Exchanging knowledge via the web might lead to the use of different representation languages because different applications could take advantage of this knowledge. In order to function properly, the interoperability of these languages must be established on a semantic ground (i.e., based on the models of the representations). Several solutions can be used for ensuring this interoperability. We present a new approach based on a set of knowledge representation languages partially ordered with regard to the transformability from one language to another by preserving a particular property. The advantages of the family of languages approach are the opportunity to choose the language in which a representation will be imported and the possibility to compose the transformations available between the members of the family. For the same set of languages, there can be several structures depending on the property used for structuring the family. We focus here on semantic properties of different strength that allow us to perform practicable but well founded transformations.