模态命题逻辑系统K、D、T、S4、S5、B之比较

Comparison between the Propositional Modal Systems K, D, T, S4, S5 and B

模态命题逻辑系统K、D、T、S4、S5、B所依据的公理有一定的差异,导致它们之间的定理有一定的差异,推理能力的大小也有所不同。由于定理集的不同导致S4、S5可进行叠置模态词的归约,而K、D、T、B不能;S5可进行嵌套模态词的归约,K、D、T、S4、B没有这种归约能力。

There is a difference between the axioms of the propositional modal systems K,D,T, S4,S5 and B are dependent upon, which results in a difference in their theorems and in their inference capability. Having different theorem sets, S4 and S5 are capable of reduction of piling modal operators while K, D, T, B are not; S5 is capable of reduction of nesting modal operators while K, D, T, S4 and B are not.