命题逻辑系统SMTL中公式的积分真度理论

Theory of Integral Truth Degrees of Formulain SMTL Propositional Logic

首先给出了强左连续-t模和SMTL命题逻辑系统的定义,证明了左连续的-t模为强左连续-t模当且仅当与之伴随的正则蕴涵算子为强正则蕴涵算子;其次,在基于强正则蕴涵算子的模糊命题逻辑系统中定义了公式的积分真度,给出了积分真度推理规则;最后,基于公式的积分真度在SMTL命题逻辑系统的全体公式集上引入了一种伪距离,提出了三种近似推理机制,从而使得在SMTL命题逻辑系统的统一框架下展开近似推理成为可能.

The concept of strong left-continuous t-norm and SMTL propositional logic system is introduced. It is proved that the left continuous t-norm is the strong left-continuous t-norm if and only if its adjoining implication operator is strong regular impli- cation operator. Based on the fuzzy propositional logic of strong regular implication operator the integral truth degree of formula is defined and inference rules w. r. t the integral truth degree of formula is proved. Moreover, a pseudo-metric is defined therefrom on the set of formulas in SMTL system,and three models for approximate reasoning are given,hence a possible framework suitable for developing approximate reasoning theory in SMTL propositional logic is established.