命题逻辑联结词完全性证明--数学归纳法的应用

Proof of the Completeness of Propositional Logic Connectives

通过比较第一数学归纳法和第二数学归纳法,阐述它们的异同。先将第一数学归纳法的基础步骤中的情形扩展为两种的情形,用这种方法给出命题逻辑中联结词完全性的证明。再用第二数学归纳法给出命题逻辑中联结词完全性的证明。

By comparing the first mathematical induction and the second mathematical induction,this paper expounds their similarities and differences.In this paper,we first expand the situation in the basic steps of the first mathematical induction to two situations,and then prove the completeness of conjunctions in propositional logic.The second mathematical induction is used to prove the completeness of conjunctions in propositional logic.