=Paper=
{{Paper
|id=Vol-2536/om2019_poster7
|storemode=property
|title=Decentralized Reasoning on a Network of Aligned Ontologies with Link Keys
|pdfUrl=https://ceur-ws.org/Vol-2536/om2019_poster7.pdf
|volume=Vol-2536
|authors=Jérémy Lhez,Chan Le Duc,Thinh Dong,Myriam Lamolle
|dblpUrl=https://dblp.org/rec/conf/semweb/LhezDDL19a
}}
==Decentralized Reasoning on a Network of Aligned Ontologies with Link Keys==
<pdf width="1500px">https://ceur-ws.org/Vol-2536/om2019_poster7.pdf</pdf>
<pre>
       Decentralized Reasoning on a Network of
         Aligned Ontologies with Link Keys

       Jérémy Lhez1 , Chan Le Duc1 , Thinh Dong2 , and Myriam Lamolle1
               1
                   LIASD, Université Paris 8 - IUT de Montreuil, France
                      {lhez,leduc,lamolle}@iut.univ-paris8.fr
                           2
                             University of Danang, Vietnam
                              dnnthinh@kontum.udn.vn


1     Introduction
Reasoning on a network of aligned ontologies has been investigated in different
contexts where the semantics given to correspondences differs from one to an-
other. In this paper, we introduce a new semantics of correspondences which is
weaker than the usual one and propose a procedure for reasoning over a network
of aligned ontologies with link keys [1] in a decentralized manner, i.e. reasoning
can be independently performed on different sites This process allows to reduce
polynomially global reasoning to local reasoning.
    To achieve such results for a network of ontologies expressed in the description
logic ALC, the semantics of a correspondence, denoted C → D where C and D
are concepts in ontologies Oi and Oj respectively, is defined as an implication
of concept unsatisfiabilities (i.e. unsatisfiability of D implies unsatisfiability of
C) rather than a concept subsumption as usual. This weakened semantics allows
to reduce the reasoning complexity over a network of aligned ontologies since
(i) only individual equalities and concept unsatisfiabilities such as a ≈ b, C v
⊥ can be propagated from one to another ontology, and (ii) if a concept is
locally unsatifiable in an ontology then it remains unsatisfiable when adding
to the ontology individual equalites or concept unsatisfiabilities. The weakened
semantics would be relevant for correspondences between ontologies of different
nature. Given two ontologies about equipment and staff and a correspondence
Computer → Developer between them. With this correspondence, the weakened
semantics tells us that if there is no developer then there is no computer. The
standard semantics is irrelevant in this case.
    We use h{Oi }ni=1 , {Aij }ni=1,j=2,i<j i to denote a network of ontologies where
each Oi is an ontology expressed in ALC and each Aij contains individual cor-
respondences, link keys with the usual semantics, or concept correspondences
with the weakened semantics. Such a network is consistent if there is a model
Ii of each ontology Oi which satisfies all correspondences in each Aij . We will
present our algorithms for a network composed of two ontologies O1 , O2 and an
alignment A12 . These algorithms can be straightforwardly extended to a general
network of aligned ontologies.
    Copyright c 2019 for this paper by its authors. Use permitted under Creative Com-
    mons License Attribution 4.0 International (CC BY 4.0).
2   Decentralized reasoning by propagating
As discussed in Section 1, the weakened semantics of alignments allows us to
decompose checking consistency of a network into two steps which consist in
propagating knowledge from one to another ontology.
Propagating individual equalities. This step discovers all inferred individual
equalities by applying link keys in the alignment and using local reasoners for
entailment on ontologies. For example, a new individual correspondence a ≈ b
will be discovered and added to A12 if {hP, Qi}linkkeyhC, Di ∈ A12 , c ≈ d ∈ A12
and P (a, c) ∈ O1 , Q(b, d) ∈ O2 . A new equality a ≈ c will be discovered and
added to O1 if a ≈ b, c ≈ b ∈ A12 . When a local reasoner is called to check
whether Oi |= a ≈ b, it needs only one Oi for reasoning.
Propagating concept unsatisfiabilities. This step uses local reasoners as-
sociated with ontologies to discover from each ontology Oi new unsatisfiable
concepts which can result from unsatisfiable concepts in Oj via concept corre-
spondences. For instance, if O1 |= C v ⊥ and C ← D ∈ A12 then a new axiom
D v ⊥ will be added to O2 . As the previous step, each local reasoner needs only
one Oi for reasoning.
The main algorithm executes these two steps until either an inconsistency is
found, or a stationary state is reached. If O1 , O2 are consistent, and A12 does not
contain any pair a ≈ b, a 6≈ b, then the network itself is consistent. Our algorithm
runs in polynomial time in the size of the network since the propagation proce-
dures add only axioms and assertions which are composed of (sub-)concepts and
named individuals occurring in the ontologies and alignments. Moreover, these
algorithms never remove anything from the network.
Implementation and tests. The algorithms has been implemented and inte-
grated within DRAOn [2]. HermiT [3] is used for local reasoners. We performed
some tests with several datasets available from the OAEI web site. We compared
the performances of DRAOn under the IDDL semantics [2] and the weakened
semantics. Better performance has been observed for the latter. For instance,
checking consistency of the network composed of SNOMED, FMA and the align-
ment took 81 seconds under the weakened semantics while it took greater than
15 minutes under the IDDL semantics. We also added to the alignments some
link keys, and ran other tests to validate the implementation of our algorithm.


References
1. Gmati, M., Atencia, M., Euzenat, J.: Tableau extensions for reasoning with link
   keys. In: Proceedings of the 11th International Workshop on Ontology Matching.
   (2016) 37–48
2. Le Duc, C., Lamolle, M., Zimmermann, A., Curé, O.: Draon: A distributed reasoner
   for aligned ontologies. In: Informal Proceedings of the 2nd International Workshop
   on OWL Reasoner Evaluation (ORE). (2013) 81–86
3. Shearer, R., Motik, B., Horrocks, I.: HermiT: A Highly-Efficient OWL Reasoner.
   In: Proc. of the 5th Int. Workshop on OWL (OWLED). (2008)

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