A Proposal for Optimizing Internetwork Matching of Ontologies

Abstract

Presentation for the article (same name) at Ontology Matching Conference (OM 2018) collocated with International Web Semantic Conference (ISWC 2018)

Full text

A Proposal for Optimizing Internetwork
Matching of Ontologies
Fabio Santos, Fernanda Baião, Kate Revoredo
Graduate Program in Informatics, UNIRIO, Brazil

Data Integration a nd systems interoperability problems
S evera l ontology artifacts for the same universe of
dis course.
Differences in severa l perspectives : terminolog ica l,
structural, sema ntic, …
2
[Source: www.webontology.org]
Thing
Car Locomotive
Big car
Horsepower
Object
Wheele d
Train
CylinderBus
Eng ine
Ontology O1
ha s
Automobile
Horsepower
ha s ha s
Autobus
Ontology O2
ha s
ha s
O1= <C, R, P, I, A>O2= <C’, R’, P,’ I,’ A’>
Introduction

Introduction
Given 2 ontologies, O1and O2, Ontology Matching Proces s
searches for ma pping s between their entities <e, e´, r, n>
3
Thing
Car Locomotive
Big ca r
Horsepower
Object
Wheeled
Train
CylinderBus
Engine
Ontology O1
ha s
Automobile
Horsepower
ha s ha s
Autobus
0.8
0.9
0.7
1.0
Ontology O2
ha s
ha s
The set of ma pping s defines a n alig nment (A).
A = {<O1.Thing , O2.Object, ≡, 0.8>, <O1.Car, O2.Automobile, ≡, 0.9>,
<O1.Locomotive, O2.Train, ≡, 0.7>, <O1.Horsepower, O2.Horsepower, ≡, 1.0>}

Introduction
S ystems of S ystems (S oS )
Set of independent information systems (IS ), providing
functiona lities derived from the interoperability among them
If ea ch IS within a S oS is conceptua lly described by a
unique ontology
…
a S oS is conceptua lly des cribed by a network of
ontologies .
Data Integration and systems interopera bility problems
are redefined: internetwork matching of ontologies

Figure 0: Internetwork matching

Introduction
The Ontology Matching Proces s ca n be done
•P a irwise
•Holistic
6

Introduction
Figure 2: Pairwise matching

Introduction
Figure 3: Holistic matching

Introduction
The Ontology Matching Proces s ca n be done
•P a irwise
•Holistic
However if we need to match networks using the
pa irwise or holistic proces s:
•All pa irs of entities from ea ch ontology that
compos es the networks ha ve to be ana lyzed
•S evere restriction in terms of sca la bility
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Problem
A network of ontolog ies is defined as Γ=< Ω, Λ>,
where:
• Ω is a finite set of ontologies
•Λ(O, O' ) is a set of a lig nments
S uppose a pa irwise internetwork matching over Γ
=< Ω, Λ> and Γ' =< Ω' , Λ' >, in which Ω = {O1, O2}
and Ω' = {O3} :
•Γx Γ‘ = (((O1 × O2) ∪(O1 × O3)) ∪(O2 × O3))
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Figure 1: Two networks of ontologies with
previous and internetwork alignments

