Analytic fuzzy tableaux

 In this paper Beth–Smullyan's tableaux method is extended to the fuzzy propositional logic. The fuzzy tableaux method is based on the concepts of t-truth and extended graded formula. As in classical logic, it is a refutation procedure. A closed fuzzy tableau beginning with the extended graded formula r, A] asserting that this is not t-true, is a tableau proof of the graded formula (A, r). The theorems of soundness, completeness, and decidability are proved.