一类3值逻辑2元Sheffer函数

A Class of Sheffer Functions of Two Variables in 3-Valued Logic

3值逻辑Sheffer函数研究是多值逻辑重要的基础理论之一。通过给出严格的相互可定义性,54个3值2元S型函数可分为相互定义的10个组,并且可分为3种类型:117型、135型和333型。其中,117型6个,135型36个,333型12个。通过严格的定义可以证明:只有333型中的6个不是Sheffer函数,其余48个均为Sheffer函数。在此基础上,可以进一步发现并证明大量的其他类Ci型和类Di型Sheffer函数。

The research on Sheffer functions in 3-valued Logic is one of the important basic theories in multiple-valued logic. With the strictly given reciprocal definability,54 3-valued S-functions of two variables can be divided into 10 mutually defined groups or 3 types including type 117,type 135 and type 333,among which there are 6 of the type 117,36 of the type 135 and 12 of the type 333. It can be proved through strict definition that among the 54 S-functions,only 6 of the type 333 are not Sheffer functions,and all of the rest fit in. On this basis,a great deal of other types of Ci and Di Sheffer functions can be discovered and proved.