Problem
However networks ma y ha ve isomorphis ms :
•in Figure 1 a matcher tool ma y find A1,1'
= {< O1.a1, O'1.a'1, => ,
< O1.b1, O'1.b'1, =>}
and trivia l alig nments:
•We alrea dy ha ve: A1,2 =< O1.b1, O2.d2, ⊑>
and A1',2' =< O'1.b'1 , O'2 .d'2, ⊑>
•We will work unneces s arily to produce:
A1,2' =< O1.b1, O'2 .d'2, ⊑> and
A1',2 =< O'1.b'1, O2.d2, ⊑>
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Approach
Considering fig ure a bove:
•S ince O2 and O'2 are identical, they do not need to
be exha ustively compared.
•Both pa irs of ontologies O1 and O'1 and O3 and O'3
share some subset of entities
•Use of alg ebraic operations to eliminate
isomorphisms
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• Let O1 = (V1,Σ1) and O2 = (V2,Σ2) be two ontologies, W be
a subset of V1, and Ψ be a set of constraints in V1.[5]
• The deprecation of Ψ from O1 = (V1,Σ1), denoted σ[Ψ](O1),
returns the ontology OD = (VD,ΣD), where VD = V1 and ΣD
= Σ1 -Ψ. [6]
• The projection of O1 = (V1,Σ1) over W, denoted π[W](O1),
returns the ontology OP = (VP,ΣP), where VP = W and ΣP is
the subset of the constraints in τ[Σ1] that use only classes
and properties in W. [5]
Algebraic Operations

• The union of O1 = (V1,Σ1) and O2 = (V2,Σ2), denoted O1
∪O2, returns the ontology OU =(VU,ΣU),where VU =V1 ∪
V2 and ΣU =Σ1 ∪Σ2. [5]
• The intersection of O1 = (V1,Σ1) and O2 = (V2,Σ2),
denoted O1 ∩ O2, returns the ontology ON = (VN,ΣN),
where V2 = V1 ∩ V2 and ΣN = τ[Σ1] ∩ τ[Σ2]. [5]
• The difference of O1 = (V1,Σ1) and O2 = (V2,Σ2), denoted
O1 - O2, returns the ontology OF = (VF,ΣF), where VF =
V1 and ΣF = τ[Σ1] -τ[Σ2]. [5]
Algebraic Operations

Example [5]
S uppose 2 ontologies created ba sed on FOAF a nd
Mus ic Ontology
http://www.foa f-project.org/
http://musicontology.com/
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Example
17

Proposal
Cons idering two networks, how to avoid cartesia n product?
Computation of: (before to send to the matcher system)
•Ω as O1 ∪O2... ∪On −O1 ∩O 1 −O1 ∩O'2 −... −On ∩O'n
•Ω' as O'1 ∪O'2 ... ∪O'n −O'1 ∩O1 −O'1 ∩O2 −... −O'n ∩O
After a matcher (Alin [7]), alig ns the res ulting sets
We compared the approa ch with Alin alig ning of all the ontologies from both
networks in a pairwise way
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Results
2x2: Ω= {conference, cmt} a nd Ω′= {cmt, sig kdd};
3x2: Ω= {conference, cmt, eka w} a nd Ω′= {cmt, sig kdd};
3x3: Ω= {conference, cmt, eka w} a nd Ω′= {cmt, sig kdd,
conference};
4x3: Ω= {conference, cmt, dblp, eka w} a nd Ω′= {cmt,
sig kdd, conference};
4‘x3: Ω= {conference, cmt, eda s, eka w} a nd Ω′= {cmt,
sig kdd, conference}.
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Results (number of comparisons)
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Experiment Pairwise SubInterNM % of Reduction
2x2 14,138 5,608 60.3
3x2 22.236 10,027 54.9
3x3 38.893 27,039 30.4
4x3 42,319 27,039 36.1
4'x357,497 43,420 24.4

Future Work
•Handle trivia l alig nments
•Handle trivia l closures
•Prediction of pos sible alig nments
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Conclusion
This work addressed the problem of internetwork
ontolog y matching .
P ossible natural evolution of the cla ssica l ontology
matching problem for hig hly interconnected
scenarios of S ystems of S ystems
Proposed an a pproa ch ca lled S ubInterNM
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References
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Mapping Study and Challenges Comparison, Technical Report. Relate-DIA/UNIRIO,
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[6] - Casanova, M. A., & Magalhães, R. (2018). An Algebra of Lightweight
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A Proposal for Optimizing Internetwork
Matching of Ontologies
Fabio Santos, Fernanda Baião, Kate Revoredo
Graduate Program in Informatics, UNIRIO, Brazil