In resource sharing P2P systems with autonomous partici- pants, each peer is free to use the ontology with which it annotates its resources. Semantic heterogeneity occurs when the peers do not use the same ontology. For example, a contributing peer A (e.g. a doctor) may annotate its photos, diagrams, data sets with some ontology of its own, while peer B (e.g. a genetician) uses another one. In order to answer a query issued in the system, peers need to know alignments that state correspondences between entities of two ontologies. Assuming that each peer has some partial initial knowledge of some alignments, we focus on correspondences sharing between the peers as a means to learn ad- ditional correspondences. We first provide several measures of semantic heterogeneity that enable to draw a semantic picture of the system and to evaluate the efficiency of protocols independently of query evaluation. We propose CorDis, a gossip-based protocol that disseminates the cor- respondences that the peers want to share in the system. To overcome the peers’ storage limitations, we propose to consider a history of past queries and to favor the correspondences involving frequently used enti- ties. We study several policies that a peer may adopt in case of inconsis- tency i.e. when shared correspondences conflict with its own knowledge. We conduct experiments with a set of 93 ontologies actively used in the biomedical domain. We evaluate the CorDis protocol with respect to the proposed measures of semantic heterogeneity and show its good behavior for decreasing them in several contexts.