This paper formally develops a type of propositional fuzzy logic which is analogous to traditional two-valued logic. A complete set of fuzzy qualifiers are defined for the first time, and as a consequence a corresponding set of modifiers. In addition, a set of rules for combining those qualifiers in a proposition have been developed. Once these rules have been established, a definition of formulae in the context of propositional fuzzy logic is proposed and a theory of inference is deduced.