一种泛逻辑代数系统

A Kind of Algebraic Systems for Universal Logic

文[3]给出了理想状态(广义相关系数h=0.5,广义自相关系数k=0.5)下泛逻辑的形式演绎系统B,证明了此系统是可靠的。该文提出理想状态下(h=k=0.5)泛逻辑学对应的代数系统-UB代数,给出它的一系列性质。证明了UB代数是一个交换剩余半群;进一步证明了U B代数与M V代数、正规FI代数是等价的。

The formal deductive system B of universal logic in the ideal condition(the generalized correlative coefficient h=0.5 and the generalized self-correlative coefficient k=0.5)has been given in paper3.We prove that the system B is sound.In this paper,we introduce UB algebras for universal logic in the ideal condition.Some properties are given.We prove that an UB algebra is a commutative residuated semigroup.Moreover,we show that an UB algebra,a MV algebra and a normal fuzzy implication algebra are equivalent.