Place of work : The position is located at INRIA Rhône-Alpes, Montbonnot (near Grenoble, France) a main computer science research lab, in a stimulating research environment. Research will be carried out in the Exmo team under the supervision of Jérôme Euzenat.
Environnement : The doctoral work is to be carried out in the Exmo team, a reputed team within the semantic web research area and particularly on ontology matching. We are in contact with the most important teams in France and Europe on these topics and this work could be the occasion of cooperation on sharing alignments.
The goal of the semantic web is to take advantage of formalised knowledge (in languages like RDF) at the scale of the worldwide web. In particular, it is based on ontologies which define concepts used for representing knowledge on the web, e.g., for annotating a picture, specifying a web service interface or expressing the relation between two persons. However, it is likely that different information sources and different actors in different contexts will use different ontologies. It is thus necessary to find correspondences between concepts of these ontologies.
The operation of finding correspondences is called ontology matching. It takes two ontologies as input and outputs a set of correspondences between entities of these ontologies, called "alignment" . A correspondence is defined by the two related entities, which can be classes, instances, properties, formulas as well as combination of those, the relation between these entities (equivalence, subsumption, incompatibility, etc.) and, if possible, a confidence measure in this correspondence. Alignments are used for importing data from one ontology to another or for translating queries.
Matching ontologies is very difficult. Hence, existing alignments are worth reusing. For that purpose, we have developed alignment servers for sharing alignments on the web . They can generate alignments on demand but can also store alignments that have been created manually or certified as correct. In order to take advantage of a potentially wide set of available alignments and ontologies, it is necessary to consider operations for alignment management .
The goal of this doctoral work is to design the foundations of an alignment algebra that can be used in this context. An alignment algebra allows for manipulating alignments, generating new ones, independently of the content of ontologies.
An alignment algebra should allow for combining alignments in different ways such as the classical union, intersection and inverse operators. Such classical operators will have to rely on the underlying structure of alignments : relation algebras  and confidence structure. For instance, during union, the correspondences between the two same entities may be merged by finding the disjunction of their relations and the maximum of their confidence. They also must support the intuitive interpretation : conjunction is used when the same correspondence is obtained by different means and disjunction is used when several correspondences are competing. Finally, they will have to preserve the semantic interpretation of alignments . Hence an alignment algebra must be designed as a coherent system.
Of special interest is the composition of alignments. Composition is a way to deduce new alignments from existing ones. If there exists an alignment between ontology O1 and ontology O2, and another one between O2 and a third ontology O3, we want to decide which correspondences hold between O1 and O3. The operation that returns this set of correspondences is called composition. For instance, consider the correspondence 1:MappleLeaf subClassOf 2:Leaf between ontology O1 and ontology O2, as well as the correspondence 2:Leaf partOf 3:Tree between O2 and O3. Composing these two correspondences could yield 1:MappleLeaf partOf 3:Tree between O1 and O3.
Since relations between ontology entities may be arbitrarily complex, composition obeys particular rules that must be investigated. One way to model this is by using algebras of relations . Alignment composition can thus be reduced to combining correspondences with regard to their relations and the structure of related entities.
An alignment algebra should also lead to operations on networks of ontologies (a set of ontologies interelated with alignments ). It should be possible to normalise such networks through closure operations which systematically apply the algebraic operators to the alignments in the network. Such closure operators will normalise the network so as to establish one minimal or maximal alignment between each ontology of the network. This normalisation, in turn, will allow for defining an order (of definiteness) between networks.
These algebraic operators can then used in work on revision of ontology networks, alignment argumentation  or alignment-space ontology distances .
The successful candidate will study these possible operations and their behaviour. Their respective benefits and drawbacks will be considered. In particular, these operations are expected to be consistent with the alignment semantics. The result of this work could be implemented in our alignment API , which already features alignments and network of ontologies.
 Jérôme Euzenat, Pavel Shvaiko, Ontology matching, Springer-Verlag, Heildelberg (DE), 2007
 Jérôme Euzenat, Alignment infrastructure for ontology mediation and other applications, in : Martin Hepp, Axel Polleres, Frank van Harmelen, Michael Genesereth (eds), Proc. 1st ICSOC international workshop on Mediation in semantic web services, Amsterdam (NL), pp81-95, 2005
 Jérôme Euzenat, Adrian Mocan, François Scharffe, Ontology alignments : an ontology management perspective, in : Martin Hepp, Pieter De Leenheer, Aldo De Moor, York Sure (eds), Ontology management : semantic web, semantic web services, and business applications, Springer, New-York (NY US), pp177-206, 2008
 Jérôme Euzenat, Algebras of ontology alignment relations, Proc. 7th ISWC, Karlsruhe (DE), Lecture notes in computer science 5318:387-402, 2008
 Antoine Zimmermann, Jérôme Euzenat, Three semantics for distributed systems and their relations with alignment composition, in : Proc. 5th conference on International semantic web conference (ISWC), Athens (GA US), Lecture notes in computer science 4273:16-29, 2006
 Cássia Trojahn dos Santos, Jérôme Euzenat, Valentina Tamma, Terry Payne, Argumentation for reconciling agent ontologies, in : Atilla Elçi, Mamadou Koné, Mehmet Orgun (eds), Semantic Agent Systems, Springer, New-York (NY US), pp89-111, 2011
 Jérôme David, Jérôme Euzenat, Ondrej Svab-Zamazal, Ontology similarity in the alignment space, Proc. 9th conference on international semantic web conference (ISWC), Shanghai (CN), Lecture notes in computer science 6496:129-144, 2010
 Jérôme David, Jérôme Euzenat, François Scharffe, Cássia Trojahn, The Alignment API 4.0, Semantic web journal, 2(1):3-10, 2011