Instance Retrieval over Heterogeneous Ontologies

1
Instance Retrieval over Heterogeneous Ontologies
2nd International Workshop on Context
Representation and Reasoning Riva del Garda, Italy

• Andrei Tamilin
• ITC-irst
• Automated Reasoning Systems Division
• tamilin_at_itc.it
• Joint work with Luciano Serafini

29 August, 2006
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Outline

• Motivation, Problem, Requirements
• Distributed Description Logic (DDL) with
  individuals
• Mechanisms of reasoning in DDL
• Distributed instance retrieval
• Implementation

3
Motivation a step back

• Where we are
• Everyone has own ontology
• Ontologies are heterogeneous
• Problem
• How to interoperate?
• How to solve
• Semantic mappings
• Reasoning support
• In particular
• Distributed Description Logics
• Distributed tableaux
• DRAGO reasoning system

4
Motivation a step forth

• Where we are
• Ontologies are populated
• Populations can be done in heterogeneous domains
• Problem
• How to query such a system?

5
A toy example
ODIT
OUniTn
? Retrieve all personal contacts
andrei.tamilin_at_unitn.it
http//dit.unitn.it/tamilin

• In case of which semantic correspondences
• the query propagation should occur?
• How the individuals should be transformed?

andrei.tamilin_at_dit.unitn.it tamilin_at_itc.it
6
Requirements / Our proposals
Requirements / Our proposals

• Formal framework reflecting conceptual and
  individual heterogeneity
• Extend Distributed Description Logics with
  individuals
• Define a querying procedure
• Extend Distributed tableaux algorithm
• Implement the querying procedure
• Extend DRAGO reasoning system

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DDL in a nutshell

• Captures the case of multiple ontologies pairwise
  linked by semantic mappings
• Ontologies correspond to DL knowledge bases
• Mappings correspond to bridge rules and
  individual correspondences

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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 i-th and j-th onto
• logies

iX jY (equivalent-bridge rule)
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(No Transcript)
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DDL syntax cont.

• 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 i-th and j-th
  onto

• An individual correspondence from i to j is an
  expression of the form
• where x and y are individuals of i-th and j-th
  ontologies

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(No Transcript)
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DDL semantics

• Family of local interpretations Ii, one for each
  ontology
• K1, K2, K3, K4, K5, K6, K7
• I1, I2, I3, I4, I5, I6, I7
• Each Ii is on its local domain ?Ii
• Family of domain relations from i to j
• rij? ?Ii x ?Ij
• A distributed interpretation (DI) of a DKB
• ?Iii?I, riji?j?I?

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DDL semantics cont.
DLii?I
Biji?j?I
Tii?I
Aii?I
Ciji?j?I
DKB??Ti ,Ai?i?I, Biji?j?I,Ciji?j?I ?
Jii?I
riji?j?I
DI ?Iii?I, riji?j?I ?
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Satisfiability in DDL

• DI?Iii?I,riji?j?I? satisfies
  DKB?Kii?I,Biji?j?I,Ciji?j?I?
• DI DKB
• If
• all Ki are satisfied (according to standard DLs
  approach), i.e., Ii Ki
• all bridge rules Bij and
• individual correspondences Cij are satisfied

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Bridge rules satisfiability
DI
iX jY
rij(XIi) ? YIj
?Ii
?Ij
rij
Y
X
rij(X)
DI
iX jY
rij(XIi) ? YIj
rij(X)
?Ii
?Ij
rij
X
Y
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Individual correspondence satisfiability
DI
? xIi,yIj ??rij
?Ii
?Ij
rij
y
x
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What are the effects of mappings?
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1) Subsumption propagation
DTB ?T1, T2, B12?
T1
T2
B
H
isA
A
G
GI2 ? r12(AI1)
r12(BI1) ? HI2
?
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2) Assertion propagation
DKB ??T1,A1?, ?T2,A2?, B12,C12?
T1
T2
B
H
isInstanceOf
isInstanceOf
A1
A2
b
h
hI2 r12(bI1)
r12(BI1) ? HI2
?
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2) Assertion propagation - II
DKB ??T1,A1?, ?T2,A2?, B12,C12?
T1
T2
B
H
isInstanceOf
isInstanceOf
f12
A1
A2
f12(b)
b
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Querying in DDL

• Instance retrieval finding all individuals that
  instantiate a given concept
• Both propagation aspects (terminological
  assertional) should be taken into account

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Instance retrieval intuition - I

• retriveInstances(jD)
• Classify j
• Retrieve local instances of D in j ? S1
• Find all subclasses C of D connected by
  into-bridge rules, i.e., iC jD
• Apply assertion propagation pattern to instances
  of iC, i.e., retrieve instances and apply
  tranfromation to them ? S2
• Return S1 U S2

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Instance retrieval intuition - I
D1
Local taxonomy
D3
D2
Local individuals
i2
i1
i3
Retrieve instances of D1 ? i1, i2
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Instance retrieval intuition - II
Bridge rules
Distributed taxonomy (terminological propagation
matters)
D1
D3
D2
Local individuals
i2
i1
i3
Retrieve instances of D1 ? i1, i2, i3
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Instance retrieval intuition - III
Bridge rules
Distributed taxonomy (terminological propagation
matters)
D1
D3
D2
Individual correspondences
Local individuals
i2
i1
i3
Distributed individuals (transformed via
individual correspondences)
i2
Retrieve instances of D1 ? i1, i2, i3, i2
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Implementation

• On top of DRAGO distributed terminological
  reasoner
• DRAGO is a peer-to-peer network of communicating
  reasoners that handle OWL ontologies coupled with
  C-OWL mappings
• For the instance retrieval the possibility to
  specify instance transformations has been added

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Conclusions and Outlook

• We addressed the problem of retrieving
  individuals over heterogeneous ontologies which
  are instantiated in semantically related domains
• We extended DDL framework with individual
  correspondences and discussed how this enables
  the propagation of assertions over ontologies
• Implemented a simple querying prototype on top of
  DRAGO reasoner

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Thank you