DRAOn : A Distributed Reasoner for Aligned Ontologies Chan LE DUC , - - PowerPoint PPT Presentation

Motivation IDDL semantics Architecture Experiments

DRAOn : A Distributed Reasoner for Aligned Ontologies

Chan LE DUC, Myriam LAMOLLE, Antoine ZIMMERMANN and Olivier CURE

Universit´ e Paris8-IUT de Montreuil, ´ Ecole Nationale Sup´ erieure des Mines, Universit´ e Marne La Vall´ ee

OWL Reasoner Evaluation Workshop, 2013

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Motivation IDDL semantics Architecture Experiments

Motivation

O1 O2 O3 O4 SemWeb client

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Motivation IDDL semantics Architecture Experiments

Motivation

O1 O2 O3 O4 SemWeb client | = α1 ? | = α2 ? | = α3 ? | = α4 ?

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Motivation IDDL semantics Architecture Experiments

Motivation

O1 O2 O3 O4 SemWeb client A12 A13 A23 A43

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Motivation IDDL semantics Architecture Experiments

Motivation

O1 O2 O3 O4 SemWeb client A12 A13 A23 A43 Is this network consistent ?

| = ?

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Motivation IDDL semantics Architecture Experiments

Formalizing a network of aligned ontologies

Standard DL (merge of all ontologies and alignments) ; DDL (Distributed Description Logics) : Drago ; E-connections : Pellet ; ... IDDL (Integrated Distributed Description Logics) : The decision procedure for IDDL (RR2008) can be implemented in a distributed way.

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Motivation IDDL semantics Architecture Experiments

IDDL Semantics

O1 O2 On−1 On A12 . . . An−1,n Syntax level

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Motivation IDDL semantics Architecture Experiments

IDDL Semantics

O1 O2 On−1 On A12 . . . An−1,n Syntax level D1 D2 Dn−1 Dn Local semantic level I1 I2 In−1 In

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Motivation IDDL semantics Architecture Experiments

IDDL Semantics

O1 O2 On−1 On A12 . . . An−1,n Syntax level D1 D2 Dn−1 Dn Local semantic level I1 I2 In−1 In D ǫ1 ǫ2 ǫn−1 ǫn Global semantic level Equalising functions

ORE 2013 4/12

Motivation IDDL semantics Architecture Experiments

IDDL Semantics

O1 O2 On−1 On A12 . . . An−1,n Syntax level D1 D2 Dn−1 Dn Local semantic level I1 I2 In−1 In D ǫ1 ǫ2 ǫn−1 ǫn Global semantic level Equalising functions Global interpretation : I = (Ii), (ǫi)

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Motivation IDDL semantics Architecture Experiments

IDDL Semantics I = (Ii), (ǫi) | =

i :C ∆i Ii j :D ∆j Ij cross-ontology subsumption ⊑ ∆ ǫi(C Ii) ⊆ ǫj(DIj) ǫi ǫj

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Motivation IDDL semantics Architecture Experiments

IDDL Semantics I = (Ii), (ǫi) | =

i :C ∆i Ii j :D ∆j Ij cross-ontology disjointness ⊥ ∆ ǫi(C Ii) ∩ ǫj(DIj) = ∅

O, A consistent iff there is a I = (Ii), (ǫi) satisfying local axioms and correspondences

ǫi ǫj

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Motivation IDDL semantics Architecture Experiments

Global concepts and alignment ontology

Global concepts are concepts that appear on the right or left side

• f a correspondence :

A12 : 1:Superman

⊑

← → 2:Person A23 : 2:Person

⊑

← → 3:Vertebrate The global concepts are 1:Superman, 2:Person and 3:Vertebrate The alignment ontology renders the correspondences in the form of DL axioms : The alignment ontology A contains the axioms 1:Superman ⊑ 2:Person 2:Person ⊑ 3:Vertebrate

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Motivation IDDL semantics Architecture Experiments

Configuration

With only cross-ontology concept subsumption : Definition A configuration Ω asserts explicitly the emptiness or non emptiness

• f global concepts.

Example Ω = { 1:Superman ⊑ ⊥, 2:Person ⊑ ⊥, 3:Vertebrate(a) }. a is a new individual name.

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Motivation IDDL semantics Architecture Experiments

Algorithm (sketched)

With only cross-ontology concept subsumption :

1 Choose a configuration Ω ; 2 If Not Consistent(

A ∪ Ω), Go To

1 3 For All i,

If Not LocallyConsistent(Ω ∪ Oi), Go To

1 4 Return TRUE ;

If all configurations were tested, Return FALSE ;

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Motivation IDDL semantics Architecture Experiments

Properties of The Algorithm

Encapsulated and parallelised local reasoners ; No upper bound on local expressiveness ; If a local reasoner is in EXPTIME class or higher, global consistency remains in the same class : EXPTIME(DL1,··· ,DLn) (no disjoint correspondences).

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Motivation IDDL semantics Architecture Experiments

Architecture of DRAOn

O1 OWL Reasoner1 O2 OWL Reasoner2

. . .

On OWL Reasonern Wrapper Wrapper Wrapper Global Reasoner

configurationi configurationi configurationi ORE 2013 10/12

Motivation IDDL semantics Architecture Experiments

Optimizations and Experiments

Optimizations :

Eliminating from configurations equivalent concepts and roles Eliminating from configurations i :C if O | = i :C(x) or O | = (i :C ⊑ ⊥) where O = A or O = Oi Testing configurations containing (i :C(x)) prior to (i :C ⊑ ⊥) Building configurations in an incremental way

ORE 2013 11/12

Motivation IDDL semantics Architecture Experiments

Optimizations and Experiments

Optimizations :

Eliminating from configurations equivalent concepts and roles Eliminating from configurations i :C if O | = i :C(x) or O | = (i :C ⊑ ⊥) where O = A or O = Oi Testing configurations containing (i :C(x)) prior to (i :C ⊑ ⊥) Building configurations in an incremental way

Experiments :

Ontology 1 Ontology 2 Alignment DL non-distr. IDDL

• distr. IDDL

Small NCI Small FMA Alcomo Map. 7,5s 46s 30s (10,000 axioms, (3,800 axioms, (2,800 corr.) 6,500 entities) 3,700 entities) Human Mouse

• Ref. Map.

6s 4.5s 4s (5,500 axioms, ( 4,500 axioms, (1516 corr.) 3,300 entities) 2,750 entities) ORE 2013 11/12

Motivation IDDL semantics Architecture Experiments

Further Work

Further experiments for a large network of aligned ontologies Optimizations for disjoint correspondences Performance of DRAOn depends on services offered by OWL Reasoners : DRAOn has to use OWLReasoner.getUnsatisfiableClasses() OWLReasoner.getTypes(OWLNamedIndividual) to check whether a given set of concepts is unsatisfiable or non-empty.

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