From the article: The fuzzy propositional logic (FPL) described in the article presents a new alternative approach to thinking about such notions as proposition, interpretation, inference. This logic generalizes classical propositional logic in two directions: (i) propositions are considered to be fuzzy, and (ii) logical variables are considered to be many-valued. Formulas of FPL are constructed from elementary propositions and interpreted over the universe, i.e., the Cartesian product of the sets of the values of all variables. The main inference rule in FPL is a fuzzy resolution which generalizes properties of traditional resolution.