Artificial intelligent agents should evaluate the information they receive based on multiple criteria: in particular, the content of the message and the trustworthiness associated to the source. The final evaluation about the quality of the information should be used both to re-organize the contents' value, and to modify the evaluation of the source of information, and this feedback has to be distribute in a sensible way among the different features of the source itself, like his competence and his sincerity. In this paper, we propose a formal system in which trust is not treated as a monolithic concept. On the contrary, the decision to trust a given piece of information depends on the interaction between two independent assessments: the sincerity of the source, and his expertise with respect to a given domain. In particular, we focus on the dynamics of feedback that, based on the assessed quality of the information, change the evaluation of the source.