Both for natural language information processing and for knowledge representation and reasoning in computer science, the discourse reasoning in natural language is the inescapable emphasis and difficulty. On the basis of the formalization for discourse reasoning by means of the generalized quantifier theory, both the validity of discourse reasoning based on traditional syllogisms and the validity of discourse reasoning based on generalized syllogisms can be judged. In other words, the discourse reasoning in natural language can be formally explained and proven by means of the generalized quantifier theory.