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In this dissertation we design a system that allows Semantic Web agents to reason within what has come to be known as the Web of Trust. We integrated reasoning about belief and trust, so agents can reason about information from different sources and deal with contradictions. Software agents interact to support users who publish, share and search for documents in a distributed repository. Each agent maintains an individualized topic taxonomy for the user it represents, updating it with information obtained from other agents. Additionally, an agent maintains and updates trust relationships with other agents. When new information leads to a contradiction, the agent performs a belief revision process informed by a degree of belief in a statement and a degree of trust an agent has for the information source. The system described has several key characteristics. First, we define a formal language with well-defined semantics within which an agent can express the relevant conditions of belief and trust, and a set of inference rules. The language uses symbolic labels for belief and trust intervals to facilitate expressing inexact statements about subjective epistemic states. Second, an agent's belief set at a given point in time is modeled using a Dynamic Reasoning System (DRS). This allows the agent's knowledge acquisition and belief revision processes to be expressed as activities that take place in time. Third, we explicitly describe reasoning processes, creating algorithms for acquiring new information and for belief revision. Fourth, we design a general architecture for system implementation. An object-oriented model presents classes and methods implementing the formal model. The database model is flexible and allows for future extensions. Finally, an external representation for system data is presented based on open Semantic Web standards.