First in this paper, an equivalent characterization of generalized tautologies in Ł_n is introduced by using the method of cut of fuzzy set, the Hamming distance, Hamming similarity degree and Hamming truth degree between formulas are defined by means of standard Hamming distance between fuzzy sets, and Hamming distance representation of the basic concepts of quantitative logic is described. Then, the truth degree decomposition theorem of formula in quantitative logic is presented. This theorem points out that in quantitative logic, the truth degree of any formula φ is equal to the sum of the truth degrees of some incompatible formulas, and the formula φ itself is logically equivalent to the join of these formulas. Finally, the problem of triple-I truth degree solution of the generalized MP problem is proposed, and the existence of the triple-I truth degree solution is discussed.