Semantic peer to peer (P2P) systems are fully decentralized overlay networks of people or machines (called peers) sharing and searching varied resources (documents, videos, photos, data, services) based on their semantic annotations using ontologies. They provide a support for the emergence of open and decentralized electronic social networks, in which no central or external authority can control the reliability of the peers participating to the network. This lack of control may however cause some of the results provided by some peers to be unsatisfactory, because of inadequate or obso- lete annotations. In this paper, we propose a probabilistic model to handle trust in a P2P setting. It supports a local computation and a simple form of propagation of the trust of peers into classes of other peers. We claim that it is well appropriate to the dynamics of P2P networks and to the freedom of each peer within the network to have different viewpoints towards the peers with which it interacts.