Trust and reputation models for distributed, collaborative systems have been studied and applied in several domains, in order to stimulate cooperation while preventing selfish and malicious behaviors. Nonetheless, such models have received less attention in the process of specifying and analyzing formally the functionalities of the systems mentioned above. The objective of this paper is to define a process algebraic framework for the modeling of systems that use (i) trust and reputation to govern the interactions among nodes, and (ii) communication models characterized by a high level of adaptiveness and flexibility. Hence, we propose a formalism for verifying, through model checking techniques, the robustness of these systems with respect to the typical attacks conducted against webs of trust.