论麦金森定理及其等价命题

麦金森定理在模态逻辑中扮演了举足轻重的作用。利用把Abs和Triv中的模态公式变为无模态公式的语法运算a与t我们可以给出麦金森定理的一个很简单的语法证明。一方面，通过这个语法证明所建立的加强的麦金森定理与波斯特完全性研究以及模态逻辑语义学中的几条基本原理等价。另一方面，麦金森定理本身清晰地提示了分裂对的两个最典型的实例，这在不完全性度的研究中是不可忽视的。

Makinson's Theorem and Its Equivalence Propositions

Appealing to the syntactical transformations a and t serving to map a modal formula into a non-modal one in Abs and Triv respectively, a rather straightforward syntactical proof of Makinson's theorem is offered. The strenghtened Makinson's theorem which is established by the syntactital proof is equivalent to certain important propositions, in nature, concerning Post completeness and modal semantics. Moreover, Makinson's theorem clearly suggests two of the most typical examples of the splitting pairs, which can not be ignored in the study of the degree of incompleteness.