In this chapter, we establish the fundamental theory of flexible-linguistic-truth-valued logicFlexible-linguistic-truth-valued logic. First, we introduce two flexible linguistic truth valuesLinguistic truth value for flexible propositionsFlexible proposition, rough-trueRough-true and rough-falseRough-false, and then, we deduce the computational modelsComputational model for the flexible linguistic truth valuesLinguistic truth value of compound flexible propositionsFlexible proposition according to the relation between numerical truth valuesNumerical truth value and flexible linguistic truth valuesLinguistic truth value and then establish the flexible-two-valued logic algebraic system. Next, we examines flexible propositional logic and flexible predicateFlexible predicate logic in the flexible-two-valued logic as well as corresponding inference, propose the concepts of rough-valid argument formRough-valid argument form, rough-trueRough-true tautology, rough-true logical implicationRough-true logical implication, and rule of rough-true inferenceRough-true inference, and establish the inference principles and methods called rough-true inference. In addition, we also discuss the approximate reasoningApproximate reasoning based on rough-true-UMP. In particular, we propose the terminology of logical semanticsLogical semantics of a proposition and define anew the linguistic truth valuesLinguistic truth value of compound flexible propositionsFlexible proposition based on the logical semanticsLogical semantics. Lastly, we sketch flexible command logicFlexible command logic, negation-contained logicNegation-contained logic, and opposite-contained logicOpposite-contained logic.