n值S-MTL命题逻辑系统中公式真度的统一理论

Unified Theory of Truth Degrees in n-Valued S-MTL Propositional Logic

给出了强正则蕴涵算子和n值S-MTL命题逻辑系统的定义.基于一般的概率测度定义了公式的真度,并给出了公式真度的积分表达式;基于公式真度的积分表达式证明了真度推理规则;在n值S-MTL命题逻辑系统的全体公式集上引入了一种伪距离,证明了逻辑运算关于这种伪距离是连续的.提出了一种近似推理机制,使得在n值S-MTL命题逻辑系统中展开近似推理成为可能.

The concept of strong regular implication operator and the n-valued S-MTL propositional logic system are introduced.Based on probability measure the truth degree of formula is defined and its integral expression is given and the inference rules w.r.t the truth degrees is proved.Moreover,similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas.The continuity of logical operators w.r.t the pseudo-distance is proved,and hence a possible framework suitable for developing approximate reasoning theory in n-valued S-MTL propositional logic is established.