Fuzzy models are specified by certain t-norms and t-conorms as conjunction and disjunction truth functions, respectively. The truth values of implication formulas are recursively defined via the truth values of smaller formulas including all subformulas. These models are characterized by a subset of classical first-order logic. This subset is specified as a sequent calculus with nonstandard implication inference rules. This logical characterization is possible due to the recursive implication truth functions, and it justifies the use of this class of truth functions in fuzzy systems.