x L(x) D
Bij
Standard tableau expansion rules
y
L(y) G,

Clash
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Algorithm formalization

• DTabj
• SHIQ-tableau expansion rules
• bridge expansion rule

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Algorithm properties

• Theorem (Termination) For any acyclic distributed
  T-box and for any SHIQ concept X, DTabj(X)
  terminates.
• Theorem (Soundness and completeness) jX is
  satisfiable in distributed T-box if and only if
  DTabj(X) can generate a complete and clash-free
  completion tree.

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DRAGO reasoning architecture
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Distributed reasoning architecture
RP3
RP1
URI3
URI1
URI7
B37
RP2
URI2
B67
URI4
URI6
URI5
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Implementation

• OWL ontologies
• C-OWL semantic mappings
• Distributed Reasoner is an extension to open
  source OWL Reasoner Pellet

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Conclusions

• Overviewed DDL formal framework for representing
  ontologies and mappings
• Described subsumption in DDL
• Introduced sound and complete decision procedure
  for cycle-free DDL
• Implemented a reasoning prototype, DRAGO,
• http//trinity.dit.unitn.it/drago

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Thank You!