The newly envisioned Semantic Web contains as a component what may be called a Web of Trust, consisting of the trust relationships held between its participants. In terms of this, the degree to which participant A believes what is believed by participant B depends on the degree to which A trusts B. This paper presents a formal language with well-defined semantics within which such a participant (or agent) can express the relevant conditions of belief and trust, and outlines some key techniques for reasoning with these expressions. Novel in this treatment is the use of linguistic, rather than numeric, measures of belief. The aim in this is to make the language and reasoning system more intuitive for the human user. Also novel is an explicit delineation of the context within which the language and reasoning techniques are to be applied.