Reasoning in fuzzy knowledge systems is usually based on fuzzy sets and is unrelated to mathematical fuzzy logic. Zadeh operators for conjunction, disjunction, and negation along with the corresponding S-implication are considered as truth functions in models of fuzzy knowledge systems. Facts and rules of fuzzy knowledge systems are mapped to nonlogical axioms in logic theories. The theories combining nonlogical axioms with inference rules of a sequent calculus for classical first-order logic and not containing logical axioms are sound and complete with respect to these models of fuzzy knowledge systems. If bounds of the truth values of the facts and rules are known, then bounds of the truth values of all derived formulas can be computed. Inference in these theories is discussed.