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The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued?ukasiewicz propositional logic system ?3. We introduce the concepts of the cotangent similarity degree, cotangent pseudo-distance and cotangent truth degree of the propositions, together with their basic properties in ?3. We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives ?,∨ and → in the?3 logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F (S), and provide several examples and basic properties of it.