Trust is a fundamental concern in large-escale open distributed sytems. It lies at the core of all interactios between the entities that have to operate in such uncertain and constantly changing environmonts. Given the complexity of the interactions, these components, and the ensuing system, are increasingly being conceptualised, desined, and built using agent-based techiques. Therefore, the presence of trust is imperative in a multi-agent system (MAS). Consequently, this work studies how to have a explicit trust model in intelligent agent, which has beliefs, desires and intentions (BDI agent). Thas is, the agent now has a fourth component called Trust. This way, a logic to include the concept of trust in an open BDI MAS is interesting, so that the different aspects of a trust model can be expressed formally and accuratelly. This is achieved by using an indexed multi-modal logic, where the possible worlds which model a multi-agent system represent which agents are in the system in a given moment. Moreover, for each one of the three original components of a BDI agent, where the components represent beliefs, desires and intentions, there is a representation of possible worlds, because these are treated as modalities. However, trust is modelled as predicate, not as a modality.