Trust and reputation models provide soft-security mechanisms that can be used to induce cooperative behaviors in user-centric communities in which user-generated services and resources are shared. The effectiveness of such models depends on several, orthogonal aspects that make their analysis a challenging issue. This paper aims to provide support to the design of trust and reputation infrastructures and to verify their adequacy in the setting of software architectures and computer networks underlying online communities. This is done by proposing a formal framework encompassing a calculus of concurrent systems, a temporal logic for trust, and model checking techniques.