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. 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.
Mathieu d'Aquin proposed measures for assessing agreement and disagreement between ontologies [2,3]. These measures are mostly based on the compatibility or redundancy of ontology assertions in the other ontology. Even if this is hidden in the initial formulation, these measures also rely on an alignment between the ontologies. They are very interesting because they assess the relation between two ontologies through an alignment without external reference: usually we evaluate alignment correctness with the help of a reference alignment .
We propose to reconsider these measures in order to provide two improvements to them:
This should also provide the opportunity to compare the measure with Christian Meilicke's coherence measure (based on the semantics of ontologies) .
Finally, because they are independent from the reference, such measures may be used as alignment improvers: it may be possible to optimise existing alignments by attempting at maximising ontology aggreement and/or minimising ontology disagreement. We propose to experiment with this idea and to apply it either to randomly generated alignments or to alignments returned by existing alignment evaluation campaigns  in order to determine if it indeed provides improvement for matchers.
 Jérôme Euzenat, Pavel Shvaiko, Ontology matching, Springer, Berlin (DE), 2007
 Mathieu d'Aquin, Formally measuring agreement and disagreement in ontologies, Proc. 5th International Conference on Knowledge Capture (K-Cap), Redondo Beach (CA US), pp145-152, 2009http://watson.kmi.open.ac.uk/DownloadsAndPublications_files/kcap09.pdf
 Mathieu d'Aquin, Enrico Motta, Visualizing consensus with online ontologies to support quality in ontology development. Proc. EKAW workshop on Ontology Quality (OntoQual), 2010.http://watson.kmi.open.ac.uk/DownloadsAndPublications_files/ontoqual2010.pdf
 Jérôme Euzenat, Christian Meilicke, Pavel Shvaiko, Heiner Stuckenschmidt, Cássia Trojahn dos Santos, Ontology alignment evaluation initiative: six years of experience, Journal on Data Semantics XV:158-192, 2011http://disi.unitn.it/~p2p/RelatedWork/Matching/OAEI-JODS.pdf
 Christian Meilicke, Heiner Stuckenschmidt, Incoherence as a basis for measuring the quality of ontology mappings, Proc. 3rd International Workshop on Ontology matching (OM), Karlsruhe (DE), pages 1-12, 2008 http://disi.unitn.it/~p2p/OM-2008/om2008_Tpaper1.pdf
 Jérôme David, Jérôme Euzenat, François Scharffe, Cássia Trojahn, The Alignment API 4.0, The semantic web journal2(1):3-10, 2011 http://www.semantic-web-journal.net/sites/default/files/swj60_1.pdf
More information at: http://exmo.inria.fr/training/M2R-2015-agreement.html