In this paper we consider P2P data sharing systems in which each participant uses an ontology to represent its data. If all the participants do not use the same ontology, the system is said to be semantically heterogeneous. This situation of heterogeneity prevents perfect interoperability. Indeed participants could be unable to treat queries for which they do not understand some concepts. Intuitively, the more heterogeneous a system, the harder to communicate. We first define several measures to characterize the semantic heterogeneity of P2P systems according to different facets. Then, we propose a solution, called CorDis, to reduce the heterogeneity by decreasing the gap between peers. The idea is to gossip correspondences through the system so that peers become less disparate from each other. The experiments use the PeerSim simulator and ontologies from OntoFarm. The results show that CorDis significantly reduces some facets of semantic heterogeneity while the network traffic and the storage space are bounded.