Trust is a critical issue for communication protocols in open systems that operate in dynamic and highly uncertain environments. It influences not only the specification of security policies but also the techniques needed to manage and implement security policies. A formal system for the specification of trust for such systems requires the ability to reason about agent beliefs as well as the evolution of the system through time. In this paper, we use a fibred logic called FL which is obtained by combining a belief logic with a temporal logic for specifying agent beliefs and establishing trust theories for communication protocols. A theory of trust for a given system is captured by a set of rules in FL that describes the trust of agents in the system. This enables automated reasoning about theories of trust using the decision procedures of FL such as axiom systems and tableaux. Theories of trust are generally established based on the initial trust of agents in the security mechanisms of the system in which they are deployed. Such theories provide a foundation for reasoning about agent beliefs as well as security properties that systems may satisfy.