Alignment overcomes divergence in the specification of the semantics of vocabularies by different but overlapping ontologies. Therefore, it enhances semantic interoperability for many web based applications. However, ontology change following applications new requirements or new perception of domain knowledges can leads to undesirable knowledge such as inconsistent and therefore to a useless alignment. Ontologies and alignments are encoded in knowledge bases allowing applications to store only some explicit knowledge while they derive implicit ones by applying reasoning services on these knowledge bases. This underlying representation of ontologies and alignments leads us to follow base revision theory to deal with alignment revision under ontology change. For that purpose, we adapt kernel contraction framework to design rational operators and to formulate the set of postulates that characterize each class of these operators. We demonstrate the connection between each class of operators and the set of postulates that characterize them. Finally, we present algorithms to compute alignment kernels and incision functions. Kernels are sets of correspondences responsible of undesirable knowledge following alignment semantics. Incision functions determine the sets of correspondences to eliminate in order to restore alignment consistency or to realize a successful contraction.

Ontology matching techniques are a solution to overcome the problem of interoperability between ontologies. However, the generated mappings suffer from logical defects that influence their usefulness. In this paper we present a detailed analysis of the problem so-called conservativity principle; alignment between ontologies should never generate new knowledge compared to those generated by reasoning solely on ontologies. We also study the sub-problems; Ontology change and Satisfiability preservation problems and compare the related works and their way to detect and repair conservativity principle. At the end we present a set of open research issues.