In this chapter, we expound briefly the basic theory of information processing with quantifiable rigid linguistic valuesQuantifiable rigid linguistic value, which is parallel or similar to the corresponding theory of information processing with flexible linguistic valuesFlexible linguistic value. Besides, we introduce the quantifiable rigid linguistic valuesQuantifiable rigid linguistic value and their measures, partial possessionPartial possession and possessing ratePossessing rate, partial implicationPartial implication and implication-degreeImplication-degree, and partial equivalencePartial equivalence and equivalence-degreeEquivalence-degree, in particular, find and present the judging condition of partial implicationPartial implication (equivalence) relation satisfying transitivity and the corresponding transitive formulas of implication-degreesImplication-degree (equivalence-degrees).