In this chapter, we propose the concept of flexible propositionsFlexible proposition and establish the corresponding truth-degree logicTruth-degreed logic and inference theories. First, we consider the representations and truth values of flexible propositionsFlexible proposition; Next, we define the numerical truth valueNumerical truth value, that is, the truth-degreeTruth-degree, of a flexible propositionFlexible proposition, introduce the formal representations of flexible propositionsFlexible proposition and the flexible propositionsFlexible proposition with composite linguistic valuesComposite linguistic value, particularly, introduce the algebraic compound flexible propositionFlexible proposition and the flexible propositionFlexible proposition with a synthetic linguistic valueSynthetic linguistic value, and then we analyze and expounds the computation principles and methods of truth-degrees of the various flexible propositionsFlexible proposition; Then, we establish the corresponding truth-degreeTruth-degree logic algebras, and then, we introduce flexible-propositional formulas and flexible-predicate formulas, extend true and false and proposes the concepts of degree-true, degree-false, near-trueNear-true, and near-falseNear-false, extend the validity of argument forms and propose the concepts of degree-valid argument formDegree-valid argument form and near-valid argument formNear-valid argument form, and extend the concepts of tautology and logical implication and propose the concepts of degree-true tautology, degree-true logical implicationDegree-true logical implication, near-trueNear-true tautology, and near-true logical implicationNear-true logical implication, thus obtaining rules of degree-true inferenceRules of degree-true inference andRules of near-true inference rules of near-true inferenceNear-true inference and establishing the principles and methods called degree-true inferenceDegree-true inference and near-true inference in truth-degree logicTruth-degree logic.