Fuzzy reasoning and fuzzy logic

Fuzzy reasoning and fuzzy logic are two related but different research fields such that both are fruitful but have not yet been well linked. The aim of the paper is to: (i) prove that it is impossible to keep all theorems in classical propositional calculus to be tautologies in fuzzy propositional calculus; (ii) establish a so called quasi-formal deduction system and prove the corresponding soundness theorem; and (iii) revise, clear and set a logic foundation for the concepts of fuzzy modus ponens and fuzzy modus tollens.