Abstract: It proposes problems of [α]- reverse FMP, collective [α]- reverse FMP, as well as [α]-reverse FMT, collective [α]-reverse FMT. By introducing a preorder in [F(S)], the solutions for these problems are given in propositional logical system [L?n]. And it clarifies that these  solutions can be brought into line with the solutions of methods of [α]- reverse triple-I. Therefore, formal reasoning system of [α]-reverse triple-I problems is provided in propositional logical system [L?n].

Key words: [α]-reverse FMP, [α]-reverse FMT, propositional logical system [L?n]

摘要： 提出了[α]-反向FMP、多重[α]-反向FMP，以及[α]-反向FMT和多重[α]-反向FMT问题。通过在[F(S)]中引入一个预序，在[L?n]系统中，给出了上述问题的解。并说明了这些解从形式上和[α]-反向三I算法的结果一致，从而在逻辑系统[L?n]中建立了反向三I算法的形式化推理机制。

关键词: [&alpha, ]-反向FMP问题；[&alpha, ]-反向FMT问题；逻辑命题系统[L?n]